Solution of the mixed problem of the theory of elasticity and the theory of plasticity of soils

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Calculation of the stress and strain of soil masses (foundations, dams, earth embankments, and slopes) to assure the maximum use of their bearing capacity should be done for any effects on them wlth consideration of the appearance and development of zones of limit stress in the soil. Such a Solution is realized in the mixed problem of the linear or nonlinear theory of elasticity and plasticity using a single model of elastoplastic soil at all loading stages [1]. The corresponding variants of its formulation within the scope of the theory of plastic flow with the use of associated and nonassociated laws for plastic deformations developing in the region of limit equilibrium were examined earlier [2,3]. Realization of the mixed problem and the results of calculations of the stress and strain of earth dams and structures within the scope of the associated model were presented in sufficient detall in articles [4,5]. Also given there with reference to flexible and rigid plates is a detailed comparison of the calculated and experimental results on the values and character of the load--settlement curves, outline of the settlement crater and its change during loading, diagrams of contact stresses, and a number of other quantities.It is shown that the calculated results qualitatively and quantitatively agree well with the data from the instrumental measurements and reliably reflect the behavior of the soils during loading, thereby justifying the use of the associated law in mixed solutions for dense and average-density soils, i.e., for practically the majority of foundations and masses that are encountered. At the same time we note that the solution of the mixed problem in the case of the nonassoclated law of flow obtained for compacted soils showed an insignificant (for dense soils within the accuracy of the calculations) deviation of the results from those obtained on the basis of the associated model of soil [3]. In particular, in the case of plane strain the use of a rate of dilatancy A =(0.5-0.8) sin~, which is characteristic for moderately dense soils, instead of A -sin ~ (associated flow) increases settlements of foundation by not more than i0-15%, i.e., both flow laws give practically the same results. However, the use of the associated law considerably shortens the program an d calculation on a computer and eliminates laborious (we add, quite inaccurate) experiments on measuring the rate of dilatancy, which is an additional parameter of the nonassociated soil model. All this determined the use of the associated law in the examples of applying the mixed problem of plane strain to calculation of the bearing capacity of certain soil masses examined below. We will dwell on the results of this application. Figure i shows for various schemes of foundations the "average pressure --settlement" curves used for determining the values of the limit pressures. In the calculations the state of strain in the foundations was determined from the external load, but in this case the natural stresses o x =~TY, Oy =TY, Zxy =0 from the...

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confidence: 74%

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confidence: 99%

Calculations of the bearing capacity of soil masses

Bugrov¹,

Zarkhi²

1979

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“…However, as the analysis showed, this method in the case of dams on undermined foundations gives a too rough estimate of the development of regions of a limit stress state of the soil. The general solution of the mixed problem of the theories of elasticity and plasticity of soils, developed earlier [8] and based on the use of the theory of plastic flow and finite-element method (FEM), is most suitable for solving the problems under consideration. Here the authors examine a variant of the mixed elastoplastic problem for the case of plane strain.…”

Section: Stress-strain State Of Earth Damsmentioning

confidence: 99%

Stress-strain state of earth dams on undermined territories

Markevich¹,

Teleshev²,

Bugrov³

1984

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with the creation of a berm skeleton from concrete blocks with simultaneous dumping of a gravel filter and intense hydraulic filling of the underwater part of the channel dam without lagging behind the berm could be technically possible and economically expedient.3. In the construction of hydrostations where the cost of stone is high it is necessary to provide for the possibility of using methods of damming with the maximum use of hydraulicking. The flexible scheme of organizing damming used at the Cheboksary hydrostation completely meets this requirement.4. Damming of large rivers with the use of hydraulicking is possible also in the period of intense ice formation with a sufficient guarantee of providing a good quality of construction of the structures.5. In the case of an erodible channel it is necessary to dump the berm from both banks simultaneously to prevent deep scouring of the bottom. To reduce the consumption of stone materials, it is expedient to carry out hydraulic filling of the underwater part of the dam simultaneously with dumping the berm without lagging behind it.6. In the case of pioneer damming of rivers with an erodible channel, reliable protection of the bottom of the gap is necessary. Protection by a train of stone and rubble with a thickness of 1 m is no guarantee against scouring. The size of the stone of the train should correspond to the velocity in the gap. It should be dumped as an even layer without the formation of mounds. The need for good clearing away of the cofferdams acquires particular importance in this case.7. In the case of dumping a berm skeleton composed of large concrete blocks and elimination of the construction of a filter on its upstream slope, the formation of individual washouts at the site of closing the gap, threatening the integrity of the berm, is possible after completing the works.

“…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]. 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]. 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.…”

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confidence: 99%

“…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. 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]. A nonlinear relation a=aM,…”

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confidence: 99%

Calculation of the resistance of backfill to displacements of retaining walls

Bugrov¹

1978

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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"...