4.1 Frequency content
The investigations revealed that the scale, formation mechanism, and the development characteristics of the earth fissures in the two regions are different. The earth fissures in Region I were formed by the coupling of the creep deformation of the buried faults and the over-exploitation of groundwater. The number of secondary fissures around the main fissures in this area is small, and the activity is also small. The large-scale earth fissure groups in Region II were formed under the control of the buried fault on the basin’s margin, the regional stress provides the environment for fissure expansion, and the over-exploitation of groundwater accelerates the expansion process. The secondary fissures distributed in the steps on both sides of the main fissure have ruptured the surface, forming dislocation steps. Region I can be regarded as a site with only a single fissure, while region II can be regarded as a site with a main fissure and secondary fissures. After processing the microtremor data, it was found that the spectral characteristics of the earth fissures in the same region are similar. Therefore, taking survey L1 in Baigui Village (Region I) and survey line L5 in Wenshui (Region II) as representative lines in the two regions, the spectrum frequency contents of the sites with earth fissures were described in detail as follows.
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Region I (L2 in Baigui)
As shown in Fig. 7a, the direct Fourier spectrum and HVSR, which reflect the inherent information of the site, have the following characteristics. (1) The dominant frequency peaks of the Fourier spectrum of the measurement points within 10 m on both sides of the fissure are significantly prominent. The average predominant frequency in each direction is 2–4 Hz. (2) The spectrum curves at the measurement points far away from the earth fissure are relatively smooth, and the spectrum peaks are not very prominent. That is, the microtremor propagation at the measurement points 20 m away from the earth fissure is hardly affected by the earth fissure. (3) The horizontal and vertical Fourier spectrum peaks rise rapidly at the earth fissure and gradually attenuate about 20–25 m from the fissure. (4) A greater amplification effect occurs on the hanging wall of the earth fissure. The peak value of the Fourier spectrum within 3 m of the hanging wall of the fissure is significantly larger than that of the footwall. Moreover, the attenuation speed of the peak value of the measurement points on the hanging wall is also lower than those on the footwall.
In order to determine the dynamic response characteristics of the structures in the site containing earth fissures, the acceleration response spectrum was used to reflect the variation in the acceleration response of the single particle system with a natural particle vibration period. The response acceleration is shown in Fig. 7b. (1) The bandwidth of the response acceleration spectrum is narrow, and the peak form is mainly a single peak. (2) At measurement points A1, A2, B1, and B2, which are within 3 m of the earth fissure, the spectrum’s peaks are more prominent. (3) The response acceleration peak attenuates as it moves away from the earth fissure, and it remains stable beyond 15–20 m. (4) The peak value on the hanging wall is slightly larger than that on the footwall. The dynamic response of the site with normal-type earth fissures is greater on the hanging wall.
The Arias intensity reflects the variation characteristics of the microtremor accumulated over time, thereby the dynamic response of the different positions can be determined. The Arias intensity curves of the 18 measurement points on both sides of the earth fissure (Fig. 7c) have the following characteristics. (1) The intensity of the microtremor continues to increase over time until it reaches its maximum value. Moreover, the Arias intensity increases faster, and the peak value is higher near the earth fissure. (2) A greater amplification also occurs on the hanging wall of the earth fissure. (3) The intensity curves of the points that are 20 m away from the earth fissure are relatively smooth. The intensity peaks at these points are low and are basically the same, which can be regarded as the original intensity of the site when it was barely affected by earth fissures.
2. Region II (L5 in Wenshui)
As shown in Fig. 8, the Fourier spectrum and HVSR of survey line L5 in Region II have the following characteristics. (1) The peaks of the spectrum are sharp, narrow, and multimodal, with three or more secondary peaks near the main peak. The occurrence of multiple secondary peaks is due to the large number of sand and gravel layers in the shallow surface. (2) The predominant frequency of this site is about 2.9–4.1 Hz. There is no obvious relationship between the predominant frequency and the distance from the earth fissure. (3) The spectrum peaks of the measurement points near the earth fissure are sharper and more prominent than those far from the earth fissure, especially at A1–A3 and B1–B3. The spectrum peak gradually decays to a low and stable value with distance from earth fissure. (4) The spectrum peaks of the measurement points on the hanging wall (especially at A1 and A2) are higher than those on the footwall, indicating the greater amplification effect of the hanging wall.
