A four-story industrial building with a five-story annex in axes 1-3, and a basement in axes 3-9 and E-F ( Fig. 1, a, b, c), which was placed in service in 1952 (building 23), was located at the site of the Pridneprovsk Chemical Plant in Dneprodzerzhinsk. The framework of the building is a truss frame of monolithic reinforced concrete with rigid reinforcement in the form of welded steel structures with the addition of flexible reinforcement, and self-bearing brick walls.Transverse stiffness of the building was afforded by five-span frames, vertical steel trusses, which are installed in the plane of the frames along axes 3 and 9, and brick end walls along the same axes. The transverse frames along the building were connected to rigid plates of the ribbed reinforcedconcrete ceilings. The annex was stiffened by frame connections in both directions, the plates of the reinforced-concrete ceilings and roof, the brick walls, and by the vertical steel trusses along axes A and F. The foundations are columnar beneath the columns, and strip, which broaden out at points where the columns are supported on the basement walls, beneath the basement.Use of reinforced concrete with rigid reinforcement in the form of a steel cage provides for increased stiffness and longevity of the building. The section of rigid reinforcement is usually calculated into the loads that act during construction, disregarding the work of the concrete. For the case in question, a cage formed from rigid reinforcement was calculated for the full service load to take up the increase in load, which had been suggested in the prospective projection. This additionally increased the building's stiffness, since the loads would not be increased during service.The bed of the building's foundations is comprised of loess soils, the thickness of which is 27.5-28.0 m on the side of axis A, and 31.3-34.3 m on the side of axis E. Based on the status in 1994, the loess stratum exhibited slump-type-settlement properties to a depth of 10-15 m, and was classed as type-II soil in terms of proneness to slump-type settlement. The loess soils were partly underlain by neogenic bedrock, and partly by Quaternary deposits. The geologic section from the surface downward (based on survey data acquired from 1990 through 1994) is represented by the following basic geologic-engineering elements (Fig. 1, d).Alternate schemes are examined for the restoration of a multistory frame building formed from monolithic reinforced-concrete with stiff reinforcement by lowering the water table, strengthening the bed with micropiles, and reinforcing the structure on the basis of analysis of the "building-foundation-bed" system.

All six stress components in the foundation bed of a semi-infinitely long strip situated on the surface of an elastic half space and subjected to a uniform vertical load are found as a result of solution of the three-dimensional problem. The distribution of these stresses in the foundation at the end of the strip, and also a certain distance from it is investigated, and the expediency of their consideration demonstrated in solving certain design problems.The solutions of a number of plane and three-dimensional problems, which define the stress-strain state within an elastic half space subjected to a vertical load on a portion of the surface are familiar as models of this half space. The plane problems therefore encompass an infinitely long loaded strip, as well as a uniform load on half of the boundary plane in a different manner. The three-dimensional problem contains solutions corresponding to loads acting over the area of a rectangle, circle, ring, right triangle, and polygon.Kushner and Khain [1] present a solution of the three-dimensional problem, which defines the stresses ~ due to semi-infinitely long uniform and triangular-strip loadings and several other three-dimensional problems that ensue from this solution (a uniform load on one quarter of the boundary plane and on the corner section of a strip foundation). This has introduced significant more precise definitions to the distribution of cr z under a strip foundation. To obtain a complete representation of the stress state of the foundation bed at the end, and near the end of this same strip (strip foundation), however, it is necessary, in addition to tr, to know all other stress components that can be found on the basis of Boussinesq's solution (1885) for a concentrated force on the surface of an elastic half space. A number of author's [2-4] have reduced Boussinesq's solution to Cartesian coordinates. The formulas for the normal ~ and ~ and tangential r~y stresses, which are cited in [2], are identical to the formulas in [3], but differ considerably from those in [4]. We confirmed these formulas on the basis of Mindlin's solution [5] for a vertical concentrated load applied at a depth c from the surface of an elastic half space, proceeding from the conditions c = 0 and R~ = R 2 = R, which verified the correctness of the expressions cited in [2, 3], and demonstrated that it is necessary to use the solution from [4].After replacing N in the expressions for the stresses from [2, 3] by the elementary concentrated force dN = qd~drl and integrating them from -b/2 to b/2 and from 0 to oo (where q is the intensity of the uniform load, and ~ and 17 are the current coordinates (Fig. la)), we obtain the following values of the stress components due to a uniform strip load of semi-infinite length:

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All stress and displacement components in a linearly deformable layer of finite thickness on a compressible bed due to arbitra~ vertical and tangential loadings are determined for simple deformation Solutions are obtained for both the laver, that is unbounded in the horizontal direction (in improper integrals), and also the layer of limited length in a simpler form (in Fourier series). The solutions cited can be used in designing the beds of foundations and embankments.In addition to the model of an elastic half-space, the model of an elastic (linearly deformable) layer of finite thickness underlain by an incompressible bed is widely used in determining foundation settlements. This model has come into use in regulatory documents on the design of foundation beds of large planform dimensions [1, 2]. The approximate solution employed here makes it possible to calculate only settlements (displacements) of the surface layer due to an absolutely flexible uniformly loaded and rigid foundations. Studies conducted by Gorbunov-Posadov (1946), Egorov (1939, 1958, 1961, 1962 and others have served as the basis for practical use of this model. Solutions that make it possible to determine the following are proposed in [3-5 and others] for a layer of finite thickness under a uniform load distributed over the area of a circle, rectangle, and infinitely long strip, as well as a rigid foundation (impression of a rigid plate): the vertical displacement (settlement) of an arbitrary point of the surface and the foundation as a whole; the average integral settlement of the entire loaded area; and, the distribution of vertical normal stresses o z on the boundary between the incompressible layer and within the layer.Two approaches to determination of the stresses and strains in a finite elastic layer are known The conventional approach [3-5] results in improper integrals, which are taken as methods of approximate integration. These methods are not. however, always effective. Some familiar successful approximations of the integrand function make it possible to obtain a finite result with an accuracy sufficient only for a narrow circle of problems.The other approach results in an approximate solution in the form of rather rapidly converging series for which the elastic layer, which is unbounded in the horizontal direction (UEL) (Fig. la), is replaced by a bounded elastic layer (BEL) (Fig. lc). This approach (Rib'er -1898, Failon -1903, and others) has been used by Shekhter [6] to determine the stresses ~r x, a z, and rxz within the layer and the vertical displacements of its surface due to a uniform strip load (displacements of the surface are determined not only for a BEL, but also for a UEL in the form of an improper integral, and are given appropriate plots). A similar approach with the use of a BEL is adopted in [7] for determination of the stresses a x, Crz, rxz, and Oavg due to the same load as that in [6], and %vg due to a load that varies in accordance with the cosine law. The formulas obtained in [6, 7] apply, however, to the ...

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