On the issue of determining the dimensions of the rock massif cavity sufficient for the formation of a sinkhole in the overlying soil stratum

Introduction. The procedure currently recommended for karst hazard assessment includes a comparison of the cavity dimensions at the top of the karst massif with a “critical” value, sufficient for a shift of the cylindrical volume in the soil stratum. The scheme of calculating the “critical” value, proposed 40 years ago, is widely used due to its proven efficiency. However, in some cases, this procedure leads to an incorrect assessment of sinkhole development conditions, i.e., to incorrect decisions about the parameters of anti-karst measures.

Aim. To adjust the procedure for calculating the “critical dimensions”, depending on the stratum structure and soil characteristics, as well as the load from the foundation.

Materials and methods. The calculation formulas, transformed for computer calculations, are corrected by the introduction of a variable stability factor, the refinement of the schemes for accounting the effect of a surface load on the forces, acting along the side surface of the “shifting” volume, as well as by accounting, under the fulfillment of conditions for the general stability of a soil cylinder, the possibility of destroying the lower soil bearing layer, which is modeled as the clamped plate, loaded according to two different schemes depending on the properties of overlying soils.

Results. The results of comparative calculations performed using the Mathcad software package for “standard” conditions are analyzed, and conclusions about the significance of the proposed corrections are drawn.

Conclusion. When determining critical dimensions, it is necessary to introduce the values of the stability coefficient for the “shifting” soil volume, which are standard for geotechnics. In the case of using slab foundations, recommended in “karst-hazardous” areas, the effect of a surface load on the soil shift should be taken into account only when determining horizontal stresses on the side surface. Moreover, accounting can be carried out according to simple, but sufficiently justified, schemes. When the possibility of the lower layer destruction is accounted, the formation of a sinkhole is predicted at a smaller cavity span as compared to the proposed procedures.

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