As can be seen from Fig. 8b, the response acceleration curves are mostly multimodal. The amplification effect can also be seen near the earth fissure. The Arias intensity curves are shown in Fig. 8c. The intensity of the microtremor increases with time. Moreover, the increases in the velocity and peak value of the intensity near the earth fissure are higher. While the intensity 20–25 m away from earth fissure is low and hardly changes.
In addition to the previously mentioned lines L2 and L5, the spectrum content of each survey line in the Taiyuan Basin is slightly different. As the ground conditions change, the frequency content, which reflects the inherent conditions of the site, changes, including the peak type, predominant frequency, and bandwidth. However, a similar amplification effect occurred for seven of the survey lines. The amplification effect of the earth fissure on the dynamic response of the site is significantly obvious in the Fourier spectrum, HVSR, response acceleration, and Arias intensity. However, the amplitudes of the four methods have different meanings, and the magnitudes of their peaks are also different for the different sites. Therefore, the ratio of the affected peak value to the unaffected peak is used as a unified scale for determining the amplification effect.
4.2 Amplification effect
The spectrum contents of the representative earth fissures in the Taiyuan Basin show that the existence of earth fissures amplifies the dynamic response of the site. The results show that the spectrum peaks attenuate to a stable value about 25 m away from the fissure. Therefore, these peak values can be regarded as the original value of the site, i.e., when it was not affected by the earth fissures. The amplification factor of the earth fissure on the dynamic response of the site is defined as the ratio of the spectral peak value of each point to the unaffected peak value. In this way, the amplification effects in different regions, due to different earth fissures, and observed using different spectra can be compared intuitively. Figure 9 shows the amplification factors of seven representative earth fissures obtained using four methods.
As can be seen from the curves, the amplification factors are higher near the fissure. As the distance from the earth fissure increases, the factors attenuate and stabilize at 20–25 m from the earth fissure. By comparing the amplification factor curves of the hanging wall and the footwall of an earth fissure, it was found that a greater amplification occurs in the hanging wall. The amplification factor of a measurement point 3–5 m from the fissure on the hanging wall is consistent with that of a measurement point close to the fissure on the footwall. Although a common amplification effect was observed for the sites containing earth fissures in the Taiyuan Basin, the magnification and the attenuation process of the factors are slightly different.
Survey lines L1–L4 were located in the Qixian-Taigu earth fissure zone (Region I). The earth fissures in this area are mostly single fissures with small, shallow secondary fissures. Because they are only affected by a single earth fissure, the amplification factor curves of lines L1–L4 decay smoothly and quickly. They attenuate to 1 at about 16–20 m from the earth fissure on the hanging wall and attenuate to 1 less than 16 m from the earth fissure on the footwall. As shown in Fig. 9, the shapes of the amplification curves of survey lines L5–L7 in Region II are different from those in Region I.
This investigation has shown that there are very active secondary fissures on both sides of the main fissures in Region II. These secondary fissures have large dislocations and have ruptured the ground surface. Affected by these secondary fissures, amplification factor is slightly higher at 15 m from the fissure on the hanging wall for line L5, 20 m on the hanging wall for line L6, and 8 m on the footwall for line L7. After this, the amplification factor starts to decay again and forms a larger amplification range. Unlike in Region I, the amplification factor of line L5 for an earth fissure in Wenshui attenuates to 1 at about 20 m from the fissure on the hanging wall. However, the attenuation is relatively faster on the footwall, approaching 1 at about 8–16 m from the fissure. The secondary fissure located 20 m from the main fissure on the hanging wall of the earth fissure in Jiaocheng leads to a slower attenuation of the amplification factor for line L6. After a small increase at 20 m, the amplification factor decreases again and approaches 1 at about 25 m from the fissure. It becomes almost stable before 20 m from the earth fissure on the footwall. The secondary fissure on the footwall of the Qingxu fissure slows down the attenuation process of the amplification effect for line L7. Therefore, the amplification effect on the hanging wall and footwall of the Qingxu earth fissure is similar, becoming stable at about 24 m from the fissure.
By analyzing the amplification factors of the representative earth fissures in the Taiyuan Basin, it was found that an earth fissure will stimulate the amplification effect of the dynamic response of the site. The amplification will attenuate with increasing distance from the fissure. Moreover, the amplification effect is more prominent in the hanging wall. In order to reveal the influence range of the amplification and the seismic fortification distance, the amplification factors of the representative earth fissures in the basin were fitted.
