Detection of Beaded Karst Caves in Subway Works by Mixed-Source Surface Wave Survey: A Case Study Open Access

With the rapid development of the urban construction, the shield tunnel plays an increasingly important role in urban traffic. However, the geological conditions in urban areas are complex. Underground obstacles such as groundwater, karst caves, boulders, and pile foundations may seriously hinder the construction of shield tunnels [1, 2]. Karst cave is one of the most common and harmful geological disasters. If the location of the karst cave cannot be detected in advance during the construction of the shield tunnel, it will cause the shield machine to be deflected and result in large losses [3, 4].

Some scholars have used various geophysical methods to detect karst caves [5-7]. One of the widely used detection methods is the electrical resistivity tomography method [8, 9]. However, it is difficult to lay out the electrodes because urban areas are usually covered with cement and the space is limited [10]. Geological radar detection is famous for its convenient and efficient [11, 12]. However, the attenuation of radar wave is fast. The radar wave may not meet the depth requirements of practical engineering in the deep buried tunnel project [13]. The transient electromagnetic method can effectively cover the depth range of shield tunnel, but it is easily disturbed by electromagnetic waves in urban areas [14, 15]. The cross-hole geophysical prospecting method is not limited by the detection depth, but it is difficult to drill in urban area and the cost is high [16].

In order to meet the special construction conditions and requirements in urban areas, the microtremor survey is introduced into the urban geophysical detection [17-20]. The microtremor survey detects the underground space by analyzing and processing ambient noise [21, 22]. Zhang et al. [23] performed passive microtremor array measurements to construct a two-dimensional (2D) shear wave velocity profile at a site in Singapore. Ning et al. [24] conducted a field study on high-frequency passive surface waves in Hetian town of Zhejiang Province. Results show that multichannel analysis of passive surface (MAPS) waves has a great potential for the fault investigation in the urban area.

The microtremor survey merely uses low-frequency signals such as traffic noise, and the high-frequency signal is insufficient, resulting in low resolution in the shallow layer [25]. Therefore, many scholars have proposed the combined active–passive surface wave method (“combined method” for short), which combines the high-frequency part of the active surface wave method and low-frequency part of the passive surface wave method [26-30]. Gouveia et al. [31] determined the stiff soil in urban environment within a limited area through the joint inversion of dispersion curves computed from active linear and passive nonlinear array data. Hu et al. [32] used the active and passive surface wave methods to characterize a landfill and delineate its base. Experimental results show that the combination of active and passive surface waves is feasible to resolve the Vs model of landfills from the surface to deep formations. However, previous studies [33] have proven that the choice of frequency range in combined method has significant influences on detection accuracy. In addition, the processing of combined dispersion curves requires the engineers to have professional geophysical knowledge and experiences. This greatly increases the application threshold of the combined method in the practical engineering. Therefore, there is an urgent need for a more convenient and easily understandable combined active–passive surface wave method.

Ji'nan is a city famous for its underground spring water, and there are a large number of karst caves in its lower part. Drilling results show that there are two or three karst caves at different depths in the same position in the tunnel area. This type of karst cave is called beaded karst cave and more difficult to be determined. During the construction of the Ji'nan subway, these beaded karst caves greatly delayed construction progress. Some geophysical methods such as geological radar and transient electromagnetic have been used in practical engineering but have not yielded good results. Therefore, an advanced combined active–passive surface wave method called “mixed-source surface wave method (MSW)” was proposed and applied to one-dimensional (1D) and 2D detection of beaded karst caves. The advanced method was realized through imposing active sources during continuous passive surface wave observation. Combined with a single method (active or passive surface wave method), the effective frequency range of MSW is wider and the detection range of MSW is larger. It can effectively overcome the shortcomings of the single method. The data processing of traditional combined active–passive surface wave methods requires more geophysical knowledge and experience. In contrast, MSW is more likely to be realized and used in practical engineering. The influence of ambient noise, the array type, and other factors on the detection accuracy was studied. The MSW was compared with combined method. The experimental results show that MSW can effectively delineate the location and range of beaded karst caves, which provides significant references for practical engineering.

Spatial autocorrelation (SPAC) is the earliest developed passive surface wave method and plays an important role in the exploration of shallow areas. This method was first proposed by Aki in 1957 [34, 35]. The experimental results show that useful information can be extracted from disordered and chaotic background noise. The dispersion curve can be extracted from the useful information, and then, the structure of the shear wave velocity in the subsurface can be described by Equation (1).

where r is the spacing of station pair, ω₀ is angular frequency, ρ is SPAC coefficients, c is phase velocity of surface waves, and J₀ is the first kind of zero-order Bessel functions.

