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investigation and subsequently improve understanding of the underlying physical process. In this
study, we use the HHT to characterize the structural damage from the recordings and model-based
simulated data of controlled field vibration tests of two substructures in Trinity River Relief (TRR)
Bridge in Texas in its intact, minor- and severe-damage stages.
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HHT ANALYSIS OF DESTRUCTIVE VIBRATION TESTING DATA
The bndge for the case study is the Trinity River Relief (TRR) Bridge, located on old US Hwy 90 on
the west side of Liberty, Texas. The three stages of the bent shown in Fig. 1 is in order:
(1) Intact stage: the column with sensor 15 was not broken and soil around the pile had the same
height as the soil around the pile with sensor 13.
(2) Minor-damage stage: the pile with sensor 15 was not broken, but soil around the pile was
excavated, which was simulated for flood-induced minor scour with partial loss of load capacity.
(3) Severe-damage stage: the pile with sensor 15 was broken with the steel bars left only and soil
around the pile was excavated, which could be regarded as equivalent damage of the column due to
earthquake-induced liquefaction or severe scour with complete loss of load capacity.
Figs. 2a and 2b show respectively the time histories of vertical excitation force and its corresponding
vertical vibration response at sensor 15 with the structure in intact stage. Both time histories are
highly nonstationary, with the frequency sweeping almost linearly from 4 Hz at 0.3 s to 72 Hz at 5.7 s,
referred to as chirp frequency for later use. Therefore, their Fourier spectra are unable to provide
faithful time-dependent frequency content of the data.
Fig. 3 a shows that the excitation contains a dominant energy with the chirp frequency increasing with
time from 4 Hz at 0.3 s to 72 Hz at 5.7 s. The excitation also has energy at other frequencies such as
high frequencies ranging from 20 to 50 Hz between 0.4 and l.ls shown in Fig. 3a, which can be
visually verified from the excitation time history shown in Fig. 2a.
It is known that the frequency content of the vibration response should contain primarily both the
driving frequencies and the natural frequencies of the structure. This is confirmed by Fig. 3b.
Specifically, Fig. 3b shows the energy with a primary frequency content linearly increasing with time,
which is the signature of excitation with the chirp frequency. By comparing with Fig. 3 a, the signature
of excitation in Fig. 3b can also be found at frequency band of 20-30 Hz between 0.4-0.8 s and of 0-30
Hz between 4.7-5.7 s, among others. In addition to the above excitation-inherited energy, Fig. 3b also
illustrates energy concentration in the frequency range of 10-20 Hz (others in 20-75 Hz) between 1-2 s.
This is not inherent from the excitation in Fig. 3 a but rather the energy contributed from the structural
vibration modes at a couple of lower (higher) natural frequencies, or the signature of the structure.
This, together with the subsequent interpretation, will be verified later by a model-based analysis. The
aforementioned vibration with 10-20 Hz at 1-2 s is likely excited by the force with a low-frequency
band in 4-15 Hz at 0.4-1 s (see Figs. 2a and 3a,b). As time goes on (say 2-3 s), the vibration at the
low-frequency band dies down quickly due to damping, or is too small to be shown in the figure in
comparison with strong excitation-inherited energy. Since the first mode of vertical vibration motion
should be dominant in the low-frequency band, the above observation and assertion suggests that the
fundamental natural frequency can be found from the Hilbert amplitude spectrum by identifying the
corresponding dominant structural energy, particularly around 1-2 s.
Fig. 4a enlarges the Hilbert amplitude spectrum in Fig. 3b. Except the excitation energy at chirp
frequency and at high-frequency band of 15-30 Hz between 0.5-0.7 s, all the other energy
concentration shown in Fig. 4a is attributed primarily by the structure itself. We now focus on the