3.1 Data acquisition and monitoring profile
The monitoring profiles along the Xianhuihe, Tuosuohu, and Huayingshan faults have been established by the State Key Laboratory of Geohazard Prevention and Geoenvironment Protection (SKLGP) since 2008. The stations are equipped with the G01NET-3 seismic dynamic data acquisition instrument, developed by the Institute of Engineering Mechanics, China Earthquake Administration, featuring a fundamental sensitivity parameter of 1.1V/G.
The earthquake monitoring profile is situated in Shimian County, Ya'an City, Sichuan Province, China, approximately 137 km from the epicenter. This region exhibits high seismic activity, establishing it as one of most seismically active areas China (He et al. 2020; Allen et al. 1991). The monitoring profile extends northeastward along the Nanya River, featuring a vertical elevation difference of approximately 750 m. The profile features an average slope angle of approximately 40°. The lithology comprises early Sinian granite, with residual slope deposits covering the slopes on both sides. Monitoring site 1# is located on the relatively flat bedrock of an adit, situated at an elevation of 1160 m within the Jigongshan Mountains, approximately 410 m above the riverbed. The lithology predominantly comprises granite. Monitoring site 2# is positioned on the ridge in the upper half of Jigongshan Mountain, at an elevation of 1060 m, approximately 310 m higher than the riverbed. Site 3#, situated at an elevation of 900 m above sea level, is about 150 m distant from the riverbed. The overburden thickness ranges from 10 to 15 m and consists of strongly weathered granite layers. A fault known as the Shimian fault has been identified in close proximity to site 3#. (Fig. 5).
Several earthquakes had been recorded at the monitoring profile, notable including Lushan Ms6.1 earthquake in 2022, Lushan Ms4.5 earthquake in 2022, Changning Ms6.0 earthquake in 2019 and Changning Ms5.4 earthquake in 2019 (Table 1).
Figure 5 Monitoring profile of seismic station
Table 1
| Date | Time | Lat (°N) | Lon (°E) | Depth (km) | Ms |
1 | 01/06/2022 | 17:00:08 | 30.37 | 102.94 | 17 | 6.1 |
2 | 01/06/2022 | 17:03:09 | 30.37 | 102.92 | 18 | 4.5 |
3 | 17/06/2019 | 22:55:43 | 28.34 | 104.90 | 16 | 6.0 |
4 | 22/06/2019 | 22:29:56 | 28.43 | 104.77 | 10 | 5.4 |
3.2 Data analysis and results
The time history of acceleration was baseline corrected and filtered using a Butterworth bandpass filter set to a frequency range of 0.5–30 Hz in MATLAB. Subsequently, parameters such as Fourier spectrum and Arias intensity, along with other relevant metrics, were analyzed to investigate the seismic response characteristics of the slope.
PGA and Arias intensity analyses
The acceleration time history curve is derived from processed seismic data (Fig. 6), capturing the peak ground acceleration (PGA) and Fourier spectrum of the earthquake (Fig. 7, Fig. 8). Arias intensity serves as a fundamental metric for quantifying vibrational energy, reflecting the continuous transformation of kinetic and potential energies of objects during vibration, consistent with the principles of energy conservation.
The mass of the vibrating object remains constant throughout the seismic process. Velocity is utilized to characterize its kinetic energy. The Arias intensity formula entails integrating the square of the acceleration of the object over time during vibration, as exemplified by Formula (1):
$${\text{I}}a=\frac{\pi }{{2g}}\int\limits_{0}^{{td}} {\mathop {\left( {at} \right)}\nolimits^{2} } dt$$
1
where \(Ia\) is the Arias intensity, \(td\)is the vibration duration, is the gravitational acceleration.
Figure 6 Lushan Ms6.1 mainshock time history curve
The comparison of multiple datasets in Fig. 6 highlights the performance enhancement of horizontal (E-W, N-S) PGA at monitoring points. Horizontal amplitudes generally exceed the vertical (U-D) amplitude across all points, except for the 1# monitoring site during the Ms6.1 mainshock. Specifically, the amplitudes in each direction at the 1# monitoring point are lower compared to other sites, whereas the 3# monitoring point has the highest amplitudes among all. The peak of the time history curve corresponds to the PGA. Horizontal PGA (E-W, N-S) values also consistently exceed vertical PGA (U-D) values across all sites during the Lushan Ms4.5 earthquake. The PGA recorded at the 1# monitoring site is the smallest, while the PGA at the 3# monitoring site is the largest.
