4
M. D. Martínez-Rodrigo et al.
3 Sensitivity Analysis over Track Parameters
First, a sensitivity analysis is performed on four track parameters: the stiffness and
damping coefficients of the rail pads, K p and C p , and of the ballast, K b and C b .
In the last years, different authors have proposed discrete track models for the analysis
of railway induced vibrations. Figure 4 shows the evident dispersity in the values for these
four parameters admitted in previous publications. First, a set of nominal or reference
values for all the track parameters is defined on the basis of the literature review. Then, the
bridge parameters, assumed identical in both bays, (Modulus of Elasticity E bi , moment
of inertia I zbi and linear mass m bi ) are adjusted in order to reproduce static and dynamic
tests performed on the structure right before its opening. In Table 1 the bridge and
track reference parameters assumed are included. These will be the ones used in the
experimental validation (Sect. 4). The fundamental frequency of the track-bridge system
for these parameters equals 10.07 Hz. A damping ratio of 1.565% is assigned to any
mode as per [23] for pre-stressed concrete bridges of the particular span length.
K (MN/m)
p
K (MN/m)
b
C (MNs/m)
b
C (MNs/m)
p
Kouroussis (2015)
Kouroussis (2011)
Kouroussis (2011)
Kouroussis (2011)
Kouroussis (2015)
Kouroussis (2015)
Kouroussis (2011)
Kouroussis (2015)
Fig. 4. Rail pad and ballast layer stiffness and damping values admitted by different authors in
the past for comparable ballast layers thicknesses and sleepers distances [6, 9–20]
As per the subgrade stiffness and damping coefficients inside the bridge, 100 K f
and 0 Ns/m have been assigned as it is assumed that the ballast layer rests directly on
the concrete slab inside the bridge. A track length of 20 m is included before and after
the two-span bridge, equivalent to more than 30 times the sleeper distance, which is
considered adequate attending to previous publications [21, 22]. A sensitivity analysis
is performed on this length ensuring the convergence of results.
For the sensitivity analysis the response of the bridge is obtained under the circulation
of an artificial train of 20 equidistant loads of 210 kN separated 18 m, with the aim of
inducing two clear resonances on the structure. The bridge time-history response in
terms of displacements and accelerations is obtained for 60 velocities of circulation in
M. D. Martínez-Rodrigo et al.
3 Sensitivity Analysis over Track Parameters
First, a sensitivity analysis is performed on four track parameters: the stiffness and
damping coefficients of the rail pads, K p and C p , and of the ballast, K b and C b .
In the last years, different authors have proposed discrete track models for the analysis
of railway induced vibrations. Figure 4 shows the evident dispersity in the values for these
four parameters admitted in previous publications. First, a set of nominal or reference
values for all the track parameters is defined on the basis of the literature review. Then, the
bridge parameters, assumed identical in both bays, (Modulus of Elasticity E bi , moment
of inertia I zbi and linear mass m bi ) are adjusted in order to reproduce static and dynamic
tests performed on the structure right before its opening. In Table 1 the bridge and
track reference parameters assumed are included. These will be the ones used in the
experimental validation (Sect. 4). The fundamental frequency of the track-bridge system
for these parameters equals 10.07 Hz. A damping ratio of 1.565% is assigned to any
mode as per [23] for pre-stressed concrete bridges of the particular span length.
K (MN/m)
p
K (MN/m)
b
C (MNs/m)
b
C (MNs/m)
p
Kouroussis (2015)
Kouroussis (2011)
Kouroussis (2011)
Kouroussis (2011)
Kouroussis (2015)
Kouroussis (2015)
Kouroussis (2011)
Kouroussis (2015)
Fig. 4. Rail pad and ballast layer stiffness and damping values admitted by different authors in
the past for comparable ballast layers thicknesses and sleepers distances [6, 9–20]
As per the subgrade stiffness and damping coefficients inside the bridge, 100 K f
and 0 Ns/m have been assigned as it is assumed that the ballast layer rests directly on
the concrete slab inside the bridge. A track length of 20 m is included before and after
the two-span bridge, equivalent to more than 30 times the sleeper distance, which is
considered adequate attending to previous publications [21, 22]. A sensitivity analysis
is performed on this length ensuring the convergence of results.
For the sensitivity analysis the response of the bridge is obtained under the circulation
of an artificial train of 20 equidistant loads of 210 kN separated 18 m, with the aim of
inducing two clear resonances on the structure. The bridge time-history response in
terms of displacements and accelerations is obtained for 60 velocities of circulation in