A simple finite element for nonlinear wheel/rail contact and separation simulations4/27 2012 Shen-Haw JuDepartment of Civil Engineering, National Cheng-Kung University

Introduction

This study investigates the derailment of high-speed trains. A moving wheel finite element containing contact and separation modes was developed. We would like to find the reasons of the derailment event for Taiwan High Speed Rail during Jiasian earthquake on March 4, 2010 in Taiwan.

An earthquake with a magnitude of 6.8 occurred in Chuetsu region of Niigata Prefecture of Japan on October 23, 2004 at 17:56 causing the derailment of the Shinkansen train (arranged from Yomiuri Newspaper and Internet web-sites)

Shinkansen train was traveling at a speed of 200 kph when the earthquake hit.

The recorded ground accelerations were 1308 gal.

(3) The train derailment seems reasonable, because the earthquake was over 1 g.

Taiwan High Speed Rail slightly derailing in southern Taiwan due to the Jiasian earthquake on March 4, 2010

The damage of rail concrete slab due to the derailment of Taiwan High Speed Rail on March 4, 2010

The train speed was 298 kph at the beginning of the earthquake, and stopped after running a distance of 3.62 km.

The maximum ground acceleration was 171 gal.

It is not reasonable to derail a train at this earthquake level.

2. Nonlinear bridge-train interaction analysisWheel element

The element includes a wheel node and a number of target nodes. The wheel node can move on these taeget nodes.

If the two target nodes and the wheel node are nodes 1, 3 and 2 respectively, the three-node element stiffness for the nodal displacements is:Ni = the cubic Hermitian interpolation functions.

The irregularity element forces fr:

The internal force vector of the wheel element:The value of f2 is the contact force between the wheel and rail. If it is compression, the wheel and rail are contacted together. If it is tension, the wheel and rail are separated, and kr will be set to zero for the next Newton-Raphson iteration.

KN/m

(2) Spring-damper with the rigid link effect

For a spring or damper connected to two master nodes, the stiffness or damping matrix is:

The high-speed train is the SKS-700 type, which has 12 carriages moving in the X direction. Each carriage contains two bogies, and each bogie contains two wheel sets (48 wheel sets in total).

3. Validation

Displacement at the wheel center changing with time

4. Finite element model of bridge-train interaction analysesThe railway bridges are multi simply supported beams with a span of 30 m.

(1) With rail irregularities, the derailment coefficients of the train speed over 250 km/h are larger than or near 0.8, which is near the safety condition. The train deceleration from 300 to 250 km/h requires 17 s.

8. Conclusions

Generally, when a high-speed train moves on the multi-span simply supported bridges, the derailment coefficients due to rail irregularities or seismic loads are enlarged with the increase in train speed.

The bridge may magnify the seismic load, especially due to a resonance between bridges and earthquakes. Moreover, the X-direction earthquake causes a large sharp vertical displacement between two simply supported girders, so large derailment coefficients are generated. Due to these reasons, a moderate earthquake may derail a high-speed train.

Many thanks for your attention