## 2 Materials and Methods
### Tests on a Real Building
#### 2.1.1 Subsoil Examination  
Lublin is located in the area of the Naleczow Plateau with loess covers (Figure 4). Basically, only in the valleys there are river formations from the ground level. In the uplands there are mainly loess soils, which are the basis for the foundations of buildings. In order to determine soil characteristics, laboratory tests (among other, oedometric and triaxial compression tests) and field tests (CPT and SDMT) were performed, the location of which is shown in Figure 3b. A selected representative CPT chart is presented in Figure 5, and a detailed description of field tests can be found in [34]. Figure 4: A geological map of the research area. Figure 3: The analyzed building: (**a**) view of the real object [33]; (**b**) map with the location of geotechnical tests (CPT and SDMT), benchmarks (Z1 \(\div\) Z10) and division into computational areas (A \(\div\) E). During CPT tests, \(q_{c}\)--tip resistance and \(f_{s}\)--sleeve resistance are measured, which are the basis for determining other geotechnical parameters. The most important parameter for the purposes of the analysis was the constrained modulus \(M_{\text{CPT}}\), which was determined from the formula defined by [PERSON] [35]:  
\[M_{CPT}=\alpha_{m}q_{c} \tag{1}\]  
A slightly altered version of the formula is proposed by [PERSON] [36]  
\[M_{\text{CPT}}=\alpha_{m}(q_{t}-\sigma_{v0}), \tag{2}\]  
where \(q_{t}\)--total cone tip resistance, \(\sigma_{v0}\)--vertical overburden stress. Both in [PERSON]'s (Equation (1)) and [PERSON]'s (Equation (2)) formula, it is extremely important to select the empirical coefficient \(\alpha\)m, which can assume a value in the wide range of \(1\div 15\)[35; 37; 38]. Although the CPT test is performed in the presence of large deformations, by choosing a well-calibrated \(\alpha_{m}\) coefficient, the constrained modulus can be derived for any range of deformations, as in Figure 2. For loess from the vicinity of Lancut, [PERSON] and [PERSON] [39; 40] assumed the relationship Equation (2) with the coefficient \(\alpha_{m}=8.25\). For loess from Kazimierz Dolny, [PERSON] [24] determined a much smaller coefficient \(\alpha_{m}=2.5\) for Equation (1). This coefficient was calibrated in relation to the constrained modulus from oedometric tests, i.e., in conditions of large deformations. Taking into account the above literature data and after the analyses conducted by the author of the present study [34], the relationship Equation (1) with the coefficient \(\alpha_{m}=6\) was adopted for loess soils. Further calculations confirmed that this is a correct value. As far as SDMT tests are concerned, the most significant values for the purposes of the present analysis were the dilatometric constrained modulus \(M_{DMT}\), which was calculated using the Marchetti formula [41] and the lateral stress coefficient \(K_{D}\) used to assess soil preconsolidation. These parameters are shown in Figure 6.  
Figure 5: CPT-1 parameters. Loess soils from the vicinity of Lublin are normally consolidated (NC) due to their genesis. In order to confirm this, preconsolidation stress \(p_{0}\) from oedometric tests was analysed, as well as the distribution of K\({}_{\rm D}\) coefficient with depth from SDMT tests. The results of oedometric tests confirm that the soil is normally consolidated, because the preconsolidation stresses from the study corresponded to the geostatic stress from the sampling depth. The assessment of the degree of soil consolidation is expressed by the \(OCR\) indicator, which in DMT tests is not a directly measured parameter, but interpreted only on the basis of \(K_{\rm D}\) coefficient. The determination of the \(OCR\) indicator from DMT tests is related to the type of soil and local relationships. For cohesive soils, there are many regional interpretations, while for sandy soils, i.e., with \(I_{D}>1.2\), determining \(OCR\) is much more difficult and according to the latest research, tip resistance \(q_{c}\) from CPT probing is needed [42, 43].