## MATHEMATICAL MODELLING AND THEORETICAL STUDY ON THE TUNNEL+SOIL SYSTEMS

1ST INTERNATIONAL CONFERENCE ON INNOVATIONS IN NATURAL SCIENCE AND ENGINEERING, Famagusta, Cyprus (Kktc), 03 January 2018, vol.1, no.1, pp.5-6

• Publication Type: Conference Paper / Full Text
• Volume: 1
• City: Famagusta
• Country: Cyprus (Kktc)
• Page Numbers: pp.5-6
• Yıldız Technical University Affiliated: Yes

#### Abstract

A safe and reliable use of the modern high-speed underground trains and other types of
underground moving wheels requires theoretical investigations of corresponding dynamical problems. Under such investigations, underground structures into which the mentioned high-speed wheels move are modelled as infinite hollow cylinders surrounded by an elastic or viscoelastic medium. At the same time, the high-speed wheels are modelled as moving load or oscillatingmoving load. Consequently, the study of the dynamics of the tunnel + soil systems is reduced to the investigations of the problems related to the dynamics of the moving or oscillating moving load acting on the interior of the interior of the hollow cylinder surrounded by elastic or viscoelastic medium. The present work is related, namely, to these studies. Mathematical formulation of the considered problems as in [1, 2 and 3], is made within the framework of piecewise homogeneous body model with utilizing of the exact equations and relations of elastodynamics. It is assumed that on the interface surface between the hollow cylinder
and surrounded elastic medium the shear-spring type imperfect contact conditions are satisfied. The method of solution to the corresponding boundary and contact problems is developed by employing the moving coordinate method and the Fourier transform method with respect to the axial coordinate. The originals of the Fourier transforms are found numerically. Numerical results on the critical velocity of the moving load and on the interface stresses are presented and discussed. In particular, it is established that the imperfectness of the contact between the constituents reduces the values of the critical velocity under which the resonance type accidents take place.