Explanation and Application of the Evolving Contact Traction Fields in Shallow Foundation Systems

The present paper provides a qualitative discussion of the evolution of contact traction fields beneath rigid shallow foundations resting on granular materials. A phenomenological similarity is recognized in the measured contact traction fields of rigid footings and at the bases of sandpiles. This observation leads to the hypothesis that the stress distributions are brought about by the same physical phenomena, namely the development of arching effects through force chains and mobilized intergranular friction. A set of semi-empirical equations are suggested for the normal and tangential components of this contact traction based on past experimental measurements and phenomenological assumptions of frictional behaviors at the foundation system scale. These equations are then applied to the prescribed boundary conditions for the analysis of the settlement, resistance, and stress fields in supporting granular materials beneath the footing. A parametric sensitivity study is performed on the proposed modelling method, highlighting solutions to the boundary-value problems in an isotropic, homogeneous elastic half-space.

MATHEMATICAL MODELING OF ELASTIC WAVE PROPAGATION IN A BODY WITH A DEFECT

The solution of the dynamic problem of calculation the wave field of displacements on the surface of an elastic half-space caused by the opening of an internal crack under the action of torsional forces is presented. Based on the solutions of the boundary integral equations, the nature of the change in the amplitude-frequency characteristics of elastic oscillations on the surface of a rigid body depending on the size of the defect is shown.

RESEARCH OF ACOUSTIC EMISSIONS FROM THE SYSTEM OF COMPLANARY CRACKS

The dynamic problem of the displacement field in an elastic half-space caused by the time-steady displacement of the surfaces of the system of disc-shaped coplanar cracks is solved. The solutions are obtained by the method of boundary integral equations. The dependences of elastic displacements on the surface of the half-space on the wave number, the number of defects and the depths of their occurrence are constructed.

Modeling of relative shear deformation zones before strong earthquakes in Kamchatka from 2018-2021

Представлено сравнительное моделирование зон относительных сдвиговых деформаций для четырех камчатских землетрясений с Mw ≥ 4.8, произошедших в период с декабря 2018 г. по март 2021 г., основанное на статической модели деформационного поля в рамках теории упругости. Земная кора рассмотрена как однородное изотропное упругое полупространство, в котором присутствуют различные источники напряжения, описывающие очаг землетрясения: точечный источник в виде единичной силы, точечный источник в виде комбинации девяти двойных сил, распределенный источник в виде прямоугольной площадки. We present a comparative modeling of the zones of relative shear deformation for four Kamchatka earthquakes Mw≥4.8 that occurred between December 2018 and March 2021. Modeling based on a static model of the deformation field in the framework of the theory of elasticity. The Earth’s crust is considered as a homogeneous isotropic elastic half-space, in which there are different sources of stress describing the source of the earthquake: a point source in the form of a single force, a point source in the form of a combination of nine double forces, a distributed source in the form of a rectangular area.

Nonlinear oscillations in a constant gravitational field

Exploring non-linear oscillations is a challenging task since the related differential equations cannot be directly solved in terms of elementary functions. Thus, complicated mathematical or numerical methods are usually employed to find accurate or approximate expressions that describe the behavior of the system with respect to time. In this paper, the vertical oscillations of an object under the influence of its weight and an opposite force with magnitude F=cyn, where n>0 are being explored. Accurate and approximate simple solutions regarding the object’s position with respect to time are presented and the dependence of the oscillation’s period from the oscillation’s range of displacements and the exponent n is revealed. In addition, the special case in which n=3/2 (which describes the oscillation of a rigid sphere on an elastic half space) is also highlighted. Lastly, it is shown that similar cases (such as the case of a force with magnitude F=kx+λx2) can be also treated using the same approach.

Computation of synthetic seismogram in real earth model by eigen function expansion

The method of eigen function expansion has been used in the present study to compute synthetic or theoretical seismogram in layered elastic half-space of real earth model. Simple dislocation source model has been considered. The transverse (SH) or radial and vertical (P-SV) components of displacement field have been computed as summed modes and compared by using both exact and numerical techniques. The methods used in the study, include exact evaluation by propagator matrix approach using Reflection-Transmission coefficients as well as numerical computations using Runge-Kutta method of order 4. The specialty of the present study is to evaluate approximate displacement field for the earth models with homogeneous and / or inhomogeneous layers. The normalization technique has been used in the study to control the overflow errors. The study has an advantage to get an idea of earth structure or source model by an inverse iterative technique.

Thermomechanical Slip in Elastic Contact Between Identical Materials

The contact problem for interaction between an elastic sphere and an elastic half-space is considered taking into account partial thermomechanical frictional slip induced by thermal expansion of the half-space. The elastic constants of the bodies are assumed to be identical. The Amontons–Coulomb law is used to account for friction. The problem is reduced to non-linear boundary integral equations that correspond to the initial stage of mechanical loading and the subsequent stage of thermal loading. The dependences of the contact stress distribution, relative displacements of the contacting surfaces, dimensions of the stick and slip zones on temperature of the half-space are studied numerically. It was revealed that an increase in temperature causes increases in the shear contact stress and the relative shear displacements of the contacting surfaces. The absolute values of the shear contact stress reach their maximum at the boundaries of the stick zones. The greatest value of the moduli of the relative shear displacements are reached at the boundary of the contact region. The stick zone radius decreases monotonically according to a nonlinear law with increasing temperature.

An Elastic Half Space with a Moving Punch

The dynamic problem of a punch with rounded tips moving in an elastic half-space in a fixed direction has been considered. The static problem of determining stress component under the contact region of a punch has also been solved. Fourier integral transform has been employed to reduce the problems in solving dual integral equations. These integral equations have been solved using Cooke’s [1] result (1970) to obtain the stress component. Finally, exact expressions for stress components under the punch and the normal displacement component in the region outside the punch have been derived. Numerical results for stress intensity factor at the punch end and torque applied over the contact region have been presented in the form of graph.