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The calculations of retaining walls used so far are considerably simplified, which is explained by the outward simplicity of these structures andthelr widespread use. Yet retaining walls, being a three-dlmensional structure, despite the seeming simplicity of design, are in a complex stress--strain state, especially the retaining walls of hydraulic structures with a height of 20-30 m and more.Retaining walls with a height of more than 30 m are unique and are under even more complex conditions than concrete dams, for which there are special standards.In particular, the cross sections in the embedment of wall more than 30 m high increase to 10 m and more, whereas temperature fluctuations do not penetrate deeper than 4-5 m from the face. Variations of the air and water temperature create internal shear stresses in concrete without movement of the walls into the depths of the backfill, which could cause passive resistance.Calculations of such walls cannot be performed on the basis of general standards and regulations for walls with a height of 5-30 m and should be carried out individually with the use of independent technical specifications.The two-dimensional problem is usually selected for calculating retaining walls: a strip is cut out along the cross ~ection of the wall and is calculated for the effect of the loads applied to it. If the wall has a variable height in the longitudinal direction, two-three strips are cut, each being calculated independently and reinforced on the basis of these calculations.The interactlo= of these strips is not taken into account, although the higher (and more loaded) strips, resting on the adjacent lower, more rigid (and less loaded) strips increase the load on the latter, hut they themselves in this case are partially unloaded. The movements of the crest of such a wall along its length are different and cause curvature of its plane. However, this is not the only deviation of the actual state of retaining walls from the design model.
The calculations of retaining walls used so far are considerably simplified, which is explained by the outward simplicity of these structures andthelr widespread use. Yet retaining walls, being a three-dlmensional structure, despite the seeming simplicity of design, are in a complex stress--strain state, especially the retaining walls of hydraulic structures with a height of 20-30 m and more.Retaining walls with a height of more than 30 m are unique and are under even more complex conditions than concrete dams, for which there are special standards.In particular, the cross sections in the embedment of wall more than 30 m high increase to 10 m and more, whereas temperature fluctuations do not penetrate deeper than 4-5 m from the face. Variations of the air and water temperature create internal shear stresses in concrete without movement of the walls into the depths of the backfill, which could cause passive resistance.Calculations of such walls cannot be performed on the basis of general standards and regulations for walls with a height of 5-30 m and should be carried out individually with the use of independent technical specifications.The two-dimensional problem is usually selected for calculating retaining walls: a strip is cut out along the cross ~ection of the wall and is calculated for the effect of the loads applied to it. If the wall has a variable height in the longitudinal direction, two-three strips are cut, each being calculated independently and reinforced on the basis of these calculations.The interactlo= of these strips is not taken into account, although the higher (and more loaded) strips, resting on the adjacent lower, more rigid (and less loaded) strips increase the load on the latter, hut they themselves in this case are partially unloaded. The movements of the crest of such a wall along its length are different and cause curvature of its plane. However, this is not the only deviation of the actual state of retaining walls from the design model.
The interaction of backfill with a retaining wall which is being displaced toward the backfill is most often described by a linear relation between the reaction pressure Pr (over and above the active pressure created by the weight) acting at a given contact point and the displacement of this point A p,=cA. (l)The modulus of subgrade reaction (Winkler model) or coefficient of compressive strength of the backfill is the proportionality factor [1-3]. It is well known that in this case the results of the calculations (e.g., the diagram of the reaction pressure) depend substantially on the adopted law of variation of the modulus of subgrade reaction (resistance) of the backfill with increase in depth and do not always agree with the data from measurements [2,3]. In [2] a refinement of the calculations is related, in partlcular, to an evaluation of the magnitude and character of the change in the compressive strength of the backfill with increase in depth on the basis of determining the size of the active compressible soil stratum. In [4,5] attention was called to the experimentally obtained dependence of the character of the change of C with depth on the type of wall displacement and the need to take into account this circumstance in calculations using the Winkler model. A nonlinear relation a=aM,which reflects better the behavior of the backfill than Eq. (I), was proposed and used in examples there.The indicated refinements are of practical interest and permit more reliable calculations. At the same time, a further development of calculations of the interaction between structures and backfill is related to their representation by fundamentally new models differing from those indicated above and more fully reflecting the properties and behavior of soils. First of all we need mention the model of an elastoplastic foundation.In this case the broadest possibilities are realized when solving the so-called mixed problem of the theory of elasticity and plasticity of soil, permitting a determination of stresses and strains within the design region having zones of both a prelimit (elastic) and limit (plastic) state of the soil in accord with the adopted yield (plasticity) condition [6,7]. The formulation of the mixed problem within the framework of the theory of plastic flow and the algorithm for its solution by the numerical finite element method (FEM) were presented earlier [7]. The qualitative and quantitative agreement of the results with data from instrumental measurements was established by solving mixed problems for experimental foundations loaded by flexible and rigid test plates [8,12].The examples given below were calculated according to the SUPZ-GP program* for solving mixed elastoplastic problems of plane strain on a BESM-6 computer and take into account the experience gained in using a similar progra M developed earlier [8]. The use of triangular (TFE) and rectangular (RFE) finite elements, separately and combined, is provided for in the SUPZ-GP program. The design region can be separated into RFE "automatically"...
Comparatively recently, the analysis of dock-type lock chambers was performed for the action of external loads (including earth pressure from the backfill in the state of limiting equilibrium or repose) without taking into account the compatibility of the deformations of the structure and the surrounding soil.The lock walls were considered as cantilever beams whose relations were applied to the bottom slab together with its dead loads as in a beam on an elastic foundation of any type.In works by V. I. Vutsel', V. M. Gogolitsyna and S. A. Frid, G. K. Klein, B. N. Leont'ev, A. V. Mikhailov, A. B. Moshkov, I. K. Samarin, and others, substantial improvements of the above scheme have been introduced, in which the compatibility of the deformations of the structure and the surrounding soil is considered, and a separate analysis of the bottom slab and wall, which constitute a single structure, is rejected.In the limiting and beyond-limiting stress state, the soil behaves as a granular medium whose pressure on a barrier opposing the formation of the natural slope is determined by the action of the forces of gravity and internal friction.Under these conditions, dock structures are statically indeterminate.However, in the prelimiting stress state of the soil, which is produced in the absence of displacements, or for displacements of the barrier toward the backfill resulting in its compaction without formation of through-flow zones, the granular medium performs elastically.In this case, when the condition of compatibility of the deformations of the retaining structure and the soil is met, static indeterminacy arises which can be solved by static analysis of the structure in an elastic medium.A characteristic of the behavior of dock structures for locks is their joint operation with the surrounding soil as a result of cyclic rises of the water level in the chambers and seasonal variation of the ambient temperature, for which beside the basic loads, additional soil reactions occurring in the zones of additional compaction act on the wall.In analyses of dock structures these additional soil reactions must be taken into account when determining the internal forces.The complexity of the solution lies in the fact that movement of portions of the wall away from the backfill is not attended by substantial variation of the earth pressure (it may decrease from the values during the state of repose to the values during the state of limiting equilibrium), by development of a soil compaction reaction in addition to the basic (acting on the unmoved wall).Yet, in the region of contact between the bottom slab and the foundation soil, any absolute increase in the reaction pressure (equal to the weight of the suspended structure) is impossible, but there is a redistribution in the intensity of this pressure along the bottom slab as a result of variations in the shape of its elastic curve.In order to determine the internal design forces when selecting the reinforcement, a continuous reinforced-concrete dock structure should be analyzed as a si...
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