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The paper presents a mathematical problem involving quasistatic contact between a thermo-electro-viscoelastic body and a lubricated foundation, where the contact is described using a version of Coulomb’s law of friction that includes normal damped response conditions and heat exchange with a conductive foundation. The constitutive law for the material is thermo-electro-viscoelastic. The problem is formulated as a system that includes a parabolic equation of the first kind for the temperature, an evolutionary elliptic quasivariational inequality for the displacement and a variational elliptic equality for the electric stress. The author establishes the existence of a unique weak solution to the problem by utilizing classical results for evolutionary quasivariational elliptic inequalities, parabolic differential equations and fixed point arguments.

The author establishes a variational formulation for the model and proves the existence of a unique weak solution to the problem using classical results for evolutionary quasivariational elliptic inequalities, parabolic difierential equations and fixed point arguments.

The author proves the existence of a unique weak solution to the problem using classical results for evolutionary quasivariational elliptic inequalities, parabolic difierential equations and fixed point arguments.

The author studies a mathematical problem between a thermo-electro-viscoelastic body and a lubricated foundation using a version of Coulomb’s law of friction including the normal damped response conditions and the heat exchange with a conductive foundation, which is original and requires a good understanding of modeling and mathematical tools.

The main objective of the present research is to investigate the benefits of using geogrid reinforcement in minimizing the rate of deterioration of ballasted rail track geometry resting on soft clay and to explore the effect of load amplitude, load frequency, presence of geogrid layer in ballast layer and ballast layer thickness on the behavior of track system. These variables are studied both experimentally and numerically. This paper examines the effect of geogrid reinforced ballast laying on a layer of clayey soil as a subgrade layer, where a half full scale railway tests are conducted as well as a theoretical analysis is performed.

The experimental tests work consists of laboratory model tests to investigate the reduction in the compressibility and stress distribution induced in soft clay under a ballast railway reinforced by geogrid reinforcement subjected to dynamic load. Experimental model based on an approximate half scale for general rail track engineering practice is adopted in this study which is used in Iraqi railways. The investigated parameters are load amplitude, load frequency and presence of geogrid reinforcement layer. A half full-scale railway was constructed for carrying out the tests, which consists of two rails 800 mm in length with three wooden sleepers (900 mm × 90 mm × 90 mm). The ballast was overlying 500 mm thick clay layer. The tests were carried out with and without geogrid reinforcement, the tests were carried out in a well tied steel box of 1.5 m length × 1 m width × 1 m height. A series of laboratory tests were conducted to investigate the response of the ballast and the clay layers where the ballast was reinforced by a geogrid. Settlement in ballast and clay, was measured in reinforced and unreinforced ballast cases. In addition to the laboratory tests, the application of numerical analysis was made by using the finite element program PLAXIS 3D 2013.

It was concluded that the settlement increased with increasing the simulated train load amplitude, there is a sharp increase in settlement up to the cycle 500 and after that, there is a gradual increase to level out between, 2,500 and 4,500 cycles depending on the load frequency. There is a little increase in the induced settlement when the load amplitude increased from 0.5 to 1 ton, but it is higher when the load amplitude increased to 2 ton, the increase in settlement depends on the geogrid existence and the other studied parameters. Both experimental and numerical results showed the same behavior. The effect of load frequency on the settlement ratio is almost constant after 500 cycles. In general, for reinforced cases, the effect of load frequency on the settlement ratio is very small ranging between 0.5 and 2% compared with the unreinforced case.

Increasing the ballast layer thickness from 20 cm to 30 cm leads to decrease the settlement by about 50%. This ascertains the efficiency of ballast in spreading the waves induced by the track.