Annually thousands of domestic, municipal and industrial buildings in Ukraine experience deformations due to the ground surface subsidence movement with underground mining (Fig. 1). Under the impact of mine workings interaction between a building and its basement is disturbed which results in structural deformations and damages. In recent years coal winning under the built-up territories became a problem. On the one hand, repeated undermining has resulted in structural deterioration and on the other hand, owing to change of ownership requirements to upkeep of buildings have become more severe. Under such conditions procedure to determine allowable undermining of buildings need to be specified.
Depending on the types and signs of ground surface movement it makes different impact on buildings being undermined (Fig. 2). At horizontal tensile deformations inclined cracks in external walls are generated which are symmetrical relative to the center of the building. Vertical bending and vertical shear cracks are typical of curvature of convexity, the bending cracks being typical of flexible buildings which lengths exceed their heights more than thrice. Shear cracks are always generated, being more typical of three-storey and a higher building than bending cracks. Under horizontal compressive deformations and curvature of concavity inclined and horizontal cracks are generated in the walls located symmetrically relative to the center of the building in the form of a triangle or trapezium. To the concentrated ground surface movement with benches inclined cracks are typical that are located compactly, directed towards the bench and confined to the onset of it.
It is known that in buildings being undermined specific deformations and damages occur which were called by Helmut Kratzsch “structural weakening”. Unlike force deformations and damages due to the structural overload, undermining effects can put to inconvenience in use of buildings and do damage but do not threaten should they be limited by corresponding to them indexes of allowable deformation of the walls that are the most sensitive to undermining. Using the concept of “structural weakening” we shall call undermining-induced deformations of buildings as structural deformations. Peculiar for the structural deformations is that they refer to visual criteria and can be controllable by mine surveying observations. Taking into account actual locations of cracks at different ground surface movement, patterns for structural deformation of wall disintegration are defined (Fig. 3).
For this purpose the following assumptions are taken. Plain deformation of a building in longitudinal or transverse directions is considered; walls represent homogeneous deformable isotropic body; undisturbed contact of building foundation with its basement being deformed is assumed; principle of independence of the influencing factors shall be used: structural deformations of horizontal shear, vertical shear and wall bending induced by ground surface horizontal movement and curvature shall be determined separately. Principle of independence application allow to estimate the influence of each of the factors and to employ for the structural deformations the concept of pure shear at which its plane is located at an angle 45° to the line of effect of horizontal and vertical movements. The idea of generalized structural deformations for wall disintegration made it possible to define deformation patterns for buildings at any ground surface movements.
Under the smooth ground surface movement virtual are four deformation patterns. The first and the second patterns are typical of the horizontal tensile deformations, curvature of convexity and building length of more than two heights and less than two heights (Fig. 4). Deformation state of buildings is characterized by uniform horizontal shear due to the ground surface tension and by non-uniform horizontal shear and bending due to the curvature of convexity. Based on these patterns we derived formulae to determine indexes of summarized building deformations due to the tension and the curvature of convexity.
The third and the fourth patterns correspond to the compression deformations, curvature of concavity and l³2H and l≤2H (Fig. 5). The deformation state of buildings due to the compression and curvature of concavity is characterized by non-uniform horizontal and vertical shear of the middle part of the wall. The main factor that aversively affects the building is the vertical shear which creates conditions for its attendant compression to be realized. Under the influence of non-uniform vertical shear that grows towards the middle of the building inclined and horizontal cracks are generated in the walls that increase their compression deformation properties. Based on these patterns we derived formulae to determine indexes of summarized building deformations due to the compression and the curvature of concavity.
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