In order to better analyze the process and distribution of foundation liquefaction, the effective stress principle is used to determine whether the soil liquefaction occurs according to the excess pore pressure ratio, thus the excess pore water pressure is converted into the excess pore pressure ratio R, as shown in Fig. 10. The excess pore pressure ratio $R = \dfrac{{{\rm{excess}}\;{\rm{pore}}\;{\rm{water}}\;{\rm{pressure}}\;{\rm{of}}\;{\rm{soil}}}}{{{\rm{initial}}\;{\rm{effective}}\;{\rm{stress}}\;{\rm{of}}\;{\rm{soil}}}}$. When ratio R reaches 1.0, it means that the upper load of the soil has been fully borne by pore water and the soil has liquefied.
1) Excess pore pressure ratio R of MBF and CBF
The pore water pressure measure points of MBF and CBF in the test are shown in Fig. 11 and Fig. 12.
The excess pore pressure of MBF and CBF at different measure points are shown in Fig. 10, and the measure points K1, K2, K3 and K4 are shown in Fig. 12. The ratio R at the center of the bucket is the lowest, and the peak value under EI1 condition is 0.036; The ratio R of soil at 0.5D (D is the diameter of bucket) outside the bucket is the largest, and the peak value under EI1 condition is less than 1.0, without liquefaction. The ratio R of the soil inside the bucket is significantly lower than that of the soil outside the bucket, which indicates that the anti-liquefaction ability of the soil inside the bucket is improved with restraint of the bucket. The largest ratio R of CBF also appeared outside the bucket, and the difference of the ratio R at each position inside the bucket is small, among which the ratio R of K3 is the lowest, which is at the center of the bucket. And the ratio R at the center of CBF is significantly smaller than that of MBF.
Under EI2 test condition, for the soil of MBF, the ratio R at 0.5D outside the bucket has reached 1.0, indicating that the soil at this location has been liquefied. The peak value of the ratio R at the center of the bucket is only 36% of that at 0.5D outside the bucket. For CBF, the ratio R at K1 has reached 1.0, indicating that the soil at this location has undergone liquefaction. The maximum ratio R in the bucket appears at K2, with a peak value of 0.16; The ratio R at the center of the bucket is the lowest, with a peak value of 0.13. The liquefaction risk is small, indicating that the liquefaction resistance of the soil inside the bucket is significantly greater than that of the soil outside the bucket.
Under test condition of EI3, the ratio R at the inner wall, outer wall and 0.5D of CBF has reached 1.0, and liquefaction has occurred. However, the ratio R at the center of the bucket at the same height is 0.87, with a high risk of liquefaction. At this time, except the ratio R at K1 outside the bucket exceeding 1.0, the maximum ratio R appears at K2, with a peak value of 0.4, without liquefaction.
Under EI4, liquefaction has occurred at all the monitoring positions inside and outside MBF, which is also consistent with the test phenomenon of model collapse. At this time, the ratio R of CBF at K2 reaches 1.0, indicating that the soil at this location is liquefied. The ratio R at K4 is the lowest, with a peak value of 0.5; The peak value of ratio R at the center of the bucket reached 0.8, and no liquefaction occurred.
To sum up, both MBF and CBF show the same law, that is, the ratio R of the soil inside the bucket is smaller than the soil outside the bucket, and the liquefaction resistance is better. The analysis of its mechanism shows that the additional load of the superstructure of the bucket foundation and the hoop effect of the bucket wall significantly improve the initial effective stress of the soil. According to the definition of the ratio R, the greater the initial effective stress, the smaller the ratio R is, and the soil will be less prone to liquefaction; At the same time, the bucket foundation has a compaction effect on the soil particles, and the shear shrinkage of the sand becomes weaker, while the shear shrinkage of the sandy soil under the reciprocating shear stress is an important reason for the rise of pore pressure, thus the increase of the pore pressure is suppressed after compaction, and the liquefaction resistance is improved. The ratio R of the soil in the middle compartment of CBF is the smallest, which is caused by the strongest constraint effect of the bucket at this position. In addition, K4 is located adjacent to K2, but its ratio R is smaller than K2 under EI4, indicating that the response of soil in different compartments is not the same. This may be due to the larger movement of the bucket along the vibration direction during earthquakes, while the compartment where K4 is located has a certain angle with the vibration direction, and the relative motion between the inside soil and the bucket is also relatively weak.
