The acceleration response peak value and acceleration amplification factor are used to analyze the slope acceleration response characteristics. The acceleration amplification factor is defined as the ratio of the peak acceleration response of the slope measured under the excitation of unidirectional and bi-directional seismic waves at a certain measuring point to the peak acceleration response of the same direction measured on the vibrating table.
The measured acceleration time history curves of the measuring point AX2 under the excitation of WC-x and WC-xz with a peak value of 0.4g are shown in Fig. 7 below.
3.1.1 Analysis of horizontal acceleration response results
Take the horizontal acceleration response of the slope under the excitation of WC-x and WC-xz as examples.
(1) Fig. 8 shows the trend of the horizontal acceleration amplification factor of each measuring point of the slope with the relative height of the slope under different working conditions. It can be seen from Fig. 8 that under WC-x unidirectional and WC-xz bidirectional excitation, the horizontal acceleration magnification coefficients of each measuring point of the slope show nonlinear changes with the slope height.
Under WC-X excitations with peak values of 0.4 g and 0.6 g, the amplification Coefficient of acceleration decreases with the change of Slope Height due to the complex effect of coupling of multi-arch tunnel and strong seismic waves from the foot of slope to 2/5 slope height. At this time, the slope suppresses the amplification of horizontal seismic waves. However, there is no similar trend under the excitation of WC-x waves with peaks of 0.1g and 0.2g. With the progressive loading of seismic wave and the increase of the peak value of seismic wave, the strain of slope increases, the shear modulus decreases, the natural vibration frequency decreases and the damping ratio increases. At the same time, the material also exhibits nonlinear characteristics. As the input amplitude increases, the filtering effect of the material increases. These factors weaken the dynamic response of the material. Therefore, there is a phenomenon that the rock mass at the lower part of the slope suppresses seismic waves, and the acceleration amplification factor at this time is smaller than the amplification factor under the seismic wave excitation with a small peak value. Above the rock layer interface at 3/5 slope height, the acceleration magnification coefficient increases obviously, and it increases sharply near the slope top. It shows that the type of slope rock mass affects the amplification of acceleration. In addition, there is an empty surface near the top of the slope, where the complex wave field is superimposed and enhanced, and the acceleration amplification effect is more obvious.
Under the excitation of WC-xz, the acceleration amplification factor increases rapidly from the slope toe to the 3/5 height of the rock layer interface. From the height of 3/5 to the height of 4/5, the acceleration amplification coefficient increases slowly. It increases sharply near the top of the slope. When the seismic wave propagates to the slope surface through the slope, the seismic wave will split into many different types of waves due to the interaction between the seismic wave and the rock mass. There is an empty surface on the upper side of the slope. Different types of seismic waves influence and overlap each other in a limited space. This complicates the wave field. And when the seismic wave propagates near the top of the slope, the constraints are reduced, so the amplification factor has a larger increase near the top of the slope. Compared with the unidirectional excitation, under the bi-directional excitation, the weak surrounding rock has weakened the seismic wave suppression effect. As the slope height increases, the acceleration amplification factor increases sharply at the 3/5 height rock layer interface. Above 3/5 height, the acceleration amplification factor decreases. The weak surrounding rock slope of the slope has the effect of suppressing horizontal seismic waves. This is more obvious than in the case of unidirectional excitation. It can be inferred that the direction of excitation also has an impact on the amplification effect of acceleration. The analysis shows that in the tunnel overlying slope, the rock boundary is easily damaged in the earthquake, and special attention should be paid to the reinforcement of the rock boundary.
(2) Fig. 9 shows the measured acceleration Fourier spectrum of sensors AX0, AX3, and AX5 under WC-x unidirectional excitation with an excitation peak of 0.4g.
It can be seen from Fig. 9 that the excellent frequencies of the acceleration of the vibrating table are distributed in the two frequency bands of 3 ~ 5Hz and 7 ~ 12Hz, and the acceleration frequency of the measuring point AX3 near the midpoint of the slope surface is 2 ~ 5Hz and 7 ~ 10Hz. The acceleration frequency of the measuring point AX5 at the top of the slope is distributed in two frequency bands of 3 ~ 5Hz and 7 ~ 9Hz. The remarkable frequency amplitudes at the measuring points AX3 and AX5 are obviously smaller than those at the mesa measuring point. It can be seen that after the coupling of the double-arch tunnel and the slope, the seismic wave has a more significant spectral change. Because of the weak characteristics of the slope rock mass, its own damping can consume the energy of the seismic wave to a certain extent, and the existence of the double-arch tunnel itself and its inner void surface also diverges and consumes part of the energy of the seismic wave to a certain extent. Therefore, the slope has a filtering effect on the higher frequency band of seismic waves.
3.1.2 Analysis of vertical acceleration response results
The vertical acceleration response of slope under WC-z and WC-xz excitation is analyzed as examples.
