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532.546
532.72

крайова задача
напружено-деформований стан
тепло-масоперенесення
депресійна лунка
вільна поверхня
числове конформне відображення
метод скінченних різниць
boundary value problem
stress-strained state
heat and mass transfer
depressional hole
free surface
numerical conformal mapping
method of finite differences

Cформульовано постановку та проведено числове моделювання впливу тепло- масоперенесення на напружено-деформований стан (НДС) ґрунтового масиву внаслідок утворення депресійної лунки. Реалізовано числове конформне відображення криволінійної складеної області, що містить область фільтрації та область сухого ґрунту, на параметричний прямокутник в оберненій постановці. Отримано числовий розв’язок відповідної двовимірної крайової задачі НДС методом скінченних різниць. Використовуючи розроблене програмне забезпечення, проведено серію числових експериментів та здійснено їх аналіз.
The statement was formulated and the numerical modelling of the mass-transfer effect on stress-strained state (SSS) of soil mass as a result of formation of the depressional hole was carried out. The numerical conformal mapping of curvilinear composite area containing the area of filtration and the area of dry ground on parametric rectangle in inverse statement was constructed. The mathematical model of the ground array SSS taking into account the influence of heat and mass transfer in a complex area was sset. The numerical results of corresponding two-dimensional regional task of SSS have been obtained by the method of finite differences with the use of numerical conformal mappings. For the numerical decision this task is carried out in the integrated environment of the object oriented programming of Visual Studio 2012 in programming of C# language. The series of numerical experiments have been carried out and results are presented as charts of distribution of the fields of displacements, tensions, deformations and also pressure concentration of salts and temperature. The analysis of the obtained results was carried out. It is shown that taking into account the processes of heat and mass transfer in the water saturated area of the ground array and process of heat transfer in the area of soil in the natural state changes distribution of displacements, deformations and tensions, that is, displacement in the water saturated area of the ground array at taking into account the heat and mass transferring, are increased greatly comparing with the corresponding values of displacements during filtration of clean water and absence of processes of heat and mass transfer; in the area of soil in the natural state of displacement heat and mass transfer exceeds the corresponding values of displacements without heat and mass transfer; distribution of deformations considerably grows in the water saturated area and grows a little in the area of natural soil; distribution of tensions increases in the area of free surface of underground waters. Taking into account processes of heat and mass transfer in investigated area the greatest displacements are observed in water saturated soil and free underground waters. Deformations reach maximum values in the area of free underground waters and the lower part of the researched area. The maximum values of tensions are observed in the area of free underground waters and within the boundaries of the researched area.