Numerical modeling and digital mathematical analysis in the study of complex systems

Introduction. Implementation of the import substitution system requires an increase in agricultural land. Farming on rainfed land has not proven to be feasible and efficient. Guaranteed stable yield is possible with obligatory irrigation according to the technological map. It is necessary to create automated systems of water distribution and irrigation and rational use of water resources during implementation of irrigation itself.

Object. The object of research is a complex system "water conduit – ground base – vehicle load" and stress-strain state of the ground massif around the water conduit.

Materials and methods. The investigations were carried out using the finite element method. Numerical modelling was carried out using Midas GTS NX software. The proven wxMaxima software was used for the numerical mathematical analysis of the large volume of figures. These software programs allow verification of how accurately the computer model represents the underlying mathematical model when reproducing theoretical solutions. In the next step, the model is subjected to validation, when it is determined how faithfully the computer model represents the real object.

Results and conclusions. At research of work of the complex system "water conduit – ground base – load from a car" and definition of a stress-strain state of a ground massif it is established that value of a response function is determined to a considerable degree by force on a water conduit from a car, the function weakly reacts on height of clay soil above a water conduit; with increase of load the degree of influence on a response function remains constant; with increasing load, the degree of influence on the response function remains constant; at a force of 40 tonnes, the vertical stress reaches its minimum extremum, which is 350.38 kN/m² at a ground height above the conduit of 0.82 m; at a force of 20.25 tonnes, the stress function also tends to the minimum extremum; as the forces from the vehicle above the conduit decrease, the stress increments increase; at 40 tonnes the function increment is 1.39 kN/m², at 20.5 tonnes it is 6.43 kN/m², and at 5 tonnes it is 10.06 kN/m²; the relationship between the change in vertical stresses TOTAL S-YY in the soil mass of the waterway and the forces on the ground from the vehicle is linear; at the lowest force of 5.0 tonnes from the car on the water line, the vertical stress reaches the lowest value at the lowest ground height above the structure of 0.5 m, which is 288.14 kN/m². With a force of 40 tonnes on the conduit, the vertical stress reaches its highest value at the highest ground height above the structure of 1.2 m, which is 352.55 kN/m². The proposed algorithm can be used in the development of design documentation for the construction of culvert systems.

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