## 2 Materials and Methods
### Laboratory Testing  
To study the bearing capacity in laboratory conditions, reduced-scale models of conical foundations were designed, as shown in Figure 5. These models were tested on a laboratory bench to evaluate their load-bearing performance at a given value of horizontal soil displacement.  
A three-dimensional expandable model box, filled with a compacted equivalent model soil, was used to simulate the effects of horizontal soil displacements. The equivalent material was compacted uniformly to achieve the target physical and mechanical properties (density, moisture content, and cohesion). The model box was then expanded to the required dimensions by loosening the bolts that connected the steel channel sections along its sides. To prevent soil leakage during expansion, rubber gaskets were installed at all joints. When the bolts were loosened, the gaskets expanded laterally, inducing controlled horizontal tensile strains in the soil of up to 3 mm/m, 6 mm/m, and 9 mm/m, thereby simulating the convex tensile strain zone shown in Figure 2. This method replicates the horizontal displacements that may occur in zone AB due to mining-induced deformation, including settlement and potential microcracking of the foundation soil.  
A detailed description of the expandable box design is provided in [9].  
The granulometric composition and properties of the equivalent model soil were selected to match the natural soil's cohesion, plasticity characteristics, density, and water content, as summarized in Table 1. The modeling scale \(m_{l}\) was determined using the strength similarity method, based on the ratio of cohesion and unit weight between the model and natural soils:  
\[m_{l}=\frac{c_{m}}{c_{n}}.\frac{\gamma_{m}}{\gamma_{n}}\approx\frac{1}{40} \tag{1}\]  
where \(m_{l}=1/\)L--linear scale;  
\(\gamma_{m}\), \(\gamma_{m}\)--specific gravity of model and natural materials;  
\(c_{m}\), \(c_{n}\)--cohesion of model material and soil in real conditions on the site (natural condition).  
Figure 5: Conical models design for laboratory testing with stand pile: (**a**) model dimensions; (**b**) testing models.  
The model soil was prepared by mixing 97% fine sand with 3% spindle oil to enhance viscosity and achieve a target cohesion in the range of 0.8-1.0 kPa. This composition allowed the model to replicate the mechanical behavior of natural cohesive soils, while maintaining a cohesion scaling ratio of 1:40 relative to field conditions.  
Conical model foundations were manufactured from aluminum alloy, according to the dimensions in Figure 5. Each conical model was installed into the pre-compacted soil with the central pile (stand) and conical tip embedded to 70% of the cone height. Loading was applied incrementally, in steps of 0.001 MPa, and sustained until the settlement rate stabilized (defined as deformation attenuation of less than 0.01 mm over 15 min). The model was then loaded further, until the pressure reached 16.7 N/cm\({}^{2}\) over the foundation area (Figure 6).  
Vertical settlement was measured using high-precision dial gauges with a reading accuracy of 0.01 mm. The ultimate bearing capacity was taken as the load level at which the model foundation began to settle continuously. Settlement was recorded under four conditions: before horizontal displacement, during displacement at \(\varepsilon\) = 3 mm/m, \(\varepsilon\) = 6 mm/m, \(\varepsilon\) = 9 mm/m, and after the cessation of horizontal displacement.