The basic assumption of SPAC is that the background noise around the array has stationary random characteristics. The noise signals received from two different stations are cross-correlated. Then, the processing of the azimuth average is performed for the pairs of stations with the same distance in different azimuths, and the SPAC coefficient can be determined.

The specific process is as follows. First, the original recording is converted into the frequency domain by Fourier transformation. The cross-power spectrum and the self-power spectrum of the center point and their circumference point are then calculated, respectively. Finally, the SPAC coefficients can be derived using Equation (2).

where S(r, θ, ω) is the cross-spectrum of the center record and the circumferential record point, S₀(0, ω) and S_r(r, ω) are the power spectrum of the center and circumference records, respectively.

The theoretical derivation of some scholars has shown that the SPAC coefficient can be expressed as a first kind of zero-order Bessel function. Therefore, the phase velocities at different frequencies can be calculated by fitting the first kind of zero-order Bessel function with the SPAC coefficient. Finally, the dispersion curve and shear wave velocity profile can be obtained.

The combined active–passive surface wave measurement refers to the method that can combine the advantages of active and passive surface wave exploration to jointly detect the target layer structure. The combined active–passive surface wave measurement is called “combined method” for short. The passive surface wave method can extract useful information from low-frequency part (1–10 Hz) well. However, many application examples show that high-frequency (above 10 Hz) information is difficult to extract from the background noise. Therefore, the ability of passive surface wave method to characterize shallow structure is not ideal. The active surface wave has a good resolution on the superficial layer structure, which can compensate for the deficiency of passive surface wave method. Therefore, the combined application of the active and passive surface wave methods can effectively make up for the deficiency of the single method.

The active surface wave survey and passive surface wave survey are carried out, respectively, in combined method, as shown in Figure 1(a). Then, high-frequency dispersion curve is extracted from the active surface wave method, and dispersion curve with low frequency is extracted from the passive surface method. Then, the two dispersion curves are joined together to form a new dispersion curve. Finally, the depth–velocity curve can be obtained by inverting the synthetic dispersion.

However, previous literatures [33] prove that the choice of frequency range in combined method has significant influences on inversion of dispersion curve. The data processing of the combined method requires more geophysical knowledge and experience. This greatly increases the application threshold of the combined method in the practical engineering. Therefore, there is an urgent need for a new combined method, which is more likely to be realized and used in practical engineering.

As an advanced surface wave method with mixed sources, MSW is proposed. The specific working method is to continuously excite the source in a fixed time interval during the process of the passive surface wave method. Then, both the low-frequency noise signal and high-frequency hammering signal can be received by the geophones. The effective frequency range of the dispersion curve can be extended, as shown in Figure 1(b). Finally, an accurate underground velocity profiles can be acquired by inverting the extended dispersion curve. Compared with the combined method, the basic principle of MSW is easy to be understood and its operation is convenient. The data of MSW can be processed through the commercial software. Therefore, MSW is more likely to be realized and used in practical engineering.

The concept of MSW was first proposed by Cheng et al. [33]. The effects of ambient noise on the accuracy of MSW were investigated, and the dispersion curves between MSW and other methods were compared. However, the effects of array type were ignored, and the advantage of MSW was difficult to reflect in traditional scenarios [33]. Therefore, the effects of array type were further studied, and the advantage of MSW was verified through the beaded karst caves detection in this study.

Ji'nan is a city famous for its rich underground spring water and karst landform. The existence of beaded karst caves bring major difficulties during the construction of the subway. Two sites along the city’s main street (Jingshi Road) were selected for the tests, as shown in Figure 2. According to the drilling results, there are beaded karst caves at Site A, and the depth range is 11.5–13.2 m and 24.8–34 m. Two-dimensional MSW survey was carried out at Site B, and the depth of the karst cave is 10.9–12.8 m and 14.8–16.4 m.

1D microtremor measurements were carried out to investigate the effects of various factors on the beaded karst caves detection, as shown in Table 1. The measuring methods include SPAC method, multichannel analysis of surface wave (MASW), and MAPS waves. To investigate the effects of noise on the detection, two passive surface wave tests (test 1 and test 2, SPAC) were carried out. Experimental time is 16:00 and 4:00. At 16:00, there were many vehicles and pedestrians on the main road. In contrast, there are almost no vehicles on the road, except for a few large trucks for transportation at 4:00. To investigate the effects of array type, microtremor surveys with different array types (triangle array, L-shaped array, linear array perpendicular to road, and linear array along the road) were used for detection (test 3, 4, and 5, SPAC). The MASW and MAP tests (test 7 and test 8) were performed to compare the application of the combined method and MSW in practical engineering. The measuring time is 25 minutes and the hammering source is excited every 5 minutes in MSW.

