Some direct and inverse problems in land subsidence theory: V. Dimova, in: Land subsidence. Proc. international symposium, The Hague, 1995, ed. F. B. J. Barends & others, (IAHS; Publication, 234), 1995, pp 269–275

Abstract

One of the effects of the underground human activities (geotechnological or civil engineering works) is the occurrence of land subsidence. The latter creates unfavourable conditions for the functioning of surface items (buildings, equipment, bands, etc.). In connection with this, the following two problems are considered and solved in this paper. (a) Direct problem the mining system is given; determine the equation of the land subsidence. This problem is reduced to the Dirichlet problem for Fourier's equation, (b) Inverse problem the equation of the mining subsidence is given, determine the underground operations from which the given subsidence is realized. This problem is of extreme importance in the cases when mining has to be done under built-up areas. In these cases the building standards dictate the land subsidence equation. This necessitates a more rigorous formulation of a new inverse problem in the land subsidence theory. The problem is reduced to an inverse Dirichlet problem for Fourier's equation. This is an incorrectly posed problem of mathematical physics in the sense of Hadamard. Its solution is obtained by Lions' quasi-inversion method. Some generalizations of the posed problems are discussed. The posing and solving of the unique inverse problem in the applied geosciences allows to speak about laying the foundations of a modern land protection geo-engineering field.