Arias intensity is primarily influenced by earthquake acceleration and vibration duration. The Arias intensity values at each monitoring point exhibit a pattern similar to that of PGA. Specifically, Arias intensity values are higher in the horizontal directions (E-W, N-S) compared to the vertical direction (U-D). The Arias intensity at monitoring point 1# is relatively lower than at other sites, while monitoring point 3# records the highest Arias intensity among all stations. At the same monitoring profile, the seismic response parameters of slope during the Lushan Ms6.1 and Ms4.5 earthquakes show a nonlinear increasing trend in magnitude. Moreover, Arias intensity increases with higher earthquake magnitudes. The PGA and Arias intensity of the Changning Ms6.0 and Ms5.4 earthquakes follow a similar pattern to those observed during the Lushan earthquakes. Specifically, the PGA and Arias intensity of the Lushan Ms6.1 earthquake exceed those of the Lushan Ms4.5 earthquake, while the PGA and Arias intensity of the Changning Ms6.0 earthquake also surpass those of the Changning Ms5.4 earthquake (Table 2).
Table 2
Seismic response parameters of slope
Earthquake | Site | PGA/(gal) | Arias Intensity/(dm·s− 1) | Predominant Frequency/Hz |
E-W | N-S | U-D | E-W | N-S | U-D | E-W | N-S | U-D |
Lushan Ms6.1 | 1#(1160m) | 3.287 | 3.709 | 4.323 | 0.30 | 0.31 | 0.47 | 6.055 | 5.489 | 6.139 |
2#(1060m) | 4.790 | 7.099 | 3.858 | 0.73 | 0.79 | 1.14 | 6.377 | 8.475 | 6.341 |
3#(900m) | 10.738 | 8.904 | 7.383 | 1.95 | 1.62 | 1.55 | 5.865 | 7.826 | 5.871 |
Lushan Ms4.5 | 1#(1160m) | 2.429 | 1.977 | 2.128 | 0.08 | 0.09 | 0.12 | 5.912 | 5.537 | 6.586 |
2#(1060m) | 2.656 | 4.325 | 3.678 | 0.18 | 0.26 | 0.27 | 6.335 | 8.559 | 6.335 |
3#(900m) | 5.182 | 6.111 | 4.777 | 0.53 | 0.48 | 0.41 | 8.004 | 6.74 | 6.74 |
Changning Ms6.0 | 1#(1160m) | 1.303 | 2.455 | 1.848 | 0.04 | 0.12 | 0.09 | 0.960 | 2.000 | 1.020 |
2#(1060m) | 2.457 | 3.864 | 2.421 | 0.06 | 0.19 | 0.08 | 3.167 | 3.198 | 3.162 |
3#(900m) | 8.643 | 7.732 | 2.908 | 1.56 | 1.36 | 0.25 | 1.270 | 1.019 | 2.612 |
Changning Ms5.4 | 1#(1160m) | 1.006 | 1.576 | 0.953 | 0.03 | 0.08 | 0.03 | 1.21 | 2.95 | 0.94 |
2#(1060m) | 1.514 | 1.578 | 1.485 | 0.05 | 0.05 | 0.06 | 3.90 | 2.33 | 3.99 |
3#(900m) | 2.851 | 4.613 | 1.960 | 0.47 | 0.18 | 0.04 | 1.21 | 1.18 | 2.83 |
Fourier spectrum analysis
As illustrated in Fig. 7 and Fig. 8, the frequency contents of the three directions (E-W, N-S, U-D) at the monitoring points during the same earthquake do not show significant differences in obtaining peak values.
At the monitoring point, significant amplitudes are observed in the frequency range of 5–10 Hz, particularly during the Ms6.1 earthquake, which shows larger amplitudes. Amplitudes in the high-frequency band are generally lower than those in the low-frequency band. Among the monitored points, the 1# monitoring point records the smallest amplitude peak, while the 3# monitoring point registers the largest, augmented by the overlay site. The predominant frequency range of the Changning earthquake is primarily distributed within the 1–3 Hz band. The Fourier spectrum amplitude of the Lushan Ms6.1 earthquake exceeds that of the Lushan Ms4.5 aftershock, displaying non-linear growth with increasing magnitude in the low-frequency range. The predominant frequencies of the Lushan and Changning earthquakes vary within the same monitoring profile.
Figure 7 Fourier spectrum of Lushan Ms6.1 mainshock
Figure 8 Fourier spectrum of Lushan Ms4.5 aftershock
The horizontal-vertical spectral ratio (HVSR) method is a non-referenced field technique that assesses local ground motion amplification by comparing Fourier spectra from two directional components (EW/UD, NS/UD). This approach effectively mitigates site-specific amplification effects, terrain influences, and other variables. The HVSR calculation Formula (2) is presented as follows:
$$Rij(f)=\frac{{\sqrt {H1ij\mathop {\left( f \right)}\nolimits^{2} +H2ij\mathop {\left( f \right)}\nolimits^{2} } }}{{Vij\mathop {\left( f \right)}\nolimits^{2} }}=\frac{{Hij\left( f \right)}}{{Vij\left( f \right)}}$$
2
Where \(H1ij(f)\), \(H2ij(f)\), and \(Vij(f)\) represent the Fourier spectrum values of horizontal EW component, NS component and vertical UD component, respectively.
