Peculiarities of Predicting Synthetic Seismograms and Accelerograms for Heterogeneous Foundation Beddings

The article offers an improvement of the method for predicting strong ground motion displacements and accelerations, assuming that an earthquake is an instantaneous mechanical rupture of the Earth’s crust. The method uses derived theoretical formulas to calculate all three parameters of the ground motion: displacements, velocities and accelerations during strong (with magnitude M≥6.0) earthquakes for any heterogeneous (multilayer) ground beddings. The article addresses the case of heterogeneous two-layer beddings. The example provided involves the results obtained for 16 variants of two-layer heterogeneous sites in seismic categories I-IV at the magnitude M=7.0, and distance of 15 km from the expected earthquake’s rupture. A comparison of the results obtained for actual heterogeneous foundation beddings with the equivalent homogeneous beddings showed divergences of increase by 1.3-1.6 times, depending on the number of the five and three natural oscillation modes considered. Significant effects of various modes of foundation bedding natural oscillations on ground surface displacements and accelerations were identified when comparing a heterogeneous beddings to a homogeneous ones. A substantial reduction (by a factor of two or more) in the stiffness of the upper soil layer relative to the lower layer leads to a marked increase in surface ground accelerations. A recommendation is provided that the predicted values of displacements and accelerations for heterogeneous foundation beddings should be calculated with consideration of at least 5 natural oscillation modes of the ground bedding. The paper proposes a new analytical solution to the problem of an earthquake as an instantaneous mechanical rupture of the earth's crust with modified boundary and initial conditions of the problem, and also reveals the influence of the ratio of the rigidities coefficients and the geometric parameters of the layers on the amplitudes of seismograms and accelerograms on the Earth's surface.