Assessment of horizontal deformations in undermined areas

Spotlight is on assessment adequacy of horizontal ground surface deformation rates governing impact of mining on buildings, facilities and engineering infrastructures. Three methods of calculating horizontal deformations of ground surface are discussed. The first method uses the linear dependence of horizontal deformation on the displacement trough flexure; the second method is based on the empirical correlation of maximum horizontal displacements and vertical subsidences of ground surface in specific geological conditions; the third method includes mathematical modeling of change in the stress–strain behavior of undermined rock mass with ground surface deformation estimation. As a case-study of the Upper Kama Salt Deposit, the horizontal deformation calculation methods are compared in terms of a typical displacement trough. The comparison of the calculation results with the direct survey measurements of horizontal deformations shows that the accuracy of engineering estimates of horizontal deformations grows when a real-life displacement trough is closer to the classical form. In case of adjustability of dimensionless distributions of horizontal displacements, the ground surface deformations can be determined at a very high accuracy. When a displacement trough has an intricate shape, it is better to adhere to mathematical modeling, the more so 3D mathematical modeling provides distribution of maximal horizontal deformations in undermined areas and allows determining their lateral orientations. Moreover, the mathematical modeling results facilitate plotting a subsidence profile. The latter is processable using engineering methods and the obtained maximum values of horizontal deformations are used to identify the necessity of protective measures for ground surface objects.

Keywords: displacement trough, ground surface subsidence, horizontal deformations, mathematical modeling, stress–strain behavior.
For citation:

Baryakh A. A., Tenison L. O., Samodelkina N. A. Assessment of horizontal deformations in undermined areas. MIAB. Mining Inf. Anal. Bull. 2021;(11):5-18. [In Russ]. DOI: 10.25018/0236_1493_2021_11_0_5.


The study was supported by the Russian Science Foundation, Grant No. 19-77-30008.

Issue number: 11
Year: 2021
Page number: 5-18
ISBN: 0236-1493
UDK: 622.22
DOI: 10.25018/0236_1493_2021_11_0_5
Article receipt date: 03.09.2021
Date of review receipt: 21.09.2021
Date of the editorial board′s decision on the article′s publishing: 10.10.2021
About authors:

A.A. Baryakh1, Dr. Sci. (Eng.), Аcademician of Russian Academy of Sciences, Director, Perm Federal Research Center of the Ural Branch of the Russian Academy of Sciences, e-mail:,
L.O. Tenison, Cand. Sci. (Eng.), Head of Department, PJSC Uralkali, 618400, Berezniki, Russia,
N.A. Samodelkina1, Cand. Sci. (Eng.), Leading Researcher, e-mail:,
1 Mining Institute of Ural Branch, Russian Academy of Sciences, 614007, Perm, Russia.


For contacts:

A.A. Baryakh, e-mail:


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