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RTID > Dynamic Displacement Amplification > Flashcards

Dynamic Displacement Amplification Flashcards

1
Q

What causes vibration and issues on rail tracks?

A
  • Stress waves are induced by the track structural responses
  • Vibration source at the wheel-rail interface
  • Discontinuity on the track
  • Variable support
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2
Q

How does soft ground give annoyance to people?

A

Soft ground gives whole body vibration and rattling

In Sweden, soft soils cause vibration issues

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3
Q

How does hard ground give annoyance to people?

A

Hard ground gives structural borne noise

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4
Q

What are the three types of waves, and what order are they in?

A

Compression wave comes first (e.g. what you hear when someone is talking)

Shear wave comes second (e.g. slinky)

Rayleigh wave comes last

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5
Q

What is the most destructive wave, and roughly how much energy does it have?

A

Rayleigh wave - contains 67% of energy

The Rayleigh wave is about 95% of shear wave (for typical Poisson’s ratio)

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6
Q

What does ‘v’ in the compression wave equation stand for?

A

Poisson’s ratio

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7
Q

What is the shear wave equation also equal to?

A

= sq. [G/p]

Where G = shear modulus,
rho = density

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8
Q

What is a reduction of response with distance?

A

Attenuation

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9
Q

What are two example sensors for vibration measurement?

A

Geophones (velocity)

Accelerometers (acceleration)

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10
Q

What are low frequencies (e.g. 0-40 Hz) likely to cause damage to?

A
  • Damage to substructure
  • Vibration and contact noise (buildings and vehicle)
  • Damage to vehicle (carriages, bogies, axles, wheels)
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11
Q

What are high frequencies (e.g. 400-1500 Hz) likely to cause damage to?

A
  • Damage to rail (part of superstructure)
  • Radiated sound/noise to residents and passenger
  • Damage to vehicle (wheels only)
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12
Q

Define critical speed

What does it result in?

A

Critical speed is when the train speed reaches the surface ground wave velocity of a homogeneous subgrade

Results in high ground displacement and surface wave propagation

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13
Q

If there is no high track stiffness track structure at the surface (e.g. for slab track), when does critical speed occur?

A

The critical velocity in this scenario is given by the in-situ Rayleigh wave velocity

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14
Q

If there is a high-stiffness structure near the track surface, what might happen?

A

The train speed’s critical velocity might increase above the Rayleigh-wave velocity

ie. towards a critical track velocity

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15
Q

What needs to be done to run trains at high speed (higher than Rayleigh wave speed)?

A

Need to ground stabilise (increase the stiffness of the soil)

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16
Q

What is peak-to-peak displacement?

A

The distance from peak displacement as the rail moves downwards to peak displacement as the rail moves upwards

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17
Q

What is required for high-speed lines?

A

Very stiff formations (e.g. concrete slab-track)

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18
Q

For the effect of undrained shear strength on the maximum permissible speed for a homogenous subgrade (e.g. clay soils), what ratio is used?

A

NB. ratio not on eqn sheet
NB. n = Rayleigh wave percentage

The value of K_c varies with the plasticity index (I_p), and the overconsolidation ratio (OCR)

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19
Q

How is the plasticity index calculated?

A
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20
Q

What can this equation be used to calculate?

A

Undrained shear strength (C_u) required for a permissible max. train speed for a given Rayleigh wave percentage (n)

NB. C_u is sometimes written as S_u

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21
Q

What is the equation that relates undrained shear strength with depth?

A
22
Q

What is the Rayleigh wave velocity ratio (M_RWV)?

A
23
Q

What should the Rayleigh wave velocity ratio (M_RWV) be equal to?

A

0.6

24
Q

What is the critical track velocity ratio (M_CTV)?

A

NB. using ballasted track with no embankments, V_CTV should be similar to V_R (from the Rayleigh wave velocity ratio)

25
Q

Define ballast peak particle velocity (PPV)

What is it dependent on?

A

PPV of the ballast is the induced ballast velocity due to train passage
- it is the rate at which the sleeper moves up and down
- it is dependent on the train speed (see graph)

26
Q

What happens to PPV when the track reaches critical velocity?

A

A gradient change occurs (see graph)

Track dynamics start to occur

27
Q

At what point does PPV increase linearly/non-linearly with train speed?

