## 3 FE Model of a Continuous Strip Foundation  
The advanced computational three-dimensional FE model of a perfectly continuous foundation resting on a three-dimensional random subsoil verifies the prior FE solution of a subsoil block. A sufficiently long segment of the foundation is analysed to provide numerical results of a displacement of the central node of the foundation longitudinal cross-section free of any interference of the boundary elements. The considered FE model of a segment of the strip footing foundation of dimensions \(2.0\times 0.5\times 20.0\ \mathrm{[m]}\), resting on a spatially random subsoil, is presented in Figure 14. A volume of \(18.0\times 6.0\times 6.0\ \mathrm{[m]}\) is generated in the ZSoil(r) software, and the outer elements are properly constrained to accurately reflect the mechanical response of the entire subsoil under the foundation. The subsoil under the foundation level is only modelled, and the soil layers lying above the foundation-subsoil interface are replaced by a uniformly distributed load \(q=18.0\ \mathrm{ kPa}\) situated on the upper surface of the subsoil FE model. The dead load of the foundation wall is represented by a linear load \(P=1.0\) MN per FE length. The wall-foundation connection makes the deflections compatible; the rotations do not follow the rule. Probabilistic analysis requires multiple repetitions of similar computations; it is a significantly time-consuming process, so assuming an optimal refinement of the finite element mesh is necessary. Division of the subsoil into a given number of elements should ensure the desired result accuracy, also providing a relatively short calculation time of a single case. Therefore, the subsoil volume under the foundation is divided into several sub-volumes, variable in the degree of finite element mesh condensation (Figure 14). Moreover, the approach to the subsoil volume definition is also diverse, as the subsoil volume (\(10.0\times 6.0\times 6.0\) [m]) directly under the strip foundation is assumed random (marked in yellow in Figure 14), while the remaining volume is modelled deterministic (marked in pink in Figure 14). To facilitate the description of the random soil sub-volume with random fields, a regular mesh of three-dimensional continual eight-node elements (Q4 continuum 2D) with dimensions \(0.5\times 0.75\times 0.75\) [m] is adopted. This brings a total number of 3200 finite elements to constitute the random sub-volume. In the random sub-volume of the soil, [PERSON]'s modulus parameters are assumed the same as in the case of a soil cube (Chapter 2). In the deterministic part, the parameter was set to its mean value \(E=\mu_{E}=28\) MPa. The concrete of the foundation is considered elastic, and its parameters correspond to the C30/37 concrete (with [PERSON]'s modulus of \(E=33\) GPa). The soil block analysis shows an optimal finite element domain of diverse [PERSON]'s moduli equal to 12.5% (\(p_{E}=0.125\), Equation (3)) of the total FE domain. Here, the Monte Carlo results converge fast, and their dispersion is moderate. The random domain of the strip foundation subsoil model (3200 elements, Figure 14) is split into 400 smaller sub-volumes, each of them made of eight finite elements (\(400/3200\cdot 100\%=12.5\%\)). While this generated random variable is applied to each sub-volume, 400 separate [PERSON]'s modulus random variables are incorporated in a single model, \(n_{E}=400\). The computations are performed for 200 generated foundation models. To assess solution convergence, parameter variation is examined on the central point settlement of the foundation, neglecting the boundary condition impact (Figure 15). Based on the computations, variable settlement shows its mean value \(\mu_{\delta_{400}}^{strip}=0.0976\) m and standard deviation \(\sigma_{\delta_{400}}^{strip}=0.0017\) m.  
Figure 14: The FE model of a strip foundation resting on a three-dimensional random subsoil.