5.1 Analysis of slope stress law
After the excavation of the side slope of the plant was completed, finite element simulation and analysis under different seismic conditions were carried out. When seismic waves of different wave forms were applied to the slope, the distribution diagram of the maximum time history of the first principal stress was shown in Figure 5, and the third principal stress corresponding to the maximum time history of the first principal stress was shown in Figure 6.
Figure 5 showed the maximum time-history distribution of the first principal stress of the slope under seismic loads with a probability of exceeding 5% within 50 years, 2% within 100 years and 1% within 100 years in the base period. Figure 6 showed the time history distribution diagram of the third principal stress corresponding to the maximum value of the first principal stress time history under three different seismic conditions.It could be seen from Figure 5 and Figure 6 that when the slope was in the process of seismic loading with a probability of exceeding 5% within 50 years of the reference period, the maximum tensile stress generated occurred at the entrance of the diversion tunnel and was 0.25 MPa; when the slope was in the process of seismic loading with a probability of exceeding 2% within 100 years in the reference period, the maximum tensile stress generated occurred at the bottom of the sandstone, which was 0.52MPa; when the slope was in the process of seismic loading with a probability of exceeding 1% within 100 years of the reference period, the maximum tensile stress appears on the top surface of the slope near the boundary, and its value was 0.346 MPa.
5.2 Analysis of slope displacement law
After the slope excavation of the workshop was completed, when it was under seismic loads in different working conditions, the displacement of the slope in X, Y and Z directions was shown in Fig. 7-9 when the time history of the first principal stress was the maximum.
It could be seen from Figures 7-9 that when the slope was under different seismic conditions, the maximum uplift deformation of the slope along the vertical direction appeared on the surface of the rock near the foot of the slope, and the values were 2.0cm and 4.46cm, 4.31cm respectively; the deformation of the slope along the tunnel axis appeared in the middle of the shale. When the slope was under the action of an earthquake load with a probability of exceeding 5% within 50 years of the reference period, the maximum deformation of the slope along the tunnel axis was 1.5 cm, which was the minimum value of the three working conditions. At this time, the slope rock mass had obvious signs of failure; the maximum deformation of the slope along the tunnel axis occurred when the slope was under the action of an earthquake load with a probability of exceeding 2% within 100 years of the reference period. The maximum value was 5.8cm. At this time, It was more likely that the slope was sliding along the bed.
5.3 Analysis of dynamic response at foot of side slope
5.3.1 Time history analysis of dynamic displacement at slope foot
After the excavation of the plant slope was completed, when the first principal stress time history was the maximum under the action of the seismic load of different working conditions, the X, Y and Z directions corresponding to the center of the slope toe at an elevation of 94.8m The displacement was shown in Figure 7-9, and the dynamic displacement time history curve was shown in Figure 10-12.Under the action of ground motions with a probability of exceeding 5% in 50 years, 2% in 100 years and 1% in 100 years in the reference period, the maximum relative dynamic displacement in the X direction at the center of the foot of slope was close to 1.5cm, 2.8cm, and 3.2cm respectively; the maximum relative dynamic displacement in the Y direction at the center of the foot of slope was close to 1.4cm, 3.5cm, and 3.9cm, respectively; the maximum relative dynamic displacement in the Z direction at the center of the foot of slope was close to 1.5cm, 2.8cm, and 3.1cm respectively.Through comparison, it could be obtained that under the action of the seismic load with a probability of 1% of the slope in the reference period of 100 years, the displacements in all directions were larger than those of the other two working conditions; under three different seismic working conditions , the foot of slope at an elevation of 94.8m was less likely to be damaged under the action of ground motions.
5.3.2 Analysis of rock mass acceleration at slope foot
Under the action of ground motions with a probability of exceeding 5% in 50 years, 2% in 100 years and 1% in 100 years in the reference period, the rock slopes all perform similar forced vibrations in the form of exciting ground motions. The acceleration time history curve of the rock mass at the center of the slope foot at an elevation of 94.8m was shown in Figure 13-Figure 15.Under three different seismic loads, the maximum acceleration of rock mass at the central slope foot along the X direction was 0.87m/s2,1.6m/s2 and 1.6m/s2, the maximum acceleration along the Y direction was 0.62m/s2,1.3m/s2 and 1.4m/s2, and the maximum acceleration along the Z direction was 0.8m/s2,1.3m/s2 and 1.55m/s2.By comparison, it could be found that the acceleration of slope rock mass in all directions was larger than the displacement of the other two working conditions under the seismic load with a probability of exceeding 1% in 100 years in the reference period.According to the analysis of the slope dynamic acceleration, the possibility of failure at the slope foot at the elevation of 94.8m was relatively small under the action of three kinds of ground motion.
