MATHEMATICAL AND COMPUTER MODELING OF THE STRESS-STRAIN STATE OF THE ROCK MASS COMPOSED OF TWO ROCK TYPES NEAR THE CIRCULAR PRESSURE EXCAVATION

摘要

Research aim is to get the analytical solution of geomechanics topical problem of applied significancein hydrotechnical construction connected with the stress-strain state estimation of the rock masscomposed of two rock types with various stress-strain behaviours in the vicinity of the circular pressureexcavation located near the rectilinear interface between rocks. Research methodology is based on the application of the complex variable functions theory,the properties of series with complex coefficients, and the integrals of Cauchy type. Research results is the complete calculation algorithm developed, featuring iterative process computerimplementation, the first convergence of which considers the well-known problem for circular openingwithin infinite homogenous isotropic medium under internal pressure; and the influence of the interfacebetween rocks is considered by means of setting additional pressures which are defined more preciselyat the following iterations. The criterion for the iterative process completion is satisfaction withthe required accuracy of all boundary conditions assigned (during calculation, maximum inaccuracydidn't exceed 10~(-5)). The obtained results were used to develop computer model of the problem underconsideration which has been implemented in the software package of the FEM (finite elements method)with the aim of specifying the sizes of the modeling domain and for boundary conditions formation.Finally, the comparison of analytical and numerical modeling results is introduced as appliedto the specific excavation. Conclusion. The analysis of the obtained results allowed to conclude that the high accuracyof calculation with the use of FEM is achieved only in case of setting sufficient research area (each sizemust significantly exceed five radii of excavation). Obtained results application area is the development of underground structures calculation designmethodology.