(1) Fig. 10 shows the trend of the vertical acceleration magnification factor of each measuring point of the slope with the relative height of the slope. Because the acceleration amplification effect is affected by the relative elevation, slope body, double-arch tunnel, rock mass properties and other factors, under the excitation of WC-z unidirectional and WC-xz bidirectional seismic waves, the vertical the acceleration amplification factor also shows a non-linear change trend in general. Under the unidirectional excitation of WC-z, due to the coupling of seismic waves and the multi-arch tunnel and the influence of the gravity of the slope, the acceleration amplification factor increases slowly from the foot of the slope to the interface of the 3/5 slope height. Near the bottom of the slope, under the excitation of the seismic wave with a larger peak, the acceleration amplification coefficient is smaller than that under the seismic excitation with a smaller peak, which is similar to the situation under the x-directional seismic wave excitation. After the seismic wave with the smaller peak value is excited, then the large peak seismic wave is performed. The shear strength and shear modulus of the rock mass are reduced. In addition, the frequency of the rock mass is reduced and the damping ratio is increased, showing more nonlinearity, and enhancing the suppression of seismic waves. Therefore, the acceleration amplification factor under the excitation of large peak seismic waves in the lower part of the rock mass is smaller than that under the excitation of peak seismic waves. When the slope height is above 3/5 and close to the top of the slope, the acceleration amplification coefficient increases rapidly, and the value increases rapidly. It can be seen that acceleration amplification is also related to the type of slope rock mass. Under unidirectional Wenchuan wave excitation, the worse the rock mass type of the weak surrounding rock slope, the more significant the vertical acceleration amplification effect. Because the upper rock mass is less restricted and its own weight is smaller than that of the lower one, the acceleration amplification factor is larger, and the slope has more violent movement.
When WC-xz is excited, as the excitation peak value increases, the amplification factor decreases. Moreover, the magnification factor first increased and then decreased with the increase of slope height. The acceleration magnification factor reaches the maximum at the interface of the rock strata. Above this height, the vertical acceleration magnification factor decreases, which is opposite to the result under unidirectional excitation. It can be inferred that the direction of seismic wave excitation also affects the acceleration dynamic response of weak surrounding rock slopes. It can be seen from Fig. 10 that under low-peak seismic wave bidirectional excitation, the slope has a strong amplification effect on seismic wave acceleration, but under high-peak seismic wave excitation, the amplification effect is lower. This is related to the early vibration. Under the excitation of low-peak seismic waves, the soils squeeze and deform each other, resulting in elastic, elasto-plastic deformation and contact deformation. Therefore, the effective contact stress increases, the frequency of the model itself decreases, and the damping ratio increases. When multiple excitations occur, the shear strength and shear modulus of the soil decrease, its own frequency decreases, and the damping ratio increases. When the excitation peak value increases, the soil appears plastic deformation and the soil softens. As the shear strength and shear modulus decrease, the effective contact stress increases at a slower rate, and the frequency and damping ratio tend to stabilize. The slope's suppression of seismic waves becomes stronger, and the above phenomenon appears. This phenomenon is more obvious under bidirectional seismic wave excitation than under unidirectional excitation. In the process of seismic wave propagation, when encountering the interface of different media, the wave field splitting will occur. The split seismic wave will be refracted and reflected on the slope surface.
(2) Fig. 11 shows the acceleration Fourier spectrum of acceleration sensors AZ0 and AZ5 under WC-z excitation with a peak value of 0.4g. After the vertical seismic wave loaded by the vibrating table surface interacts with the slope, the frequency spectrum component changes significantly. In addition, the remarkable frequency and its amplitude have also changed greatly. The excellent frequency measured by the table is 1 ~ 3Hz and 7 ~ 13Hz, and the excellent frequency measured by AX5 is 6 ~ 10Hz. It can be inferred that the slope also has a filtering effect on vertical seismic waves.
(3) Comparing Fig. 8(a) and Fig. 10(a), it is found that the slope has different amplification characteristics for horizontal seismic waves and vertical seismic waves. Under the unidirectional excitation of WC-x, the acceleration amplification factor tends to increase greatly from the foot of the slope to the height of 3/5, and it also increases sharply near the top of the slope. Under the unidirectional excitation of WC-z, the vertical acceleration magnification coefficient increases from the foot of the slope to 3/5 of the slope height. It increases rapidly from the height of 3/5 (the boundary of the strata) to the top of the slope. At the foot of the slope, the maximum value of the vertical acceleration amplification factor is 1.597, and the peak value of the horizontal acceleration amplification factor at the same location is 1.987. Near the middle of the slope, the peak value of the amplification factor of vertical acceleration under WC-z excitation is 1.81, and the peak value of the amplification factor of horizontal acceleration under WC-x excitation is 2.12. Near the top of the slope, the peak value of the amplification factor of the vertical acceleration under WC-z excitation is 2.569, and the peak value of the amplification factor of the horizontal acceleration under WC-x excitation is 2.872. When it is near the top of the slope, the vertical acceleration magnification coefficients are not much different under the excitation of the larger peak seismic wave, which are all around 2.6. The horizontal acceleration magnification factor is distributed more scattered, and the difference is large. It can be seen that near the top of the slope, the weak surrounding rock slope is more affected by vertical seismic waves.
(4) It can be seen from Fig. 8 and Fig. 10 that under the excitation of WC-xz, when the peak value of the seismic wave increases, the magnification factor generally shows the characteristic of decreasing. Under unidirectional seismic wave excitation, as the peak value of seismic wave excitation increases, the slope horizontal and vertical acceleration amplification coefficients generally show an increasing trend, which is related to the nonlinearity of the slope rock mass and seismic wave excitation. In addition, the coupling between the Wenchuan wave and the double-arch tunnel and the existence of the interface will also affect the occurrence of this trend. As the peak value of the seismic wave increases, the slope strain will increase. At the same time, the slope shear modulus decreases, and the slope natural frequency will also be affected and reduced. In addition, due to the increase of the damping of the slope material, the nonlinear characteristics of the rock mass appear, and there are structural planes and structural planes in the slope. Therefore, the seismic waves in the propagation path are reflected and refracted. The superposition of various seismic waves results in a more complicated seismic wave field on the slope and result in the acceleration response characteristics described above.