To investigate the potential of the 2D MSW on detecting karst caves, 2D MSW tests were carried out near the park [Figure 2(a)]. The drilling results show that the depth range of the karst cave is 10.9–12.8 m and 14.8–16.4 m. The array type is the linear array perpendicular to the road. The time interval for the excitation of the hammering source is 5 minutes. In general, the moving direction for the measuring line should be consistent with the array direction. However, due to the special restrictions in urban areas, the array moves along roads, and the movement distance is 3 m.

Several microtremor tests (test 1–test 3) were carried out to investigate the effects of the hammer source and the surrounding noise on the detection accuracy. Figure 3 shows that the number and amplitude of noise at 16:00 are significantly higher than those at 4:00. As shown in dispersion energy image (Figure 4) and dispersion curve image (Figure 5), the effective frequency range of the signal at 16:00 is also greater than that at 4:00. The dispersion energy of the signal at 16:00 is also clearer and more continuous. This is because the test site is located directly on the main road and more vehicles pass by around 16:00. Passing vehicles and pedestrians provide an effective source for microtremor survey. Figure 5 shows that the effective frequency of MSW is 5–25 Hz, overmatching that at 16:00 (5–20 Hz). This shows that the effective frequency range can be broadened by the hammer source.

The least square method was used to invert the dispersion curve (fundamental model and first higher model), and the inversion results were shown in Figure 6. According to the drilling results, the true depth range of the karst caves is 11.5–13.2 m and 24.8–34 m. Figure 6 shows that the inversion results of the MSW can reflect the existence of the two karst caves. And the depth of inversion results (12.5–17.5 m and 25–37.5 m) corresponds to the drilling results. The inversion results at 16:00 may reflect the existence of karst caves but cannot distinguish the two karst caves. In addition, the corresponding depth differs from the actual results. Compared to the results of 16:00, the error of microtremor survey at 4:00 is greater. And the delineating ability on the upper surface of karst cave is worse. This is perhaps due to the fact that the signal at 4:00 lacks high-frequency signals. The wavelength of the low-frequency signal is longer, which leads to a low delineating ability on the shallow layer. At 16:00, there were more pedestrians and vehicles, and the resulting noise was perceived as a disturbance in most seismic surveys. However, experimental results show that it can provide a high-frequency signal for the microtremor survey to detect the shallow layer.

The results of the MSW show that the intermittent hammering can well complement the high-frequency signal needed for the microtremor survey, and its effect is better than the daytime traffic noise. It is worth noting that the inversion result is not completely consistent with the actual layer. It is often necessary to simplify the formation model and smooth the data results during the inversion process. Therefore, it is suggested that geotechnical engineers should collaborate with other geophysical methods or drilling methods to further improve their resolution when applying surface wave methods in practical engineering work. In summary, the detection accuracy of various microtremor surveys can be ranked as follows: MSW > microtremor survey at 16:00 > microtremor survey at 4:00.

To investigate the influence of array type on the detection accuracy, a series of microtremor survey tests were carried out (test 3, test 4, test 5, and test 6), as shown in Figure 7.

The dispersion energy and dispersion curve of MSW with various array types are shown in Figures 8 and 9. The dispersion energy of linear array perpendicular to the road is clearer and surfers less interference. The spatial aliasing phenomenon appears in the dispersion energy of linear array along the road. This indicates that array type has significant influences on the extraction of dispersion curve.

As shown in Figure 7(a), the inversion result of linear array perpendicular to the road is the best. It can delineate the actual range of the two karst caves. The inversion results of the triangular array [Figure 7(b)] show that the surface of the bottom cave is well characterized and there is a certain error in the upper cave. The results of the deeper karst cave (25.2–36.7 m) agree with the actual results. This may be because the strong anti-interference capability of the triangular array, which can effectively average the signal caused by the hammer source. In contrast, the linear array (perpendicular to the road) aligns with the azimuth of hammering source, and the hammering signal and road noise can be effectively utilized to improve imaging accuracy.

The existence of two karst caves can be observed in the results of the L-shaped array [Figure 7(c)]. However, there is a certain error between the exact location of the caves (14.6–20.8 m and 27.8–35.7 m) and the actual results. The boundary between the two caves becomes increasing blurred in the linear array along the road [Figure 7(d)]. One of the important assumptions of passive surface wave method is that the noise is uniformly distributed. However, the traffic noise in urban areas usually concentrates along the road. According to previous studies [23], when the linear array approximately aligns with the azimuth of noise source, the surface wave dispersion curve can be reliably extracted and the accuracy can be improved. In contrast, the linear array along the road may have negative effect on the extracting of dispersion curve.