A

At sub critical velocity ratios (of <0.5-0.6), PPV increases linearly with train speed

Past 0.6 the PPV increases in a non-linear way

28
Q

What test is used to determine subgrade stiffness (E_V2)

A

The plate load test

The plate load test is also used for calculation of vertical track stiffness

In the UK, the relationship between E_V2 and E_max (small strain stiffness) is given in pic

29
Q

What effect does higher baseplate stiffness (K_pla) and higher train speed have on the ballast?

A

The ballast experiences higher vibration speed and acceleration (g)

30
Q

Explain how PPV (and overall track geometry) can be improved?

A

By using pads

This can reduce high contact force (spreads it out) by slowing stress wave; slowing down the loading onto the ballast and improving track geometry

31
Q

What happens to the ballast if high accelerations (e.g. 1.4g) are experienced?

A

The ballast starts to unpack (shakes, lifts up and then down)

If PPA exceeds 0.7-0.8g unmodified ballast starts to destabalise

32
Q

Name the different parameters that PPV is related to

A
33
Q

What happens if PPV exceeds 20 mm/s?

A

Ballast decompression starts - ballast migration will lead to increased maintenance

34
Q

Which ground wave profile is above/below critical speed?

A

Top - above critical speed
Bottom - below critical speed

35
Q

What do these two models show?

A

a) quarter-train model
b) pseudo full-train model

36
Q

For this equation of motion for dynamic analysis, what are the different solution methods?

A
  • Frequency domain solutions
  • Modal superposition solutions
  • Implicit time stepping algorithms
  • Explicit time stepping algorithms

NB. don’t need to know how to solve eqn of motion in exam

37
Q

What does this ground displacement profile at Rayleigh-wave development (single moving load, homogenous soil) show?

A

Pre-critical speed

There is a ‘bowl of deformation’ when the axle is moving across slowly

38
Q

What does this ground displacement profile at Rayleigh-wave development (single moving load, homogenous soil) show?

A

Post-critical speed

At critical speed, a ‘cone’ forms

39
Q

The graphs show sleeper deflection before and passing critical speed at Ledsgard. Describe what is happening.

A
  • The response becomes out-of-phase (it ‘loses’ one of the peaks)
  • There is very high deformation at/after critical speed
  • All the frequencies collided in this case study, giving very high displacements
40
Q

For the Ledsgard case study, what factor determined whether the behaviour (for deflection*) was linear or non-linear?

A

The values of deviatoric strains

41
Q

When plasticity comes into effect, what happens to soil properties?

A

They can reduce

42
Q

For the Ledsgard soils, how do the dynamic soil properties (soil density, s-wave velocity, p-wave velocity, damping ratio) vary with depth under the rail?

A
43
Q

For the equations for non-linear modelling, what is the typical value for P_atm?

A
44
Q

In this critical velocity envelope/critical speed curve/interpolated normalised response curve for Ledsgard (in both the downward and upward directions), what is shown?

A

Dynamic amplification envelope
- shows that there is an increase in dynamic deflection as the critical velocity is approached

The downward deflections are normalised to the max. quasi-static downward deflection (likewise for upwards)

45
Q

What does this critical speed curve for the Ledsgard displacement results show?

A

Dynamic only component

Only the displacement results for the dynamic-only component of the upward and downward response
- ie. the quasi-static deflections for both the upward and downward deflections have been subtracted from the peak values

Graph shows how the dynamic component only is developed with train speed ratio (M_CTV)
- The distance between the upward and downward points represents the peak dynamic component of the propagating ground waves with train speed ratio M_CTV

46
Q

What does this train-track interaction drawing show?

A

The stiffness change from ‘floating’ to ‘fixed’ track

47
Q

What does this train-track interaction drawing show?

A

The development of hanging sleepers in the transition zone

48
Q

What does this train-track interaction drawing show?

A

It shows embankment consolidation

This leads to a larger elevation difference

49
Q

What could be introduced at a track transition point improve passenger experience?

What are example parameters that should be minimised at transition points?

A
  • Could have a rigid base (see drawing)
  • Wheel displacement
  • Wheel/rail interaction force
  • Train body vertical acceleration (g)
50
Q

What can happen if a bridge is not at 90 degrees perpendicular to the rail?

A

This can cause a cross-track fault, which could lead to flange climb and derailment

RTID (9 decks)

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