To eliminate the influence of excitation on the wavelet packet frequency band energy spectrum (ES), ES is acquired via wavelet packet decomposition of a virtual impulse response function. Based on ES, a character frequency band vector spectrum and damage eigenvector spectrum (DES) are created. Additionally, two damage identification indexes, the energy ratio standard deviation and energy ratio variation coefficient, are proposed. Based on the damage index, an updated damage identification method for retaining wall structures is advanced. The damage state of a retaining wall can be diagnosed through DES, the damage location can be detected through the damage index trend surface, and the damage intensity can be identified by establishing a quantitative relationship between the damage intensity and damage index. To verify the feasibility and validity of this damage identification method, a vibration test on a pile plate retaining wall is performed. Test results demonstrate that it can distinguish whether the retaining wall is damaged, and the location of partial damage within the retaining wall can be easily detected; in addition, the damage intensity of the wall can also be identified validly. Consequently, this damage identification theory and method may be used to identify damage within retaining wall structures.

To warn of the stability of retaining wall structures with damage, a simplified mechanical model and a finite element model of this retaining wall-soil coupling system are established. Via finite element model updating, a baseline finite element model of the wall-soil system is acquired. A damage alarming index ERSD (Energy Ratio Standard Deviation) is proposed via the wavelet packet analysis of a virtual impulse response function of dynamic responses to this baseline finite element model. The internal relationships among the alarming index, earth pressure, and damage stability of the wall are analyzed. Then, a damage stability alarming method for the retaining walls is advanced. To verify the feasibility and validity of this alarming method, vibration tests on the baseline finite element model of a pile plate retaining wall are performed. The ERSD is used as an alarm for the damage stability of the wall. Analysis results show that, with an increase in the ERSD, the stability of the wall changes from a stable state to an unstable one. The wall reaches a critical stable state when the alarming index reaches its threshold value. Thus, the damage stability of this pile plate retaining wall can be alarmed via ERSD.

To identify the damage within retaining wall structures, the Hilbert–Huang Transforms of the impulse response function and virtual impulse response function were performed. The Hilbert marginal energy ratio spectrums of the impulse response function and virtual impulse response function were acquired. To reflect damage information effectively, those bands with stronger damage sensitivity were extracted via the threshold value ε0. Then, the Hilbert feature bands, which were more sensitive to damage within retaining walls, were selected by considering the contribution of the residual band to the damage identification. Based on the feature bands, the Hilbert damage feature vector, which reflects the variations of Hilbert marginal energy ratio caused by damage, was created. Based on the damage feature vector, two damage identification indexes (the energy ration standard deviation and Energy Ration Standard Deviation), which were based on the impulse response function and virtual impulse response function, respectively, were proposed to identify damage within retaining walls. To investigate the validity of the damage indexes, vibration tests on a pile plate retaining wall were done. The test results show that the damage feature vector is a zero vector or the value of damage index is zero when the wall is undamaged. The damage feature vector is a nonzero vector or the value of the damage index is more than zero when the wall is damaged. Thus, the damage state of the wall can be detected sensitively via the damage feature vector or damage indexes. Partial damage causes greater fluctuation of trend surface of the damage index. The location of partial damage can be diagnosed validly via the coordinate of peak value in the trend surface. The quantitative relationship formula between the damage index and damage intensity is established. The damage intensity of the wall can be calculated reversely, when the damage index is available. Either the energy ration standard deviation or Energy Ration Standard Deviation can be used to detect the damage state, diagnose the damage location, and identify the damage intensity. In comparison with the energy ration standard deviation, the stability and damage sensitivity of the Energy Ration Standard Deviation is much better.

To diagnose damages within the retaining wall structure, the Hilbert marginal energy spectrum was acquired via the Hilbert–Huang transformation of virtual impulse response functions of responses to the retaining wall under ambient excitations. Based on the Hilbert marginal energy spectrum, the Hilbert damage feature vector spectrum was created. On the basis of the damage feature vector spectrum, a damage identification index was proposed. Based on the damage feature vector spectrum and damage index, the damage state of the retaining wall was detected by the damage feature vector spectrum, damage locations of the wall were diagnosed by the damage index trend surface, and the damage intensity of the wall was identified by the quantitative relationship between the damage index and damage intensity. Based on this, a damage diagnosis method for retaining wall structures was proposed. To verify the feasibility and validity of the damage diagnosis method, both model tests and field tests on a pile plate retaining wall are performed under ambient excitations. Test results show that the damage state of the wall can be detected sensitively, damage locations can be diagnosed validly, and damage intensity can be identified quantitatively via this damage diagnosis method.

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