To summarize, the detection accuracy of MSW with various array types can be ordered as follows: the linear array perpendicular to the road > triangle array > L-shaped array > linear array along the road.

The data from active surface wave tests (test 7) and passive surface wave tests (test 8) were processed by combined method and MSW, respectively. The combined method is introduced in detail in Section 2.2. Comparison of the dispersion curves (Figure 10) shows that the dispersion curves of MSW and passive surface wave method are similar. There is a little difference between the dispersion curve of MSW and active surface wave method. However, their basic trends are consistent. As shown in Figure 11, the combined method can successfully distinguish two karst caves, and the depth range of the upper cave (11.9–17.6 m) is slightly worse than that of MSW (11.9–14.6 m). This could be due to the fact that the low-frequency component of the combined method and the MSW is similar. The signal in the high-frequency range is more stable due to repeated hammering. In addition, the high- and low-frequency parts of the combined method are artificially combined, and the specific value range depends on experience, which may affect the accuracy of inversion. It must be admitted that the accuracy of MSW is similar to that of combined method. However, MSW is more convenient and applicable for practical engineering. Therefore, MSW can be an important supplement to the combined method in urban microtremor survey area.

The results of 2D MSW measurement are shown in Figure 12. There are obvious low-velocity anomalies in certain areas (9.5–11.5 m and 14.5–16.5 m). The range of anomalies is consistent with the drilling results of borehole-1 (10.9–12.8 m and 14.8–16.4 m) and can basically be judged as karst cave area. Horizontal resolution is an important indicator to evaluate the application of 2D microtremor survey [36]. To verify the horizontal resolution of 2D MSW, drilling data of some boreholes in the measuring range were collected. The drilling results of borehole-2 and borehole-3 were also consistent with inversion results. This shows that the 2D MSW method can well describe the size and location of karst caves. Compared to the 1D results, the 2D measurement results are easier to be understood and can better reflect the rough range of the beaded karst caves.

The basic principle of MSW is easy to be understood, and its operation is convenient. This is the main advantage of MSW. However, MSW may reduce the signal-to-noise ratio (SNR) of the high-frequency dispersion curve. The accuracy of MSW is not higher than traditional combined method. Therefore, it is better to separate the active signal from the continuous seismic recordings and obtain the inversion results for the shallow structure using the active data [37]. The inversion results can be combined with the passive data for the final interpretation, and then, SNR of the high-frequency band can be improved. We will investigate this advanced method in further study.

Linear array perpendicular to the road is difficult to realize due to the space limitation in urban areas. Therefore, many researchers have proposed some methods to improve the data processing of linear array [ 21, 38]. These researches are also useful for MSW. Therefore, we have added this idea into the Section 5, and we will investigate these methods in further research.

Beaded karst cave is a common geological disaster in Ji'nan, China. Compared with the single cave, the depth and range of the beaded karst cave are more difficult to detect, and the damage to the shield machine is greater. In order to effectively delineate beaded karst caves, traditional microtremor survey was improved and MSW was proposed. MSW tests were carried out in practical engineering cases, and the following conclusions can be drawn based on experimental results.

1. The ambient noise has a positive effect on improving the detection accuracy of microtremor survey, and the continuous hammering source can broaden the effective frequency range. The detection accuracy of MSW is obviously better than that of the passive surface wave method.

2. The array type has a significant influence on the detection accuracy of MSW. The detection accuracy of MSW with various array types can be ordered as follows: linear array perpendicular to road > triangle array > L-shaped array > linear array along the road.

3. The dispersion curves of MSW and passive surface wave method in low-frequency part are similar. The accuracy of MSW is similar to that of combined method. However, MSW is more convenient and applicable for practical engineering.

4. The 2D MSW can well reflect the range and location of the beaded karst cave.

In conclusion, MSW can be an effective geophysical tool for detecting the range of beaded karst cave in shield tunnel works.

The data underlying this article will be shared on reasonable request to the corresponding author.

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

This investigation was supported by the National Natural Science Foundation of China (projects No. 42307198 and no. 52379114), National science Foundation of Jiangsu Province (BK20221148), Science and Technology Project of Jiangsu Provincial Department of Science and Technology, China (BK20220025), China Postdoctoral Science Foundation (2023M733747), and Fundamental Research Funds for the Central Universities (XJ2021008101).