Ground Conditions & Track Stiffness (brief) Flashcards
What do the train bogies provide?
The suspension system of the train
They act as a hydraulic damper
Is this an articulated or non-articulated bogie?
Articulated
Power car has two bogies, but carriages have one (between carriage connections)
Is this an articulated or non-articulated bogie?
Non-articulated
Each carriage has two bogies
Name an advantage and disadvantage of articulated bogies?
Advantage - more stable at high speeds
Disadvantage - track is loaded more, as the carriage loads are not split between two bogies
What is ‘hunting’, and how is it counteracted in high-speed rail?
Hunting is where the bogies sway from side-to-side
In HSR, dampers between the carriages stiffen the bogies
What are the typical axle loads in the UK?
17.3 tonnes (high-speed trains)
25 tonnes (freight)
What is the total stress at any point within the geomaterials comprised of?
The stress from the static weight (w), and the stress from the axle load
NB. diagram shows static load, dynamic much higher
What does this equation represent?
Static weight (w)
Why is the axle load contribution quickly reduced through the granular layers?
Because of the high stiffness in these layers
What does a low support stiffness result in?
- High track deflections
- Axle shape ‘loses definition’
- Causes big ‘displacement bowl’
- Rail doesn’t return to original position before next set of axles
- High ballast and subgrade plasticity (ie. settlement)
What does a high support stiffness result in?
- Low track deflections (sleeper not bending)
- Clearly defined pulses from the individual axles
- Rail returns to original position
- High sleeper/ballast contact forces
Describe principal stress rotation
- Vertical stress/major principle stress (σ_1) changes angle as the wheel moves across the sleeper
- Due to direction of load distribution through the granular material
- As a result, the major and minor principle stresses are constantly rotating
What does high principle stress rotation cause?
High settlement
What does this equation represent?
Relationship between running dynamic load and static load
What is beam on elastic foundation (BOEF)
- An analytical track model
- Considers load moving across a beam, supported on a series of elastic supports
What does this equation represent?
The solution for rail deflection for a distance x along the rail from a single point load P
E = modulus of elasticity,
u = foundation modulus/modulus of elasticity of the track support
x,y = rail deflection
What does this equation represent?
The supporting line force
NB. use radians not degrees in the equations
What do these equations represent?
They are derivations of y(x) (rail deflection)
- slope (at any distance along the rail from the point load)
- bending moment (at any…)
- shear force (at any…)
What do these equations represent?
What can F_m be used to estimate?
The max. values for deflection/BM/supporting line force
Can be used to estimate the upper bound value of the rail seat load (Q_m)
What can the upper bound value of the rail seat load (Q_m) be used to estimate?
The ballast pressure on the sleeper
How can vertical stress distribution be estimated?
Using vertical stress distribution charts
What is the principle of superposition used for?
- Can superimpose/add together single axle results
- Should end up with a ‘w’ shape
- Can use because elastic properties
- For calcs, should only need to compute one side (other side is mirror image)
What is track modulus, and how does it differ to overall stiffness?
Track modulus is the vertical stiffness of the rail foundation (below the rail):
- it is highly non-linear
Overall stiffness covers the rail as well:
- the EI term (flexural stiffness of rail) in track modulus takes out track stiffness from consideration
- modulus doesn’t calculate the stiffness the train feels
What does this equation represent?
Track stiffness (k)
y_m = max. deflection directly under force P
What does this equation represent?
Track modulus (u)
Note the [P/y_m] term is track stiffness (k)
What does higher track modulus represent?
Better track formation, giving better track performance
However, issues (e.g. inducing rolling contact fatigue in the rail) can develop if u is too high
What value of track modulus is considered ‘average’, according the AREMA?
u = 28 MPa
What is simple elastic theory used to estimate?
Stresses under the sleeper (because subgrade material response is non-linear)
What does this equation represent?
Calculating stress (vertical) from a point load Q on the surface of an elastic medium
What is the optimum values of track stiffness, according to German standards?
What can happen if track stiffness is too low?
Plasticity can develop:
- very high rail bending
- can break the bottom of the rail (where footings are)
What can happen if track stiffness is too high?
Plasticity can develop:
- cause issues at the top of the rail, like rolling contact fatigue
What is track receptance?
It is the ‘opposite’ of stiffness:
- inverse of dynamic stiffness wrt the transmission of vibration from track to ground and/or structure
- very local
- looks at the contribution of different frequencies to the overall response
What instrument is used to measure dynamic sleeper support stiffness?
Falling weight deflectometer
