# Design of Conical Foundations with Increased Bearing Capacity in Areas of Undermined Soils
## 2 Materials and Methods  
The \"load-settlement\" interaction under the influence of horizontal forces on the soil stratum has an elastic character at the first stage and does not differ from a column foundation with an identical cross-sectional area at the level of its contact with the soil. However, the achievement of the limiting state for a conical foundation is much later than for an isolated shallow one. This phenomenon is explained by an increase in the cross-sectional area as it deepens into the base soil with horizontal movements, which accordingly increases the bearing capacity of the undermined base. Reducing the impact of horizontal forces on the structure of the upper part of the building is achieved by a rolling joint (Figure 3). However, the presence of a rolling joint practically does not eliminate the effect of horizontal forces on the underground part of the building. The use of a combination of a roller bed between the upper plane of the conical base foundation and the lower plane of the rigid basement plinth of the building determines a fundamentally new mechanism for the operation of conical foundations in undermined areas.  
The design of the conical foundation was proposed as partially immersed into the soil base with its apex downwards. Such positioning of the structure increases its load-bearing capacity under the influence of undermining impacts, since the area of the cone foundation structure increases with its immersion into the soils; that is, the settlement of the conical foundation has a positive effect on the bearing capacity of said conical foundation. The round shape of the base of the inverted cone avoids stress concentration near the corners and the formation of cracks at corner points.  
In this work, models of foundation blocks of a right circular cone shape were used. A cone with aperture \(\alpha\) was immersed in the ground to a depth of 0.75 height of the cone in order to provide a safety margin by increasing the diameter and, accordingly, the bearing area when loading the conical block (Figure 4). Based on previous studies [24; 25], the opening angle of the cones \(\alpha\) was taken as the average value from the previously considered modeling methods, and based on the results of preliminary laboratory tests, cones with an opening angle of 80-90\({}^{\circ}\) were considered in this study.  
Figure 4: Loading of conical and isolated shallow foundations: d—diameter of conical foundations at the level of the soil base surface; 1—conical foundation; 2—isolated shallow foundation; 3—base soil; \(\alpha\)—cone opening angle.  
Figure 3: Design of a building on conical foundations with deformation joint.  
The cross-sectional area of the cone at an intersection with the soil's surface is determined by the formula:  
\[\text{A}=\text{F}/\text{R} \tag{5}\]  
where: A--cross-section area at the level of the ground surface; F--load applied to the surface of the foundation; R--ultimate bearing capacity of soil.  
Comparative loading experiments of conical and isolated shallow foundation models with the same diameter were carried out to determine the settlement and the bearing capacity of soils under the horizontal soil displacement caused by horizontal tensile strains in undermined areas. When considering the behavior of the soil strata, special attention was paid to visual observation of the fracturing of the massif. The theoretical values of the maximum crack opening value were found by Formula (4).