Sammenligning imellem 2D og 3D betragtninger af en banedæmning

Abstract

Dette projekt omhandler numeriske betragtninger af banedæmninger i 2D og 3D. Hovedformålet er at opstille tendenser, som gør det muligt at simplificere tidskrævende 3D analyser til ækvivalente 2D analyser. Der er udført et state of the art for at redegøre for eksisterende studier vedrørende betydningen af simplificeringen af tre- til todimensionelle betragtninger af banedæmninger. Dette omhandler blandt andet studier vedrørende de betydningen af de geometriske variationer i tredje dimension. Desuden er et todimensionelt lineær-elastisk FE-program opbygget i MATLAB, som kan anvendes til bestemmelse af influenslængden. Dette Fe-program beskriver lastfordelingen i den tredje dimension vinkelret på dæmningstværsnittet og tager desuden højde for den trykspredning, som forekommer i dæmningen. Fe-programmet anvendes sammen med de kommercielle FE-programmer PLAXIS 2D og 3D til at opstille en tendens for influenslængden i anvendelsesgrænsetilstanden ved at sammenligne de maksimale flytninger i 2D og 3D. I brudgrænsetilstanden viste det sig at være sværere at beskrive en tendens for influenslængden, da bestemmelsen af den præcise brudlast i PLAXIS var problematisk. Dette skyldes måden hvorpå brudlasten beregnes i PLAXIS, hvilket besværliggjorde en direkte sammenligning mellem brudlasterne i 2D og 3D.

This master of science project considers 2D and 3D representations of railway embankments with a focus on constituting relationships that make it possible to simplify the computationally expensive 3D cases into equivalent 2D cases. As a result the problem formulation is stated as: - Which studies have so far been carried out concerning the simplification from 3D to 2D representations of railway embankments? -How can 3D representations of a loaded railway embankment be simplified to equivalent 2D representations based on numerically determined lengths of influence in the service limit state and ultimate limit state? A state of the art survey has been carried out to investigate existing studies within the field. From the survey it was seen that the safety factor in 3D is generally larger than the safety factor of a corresponding 2D case. The influence of geometric variations in the third dimension have also been investigated for turns and corners and these effects generally amplify the difference between the safety factors. Other studies also consider the influence of the height and the width of the embankment. In order to simplify the 3D states to equivalent 2D states a 2D linear elastic finite element program has been developed in MATLAB. A model was set up in the MATLAB program to determine the load distribution in the direction perpendicular to the cross-section plane of the embankment. Based on the MATLAB-model and models created in the commercial FE programs PLAXIS 2D and 3D it was possible to establish correlations between the length of influence for two load cases in the service limit state. In the first load case a single load of 250 kN was applied on each rail while 4 loads of the same size were applied on each rail in the second load case. Furthermore, it was verified that superposition principles were applicable to determine the corresponding deformations arising from other load cases than the two specific load cases considered. In the same way it was sought to establish a correlation in the ultimate limit state. However, it was not possible to obtain satisfactory results of the ultimate load in PLAXIS 3D due to the way that these loads are determined in PLAXIS. Consequently, it is necessary to determine the ultimate load in a different manner to obtain reliable results of the ultimate loads but this lies within a future study.

A master thesis from Aalborg University

Sammenligning imellem 2D og 3D betragtninger af en banedæmning

[Comparison between 2D and 3D considerations of a railway embankment]