доктор физико-математических наук, профессор
In engineering approaches to calculating the seismic resistance of underground structures, in particular pipelines, it is important to find experimentally the forces of interaction with the ground, as this frees us from the need to solve a difficult dynamic problem for the ground (elastic or having more complex mechanical properties). In this work inaccuracies are corrected and further development of the known from literature theory of quasistatic experiment for determining the coefficient of longitudinal interaction of soil and underground pipeline in seismic problems is given. It is shown that only the second approximation for the named coefficient in the expansion with a small parameter, equal to the ratio of the length of the pipe sample to the length of the seismic wave, takes into account the longitudinal deformation of the pipe; the first approximation corresponds to the experiment with an absolutely rigid pipe.A
strict reduction of the seismic problem to the problem for relative pipeline
movements is presented. Conditions are found on the external (remote from the
pipe) boundaries of the soil, the fulfillment of which ensures the correctness
of determining the coefficient of longitudinal interaction for seismic problems
Numerical examples are given that demonstrate a significant (sometimes by an order of magnitude) decreasing of the rod velocity in the presence of flexible joints.
Beginning with the solutions of two-dimensional Kelvin and Mindlin problems about concentrated forces acting in elastic space and inside of elastic half-space, analytical dependences between forces and average displacements in the direction of the action of forces on a circle, centered at the points of application of forces, are constructed. Based on the obtained ratios, models of the interaction of the pipeline with the ground during its bending vibrations under the influence of seismic waves are constructed. This approach is similar to the one used earlier by D.D. Barkan to find the connection between the forces acting on the foundations of buildings and ground structures and the vertical or shear displacements of the structures under dynamic influences based on classical elastic solutions of Boussinesq and Cerutti.
The solution of the problem of bending seismic vibrations of an extended pipeline obtained by the described method provides, apparently, the first theoretical justification and assessment of the accuracy of the engineering theory of "complete pinching" of an underground pipeline in the ground for the case of its bending vibrations (this theory is accepted in calculations for seismic resistance in current regulatory documents).