4.3 Seismic fortification distance
The influence range of the earth fissures on the dynamic response of the site was determined by concatenated exponential fitting of the seven amplification factor curves. The fitting curve of the Fourier spectrum amplification factor is shown in Fig. 10a. The dynamic response was amplified twice within 5 m on the hanging wall and decayed to 1.5 times at about 9 m from the fissure. Eventually, it decreased to 1 at about 24 m from the fissure. The amplification factor of the earth fissure was greater than 1.5 within 4 m, and it decayed to a safe value about 20 m away from the fissure. The fitting curve of the response acceleration amplification factor is shown in Fig. 10b. The amplification factor was greater than 2 within 6 m on the hanging wall and within 4 m on the footwall, making this the high-risk zone. The amplification effect decreased to 1.5 times between 6 and 10 m on the hanging wall and 4 and 8 m on the footwall, making this the medium-risk zone. The low-risk zone is 10–20 m from the fissure on the hanging wall and 8–16 m on the footwall. In the low-risk zone, the amplification effect dies down. However, the area more than 20 m from the fissure on the hanging wall and 16 m on the footwall is the safe original site, which is not affected by the earth fissure. The amplification factor of the Arias intensity curve reveals that the amplification is greater than 2 within 9 m of the fissure on the hanging wall. Then, it decreased to 1.5 times at about 15 m and attenuated to the original value after 24 m. As for the footwall, the high-risk zone with twice the magnification is within 6 m of the fissure. The medium-risk zone with 1.5 times the magnification is 6–10 m from the fissure. The change in the attenuation of the amplification factor determined using the HVSR method is shown in Fig. 10d. The amplification effect on the hanging wall of the earth fissure is greater than 2 within 9 m of the fissure, but it decreases rapidly to 1.5 times within 9–15 m. It is magnified by 2 within 6 m on the footwall and attenuates to 1.5 times after 10 m. The area beyond 26 m from the fissure on the hanging wall and 24 m on the footwall is the safe area without amplification.
The distances of the different amplification factors of the earth fissures in the Taiyuan Basin are presented in Table 1. The average high-risk distance is 7.3 m on the hanging wall and only 4 m on the footwall. Since the dynamic response in this range is amplified by more than 2 times, it is not recommended that any construction projects be undertaken in this area. The range in which the dynamic response amplification is 1.5–2 times is the medium-risk zone. Therefore, within 12.3 m on the hanging wall and 8 m on the footwall, only temporary buildings of low importance, with a short service life, and low seismic fortification requirements should be constructed. Further than 23.5 m from the fissure on the hanging wall and 20 m on the footwall is the low-risk area with only a slight amplification effect. Buildings can be arranged appropriately in this area, but the seismic fortification intensity of the proposed buildings should be increased to 1.5 times the designed value. When some parts of the structure or infrastructure of the building are located within the medium-risk zone, the fortification intensity of the overall structure should also be increased to at least twice that of the original design to ensure safety. In the area beyond 23.5 m from the fissure on the hanging wall and 20 m on the footwall, there is no need to consider the amplification effect of the dynamic response.
Table 1
Recommended seismic fortification distance
Amplification factor
|
Hanging wall
|
Footwall
|
1
|
1.5
|
2
|
1
|
1.5
|
2
|
Fourier amplitude
|
24.0 m
|
9.0 m
|
5.0 m
|
20.0 m
|
4.0 m
|
-
|
Response acceleration
|
20.0 m
|
10.0 m
|
6.0 m
|
16.0 m
|
8.0 m
|
4.0 m
|
Arias intensity
|
24.0 m
|
15.0 m
|
9.0m
|
20.0 m
|
10.0 m
|
6.0 m
|
HVSR
|
26.0 m
|
15.0 m
|
9.0 m
|
24.0 m
|
10.0 m
|
6.0 m
|
Average
|
23.5 m
|
12.3 m
|
7.3 m
|
20.0 m
|
8.0 m
|
4.0 m
|
Since the earth fissures in the Taiyuan Basin are mostly distributed in the piedmont on the edge of the basin and within the sedimentary areas inside the basin, the distribution characteristics, formation mechanism, and activity characteristics of earth fissures in the two regions are different. Therefore, the amplification effects of the earth fissures in the different regions were compared. The differences in the amplification factors in two regions are shown in Fig. 11. Since there are more secondary fissures in the piedmont area of Region II, and the activity of these fissures is greater, the range of each risk area is wider than that in Region I. Therefore, the seismic fortification intensity of a site with earth fissures in the piedmont area requires additional safety measures.