The monitoring station gathers data on seismic source characteristics, propagation paths, epicentral distances, and medium properties through analytical methods. In calculating the HVSR curve, MATLAB is employed for fast Fourier spectrum analysis to obtain directional components for each monitoring point. Subsequently, a simple full-period average method is applied to smooth the obtained spectra.
As depicted in Fig. 9, Particularly noteworthy is the consistency in peak HVSR values between the Lushan Ms4.5 and Ms6.1 earthquakes, both falling within similar frequency ranges. This trend is also observed in the HVSR results of the Changning earthquake. Additionally, the HVSR amplitude of the Lushan Ms6.1 earthquake exceeds that of the Lushan Ms4.5 earthquake.
Comparing the HVSR between the Lushan and Changning earthquakes can reveal significant characteristic differences. The HVSR of the Lushan earthquake exhibits multiple peaks, indicating significant energy concentration due to multiple reflections and refractions as seismic waves propagate through the monitoring profile. In contrast, the HVSR of the Changning earthquake shows a single prominent peak, primarily concentrated within the frequency range of 1–5 Hz. This difference results in the Changning earthquake displaying higher peak amplitudes compared to the Lushan earthquake. In the context of slope dynamics, seismic waves with lower amplitudes and frequencies, such as those between 1 and 5 Hz, provide more precise analysis results than waves with higher amplitudes and frequencies. Therefore, selecting seismic waves within this optimal frequency range is crucial for accurately studying the seismic responses of slopes and the development of disasters in this region.
Figure 9 HVSR response curve of monitoring point
Acceleration response spectrum analysis
The reaction spectrum is defined as the correlation between the maximum absolute reaction value and the period of a series of single-degree-of-freedom systems with identical damping ratios. The acceleration response spectrum with different damping ratio is analyzed, the maximum response state of acceleration under seismic load can be displayed (Fig. 10). The amplitude of acceleration response spectrum gradually diminishes to zero as the period increases. The shape of the acceleration response spectrum remains consistent for each monitoring point in both horizontal and vertical directions across varying damping conditions, with peak values reached simultaneously. As damping increases, the damping ratio decreases in each direction of every monitoring point. At a 5% damping ratio, acceleration amplitudes peak, while they minimize at 20%. Field medium damping characteristics impact ground motion amplitude but do not alter seismic process characteristics. Monitoring points 1# and 2# show similar acceleration response spectrum patterns, with no significant directional differences in horizontal acceleration under identical damping ratios. Conversely, the horizontal acceleration response spectrum at 3# shows greater amplitude in the E-W direction under the same damping ratio. At 1# and 2#, vertical acceleration amplitudes exceed those in the horizontal direction under the same damping ratio, while at 3#, vertical amplitudes are lower compared to horizontal ones. Monitoring point 3# displays the highest response spectrum amplitude under the same damping conditions, while monitoring point 1# exhibits the lowest. The acceleration response spectrum amplitude at each monitoring point aligns with the acceleration time history curve. These findings indicate that monitoring point 3# experiences the strongest seismic response, whereas monitoring point 1# is the weakest.
Figure 10 Lushan Ms6.1 earthquake acceleration response spectrum
According to the Fig. 10, the amplitude reaches its maximum value and the response characteristics are most pronounced under a 5% damping condition, which is commonly used in design presets. The seismic influence coefficient, denoted by α, is determined by seismic intensity, site category, characteristic period, and natural vibration period of the site. Formula (3) for calculating α is as follows:
$$\alpha =\mathop {\left( {\frac{{Tg}}{T}} \right)}\nolimits^{\gamma } =\eta \alpha \hbox{max}$$
3
where \(\alpha\) is seismic influence coefficient, \(\alpha \hbox{max}\)is the maximum value of seismic influence coefficient, is site natural vibration period, \(Tg\)is characteristic period, \(\gamma\)-curve is the attenuation index of the descending section, \(\eta\) is damping adjustment coefficient.
According to the Code for Seismic Design of Buildings (GB50011-2011), Shimian County is classified with a seismic fortification intensity of VIII degree. This classification entails a design basic seismic acceleration value of 0.20g, placing it within Group III for design category (Fig. 11).
Figure 11 Seismic influence coefficient curves
As shown in the Fig. 12, the seismic intensity values vary among monitoring points. Monitoring point 3# registers the highest intensity value, while monitoring point 1# records the lowest. The intensity value at monitoring point 3# exceeds fortification standard VI but remains within the range of fortification standard VII. None of the intensity values at any point exceed fortification standard VII. Subsequent seismic design efforts should prioritize monitoring at point 3#, situated above the overburden.
Figure 12 Seismic intensity spectra of the Lushan earthquake