Numerical Analysis of Deformations of the Shallow Square Foundations with Variable Relative Stiffness

The paper deals with numerical analysis of deformations and relative displacements (relative settlement, relative deflection and flexibility) of the shallow square foundations depending on the variable relative stiffness. For solution of the problem finite element method was used with theoretical assumptions of the linearly elastic half-space. Foundation-subsoil contact was modelled by one-directional and bi-directional bond effect. Results of the solution are presented by graphical forms.

Measurement of Vertical Track Modulus: Field Testing, Repeatability, and Effects of Track Geometry

The heavy axle loads and high speeds of modern freight trains produce high track stresses leading to quicker track degradation. Track loads can be increased by variations in vertical track stiffness — the relationship between vertical rail deflection and the vertical applied load — and vertical track modulus. Both low track modulus and large variations in track modulus (leading to increased dynamic loading) cause accelerated track degradation and associated increased maintenance requirements. The University of Nebraska, under sponsorship from the Federal Railroad Administration, continues to develop a method to measure vertical track deflection and modulus from a rail car traveling at revenue speed. This paper first summarizes past work to develop a method to measure vertical track deflection from a moving rail car. The measurement is made by attaching a beam to the sideframe of a loaded hopper car that extends along the rail toward the car’s center. Then the deflection of the rail is measured approximately four feet from the inner wheel using a camera/laser system. The measurement determines the offset between the rail and the line established by the two wheel/rail contact points. These deflection measurements can then be used to estimate track modulus. Results are presented for repeated tests on approximately three hundred miles of heavy axle load freight line over a period of about ten months. These results have shown that the measurements of the above system are extremely repeatable and are not significantly related to train speed. The measurements also show seasonal variations in track modulus caused by factors such as variations in subgrade moisture and ambient temperature. The system has shown a notable ability to identify locations at high risk of derailments. After each of the four tests, a “top ten” list was created indicating the largest changes in relative deflection in descending order (one top ten list corresponding to each of the four tests). The lists were created based on exception criteria presented by the authors at last year’s conference. Four derailments occurred over this ten month period and three of those derailments appear in the top ten lists (#2, #10, in list one and #1 in list four). Finally, simulation and experimental analysis that quantify and assess the co-relation between this system and track geometry is presented. Extreme track geometry variations can create errors as the relative deflection measurement is mapped into a specific value of track modulus. This effect is also quantified and described.