The principal object of study in rock mechanics is the rock bed and the processes taking place in it during the extraction of minerals. When a bed of rock is worked, the support for the overlying strata is removed from a certain area. This introduces a disturbance into the gravitational and tectonic stress fields existing in the bed and disrupts the equilibrium in the intact strata. Passing into a new state of equilibrium, the rocks adjacent to the workings are deformed, leading to a redistribution of stresses and strains in the bed and particularly in the vicinity of the exposed surfaces~ This picture of variation of the stressed state of rock bed being worked is commonly known and confirmed by in situ and laboratory data. Of special importance for the practice of mining is the concentration of stresses and dislocations in the '!disturbed" zone produced by the mining process.Several hypotheses on the shape and size of the working influence zone have been maintained for a long time in rock mechanics. These include the arch hypothesis [I], the friable medium hypothesis [2], and hypotheses based on the principles of civil engineering mechanics and strength of materials [3,4].

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We address the question of correct description of Lagrange dynamics for regular electrically charged structures in nonlinear electrodynamics coupled to gravity. Regular spherically symmetric configuration satisfying the weak energy condition has obligatory de Sitter center in which the electric field vanishes while the energy density of electromagnetic vacuum achieves its maximal value. The Maxwell weak field limitLF→Fasr→∞requires vanishing electric field at infinity. A field invariantFevolves between two minus zero in the center and at infinity which makes a LagrangianLFwith nonequal asymptotic limits inevitably branching. We formulate the appropriate nonuniform variational problem including the proper boundary conditions and present the example of the spherically symmetric Lagrangian describing electrically charged structure with the regular center.

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