5.3.3 Stress seismic response analysis of rock mass at slope foot
Under the action of ground motions with a probability of exceeding 5% in 50 years, 2% in 100 years and 1% in 100 years in the base period, the maximum compressive stress of the rock mass at the center of the slope foot at an elevation of 94.8m was close to 0.24MPa,0.56MPa and 0.7MPa respectively, the maximum tensile stress was close to 0.27MPa, 0.52MPa and 0.7MPa respectively.By comparing the maximum tensile stress and compressive stress at the foot of the slope under three seismic conditions, it could be obtained: under the action of ground motion with a probability of 1% in the reference period within 100 years, the value of tensile stress generated by the rock mass at the toe of the slope and the compressive stress values were all the maximum values; under three different seismic conditions, the possibility of failure of the rock mass at the foot of the slope was relatively small.
By analyzing and comparing the displacement distribution, stress distribution and dynamic response characteristics of the rock mass at the foot of the slope under three different ground motions, it could be found that the rock mass at the foot of slope was most obviously affected by the ground motion, which 1% probability of exceeding within 100 years of the reference period; under different seismic conditions, the slope rock mass structure was generally in a stable state.
5.4 Analysis of ground motion response at other positions of slope
Based on the analysis method of the dynamic response at the foot of the slope, the slope was simulated under the action of ground motion with the probability of exceeding 5% within 50 years of the reference period, 2% within 100 years, and 1% within 100 years. The characteristics of dynamic displacement time history, rock mass acceleration, rock mass stress and seismic response at the center, the center of the slope top surface, and the slope top surface near the center of the side slope. The analysis showed that different positions of the slope were under different seismic load conditions. The following variable values are shown in Table 2.
Table 2 Variable values at different locations under various seismic conditions
Working condition
|
location
|
The maximum stress
(MPa)
|
The maximum displacement
(cm)
|
The maximum acceleration
(m/s2)
|
compressive
stress
|
tensile stress
|
in X direction
|
in Y
direction
|
in Z
direction
|
in X
direction
|
in Y
direction
|
in Z
direction
|
Exceeding 5% within 50 years
|
The foot of slope
|
0.24
|
0.27
|
1.5
|
1.4
|
1.5
|
0.87
|
0.62
|
0.8
|
The Center of slope
|
0.16
|
0.17
|
1.62
|
1
|
1
|
0.83
|
0.45
|
0.7
|
The center of the top of the slope
|
0.16
|
0.16
|
1.9
|
1
|
1
|
1.05
|
0.42
|
0.58
|
the top surface near the side slope
|
0.06
|
0.07
|
2
|
1
|
1
|
1.05
|
0.41
|
0.6
|
Exceeding 2% within 100 years
|
The foot of slope
|
0.56
|
0.53
|
2.8
|
3.5
|
2.8
|
1.6
|
1.3
|
1.3
|
The Center of slope
|
0.34
|
0.39
|
3.6
|
2.1
|
1.7
|
1.7
|
0.72
|
1
|
The center of the top of the slope
|
0.35
|
0.35
|
4.5
|
2.3
|
1.3
|
2.2
|
0.85
|
0.9
|
the top surface near the side slope
|
0.13
|
0.13
|
5
|
2.1
|
1.3
|
2.3
|
0.73
|
0.82
|
Exceeding 1% within 100 years
|
The foot of slope
|
0.7
|
0.7
|
3.2
|
3.9
|
3.1
|
1.6
|
1.4
|
1.55
|
The Center of slope
|
0.42
|
0.45
|
3.6
|
2.8
|
1.9
|
1.8
|
1
|
1.05
|
The center of the top of the slope
|
0.38
|
0.4
|
4.6
|
2.6
|
1.9
|
1.8
|
1
|
1.15
|
the top surface near the side slope
|
0.15
|
0.16
|
5
|
2.7
|
1.25
|
2.42
|
1
|
1.2
|
By comparing the variable values at different positions of the slope under different seismic load conditions and combining with the data in Table 2, it could be concluded that:
(1)Under different seismic loads, the ground motion response of the slope would increase with the increase of the peak value of ground motion, and the slope would be forced vibration in accordance with the vibration form of induced ground motion;
(2)The stress, displacement and ground motion response characteristics of the slope were more obvious than those of the other two conditions when the slope is subjected to the rare earthquake with the probability of exceeding 5% within 50 years of the reference period. The maximum tensile stress on the slope surface is 0.7MPa, which was less than the tensile strength of the slope rock mass. Moreover, the maximum displacement on the surface of the slope was 5.8cm, which was less than the maximum displacement allowed by the slope rock mass, so the slope could withstand the action of strong earthquakes(Wen et al. 2016).
(3)The acceleration of ground motion at the side of the top slope was more obvious than that at the center of the top surface. In the rare earthquake with the probability of exceeding 5% within 50 years of the reference period. The failure effect of the side slope near the open surface was more obvious than that at the center of the top.