PSI - Issue 48

G. Gusev et al. / Procedia Structural Integrity 48 (2023) 169–175 Gusev et al/ StructuralIntegrity Procedia 00 (2023) 000–000

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It can be seen that regardless of the type of loading, the plots of the relative stiffness of the fragment and the energy of deformation during the loading stages, which correspond to pt. A and pt. D are sufficiently close. It allows us to suppose that for the given type of the fragment structure (the conjugation of the column - the base plate) the value of the limiting energy of deformation, which determines the carrying capacity of the fragment, depends less on the form of loading than on the characteristics of the fragment itself - the type of concrete, the type and % of reinforcement and the geometrical dimensions. This conclusion allows us to propose an energy criterion for evaluating the carrying capacity of reinforced concrete fragments in the form of a limit value of deformation energy. A similar approach has been used by Eryshev (2018) to estimate the transition of complex systems to the limit state. As an example of work according to the proposed criterion it is possible to give a comparison of the energy of deformation of the corresponding volume of supporting columns of the first floor of the monolithic reinforced concrete fragment with the height of 5 floors, which was calculated by the results of the first boundary problem (Fig. 4, line 1) and calculated by the results of the problem of deformation of the fragment (Fig. 4, line 3 and line 4). The concrete strength class of the building is taken equal to B25, the strength class of the reinforcement A400. The pitch of the supporting elements is 6 meters. The building is a slab foundation. The modulus of elasticity of the ground at the base of the building is 10 MPa. The limiting energy of deformation [U] means the energy value corresponding to the mean position of pt. D in Fig. 3 for different loading variants in case of reinforcement equal to 7% of the column cross-sectional area. This value presupposes a significant loss of relative stiffness of the "column-foundation slab" fragment (Fig. 3 pt. D). In this case, for the described properties of the column and a given percentage of reinforcement, 7%, the value of the limiting energy of deformation will be about 290 J (Fig. 4, line 3). From Fig. 4 it is seen that in case of general boundary problem of deformation of the whole structure frame, particularly for the variant of five-storey building with span of 6 m, this value of energy corresponds to the value of the limit deformation of soil mass equal to 11.5 mm/m (the intersection of lines 3 and 1 in Fig. 4). These results agree well with the estimation of the limit deformations of the soil mass according to the equivalent stresses in the elements of the monolithic frame for the whole building. In that case the value [ε] was 12 mm/m (line 2 in Fig. 4). Thus, conjugation of solutions of two boundary problems at different scale levels can be carried out by means of comparisons of deformation energies of corresponding structural elements. Moreover, knowing the limited strain energy for other types of reinforcement (line 4 in Fig. 4) from the calculations of the nodal elements, it is also possible to calculate the limited strain energy of soil in the vicinity of the foundation. In this case, it will be about 4.5 mm/m (intersection of lines 1, 5 and 4 in Fig. 4). 4. Conclusion An approach to estimate critical levels of deformations of monolithic reinforced concrete buildings in undermined territories by solving several boundary problems at different model scales: from the bearing fragment to the system "building-foundation-soil mass" is proposed. Evaluation of bearing capacity of the whole building frame is performed on the basis of the results of deformation of the bearing fragment using the energy criterion. This approach allows to determine the dependence of SSS of reinforced concrete frame on the soil deformations for different types of buildings and different floor levels and thus to estimate the maximum allowable soil deformations for buildings in the areas of technogenic impact caused by mining. Acknowledgements The study was supported by the Russian Science Foundation Grant No. 22-19-00108, https://rscf.ru/project/22 19-00108. References Baryakh, A. A., Devyatkov S.Y., Samodelkina N.A., 2016. Theoretical explanation of conditions for sinkholes after emergency flooding of potash mines. Journal of Mining Science 52(1), 36–45. Baryakh, A.A., Samodelkina N.A., 2018. Geomechanical Estimation of Deformation Intensity above the Flooded Potash Mine. Journal of Mining Science 53(4), 630–642. Eryshev, V.A., 2018. Energy Model in Calculating the Strength Characteristics of the Reinforced Concrete Components. Materials Science Forum 931, 36–41.