Fig. 13 shows the peak value of ratio R at the center of the bucket and 0.5D outside the bucket for CBF and MBF respectively. It can be found that when the same acceleration peak value is input, the ratio R at the center of the CBF is significantly smaller than that of the MBF. Under the EI3 condition, the difference between the ratio R at the center of MBF and CBF is the largest, indicating that CBF has a greater role in improving the liquefaction resistance of the soil in the bucket than MBF. This is due to the existence of the compartment plate, which divides CBF into several smaller compartments. The hoop effect of the compartment plate and the bucket wall on the inside soil is stronger. The bucket soil is more inclined to become a whole and is not easy to produce relative displacement. The soil inside the bucket is subject to greater restraint, and the effective stress is increased. At the same time, the soil particles are squeezed and the shear shrinkage is weakened, thus the soil is less prone to liquefaction. Therefore, under the action of earthquake, the increase of pore pressure and the ratio R is smaller, as the result of which, the liquefaction resistance is improved. However, the difference of the ratio R between CBF and MBF at 0.5D outside the bucket is small, indicating that the ratio R at this location is less influenced by the structure.
2) Excess pore pressure ratio R of TBJF and FBJF
The pore pressure monitoring points of TBJF and FBJF are shown in Fig. 14 and Fig. 15.
The excess pore pressure of TBJF and FBJF at different measure points are shown in Fig. 16, and the measure points K1, K2, K3, K4 and K5 are shown in Fig. 15. Under condition EI1, TBJF and FBJF are not liquefied; However, when the acceleration reaches 0.175 g, the excess pore pressure at each position of TBJF and FBJF increases significantly, and the ratio R of soil at the bottom of bucket reaches 1.0, resulting in liquefaction, but the ratio R inside FBJF is lower than that of TBJF. For TBJF, when the peak acceleration is 0.22 g, the ratio R of the soil outside the bucket and near the bucket also reaches 1.0. When the peak acceleration reaches 0.4 g, the ratio R of the soil inside the bucket reaches 1.0, at this time, the sand at each measuring point is liquefied, and the bearing capacity is lost. The sequence of sand at each measuring point reaching liquefaction state is: the bottom of bucket>outside the bucket>near the bucket foundation>inside the bucket. Besides, the ratio R of K1 is larger than K3 under EI4 condition, indicating that the response of soil in different bucket for TBJF is not the same. This may be caused by structural asymmetry, for there is only one bucket subjected to seismic load where K1 is located, while two buckets could disperse seismic loads for K3.
For FBJF, when the peak acceleration is 0.22 g, the ratio R at the bottom of the bucket and outside the bucket reaches 1.0, which corresponds to the phenomenon of a large number of bubbles near the bucket foundation on the macro level. The peak value of ratio R near the bucket wall is about 0.8, and the value in the bucket is less than 0.7. It can be concluded that the bucket foundation can improve the liquefaction resistance of sand under earthquake. When the input seismic wave acceleration is 0.4 g, the soil near the bucket wall also reaches the liquefaction state, and the soil inside the bucket still maintains a certain bearing capacity. Although the bucket foundation has a large angle of inclination, it does not topple down. It can be seen that FBJF has the better anti-liquefaction ability than TBJF.
Comparing the test results of TBJF and FBJF, it is found that both the three-bucket and four-bucket foundations show that the ratio R of the soil inside the bucket is lower than the soil outside the bucket. In addition, the soil near the bottom of bucket is greatly disturbed by the bucket wall, and the stress concentration tends to occur. During the vibration process, the soil particles are more prone to dislocation, as the result of which, the sandy soil at this location reaches the liquefaction state earlier.
The peak values of ratio R for TBJF and FBJF under the same seismic wave are compared. Select the measuring points at the center of the bucket, near the outer wall of the bucket, 1.5D (D is the bucket diameter) outside the bucket and the bottom of the bucket wall for comparison, as shown in Fig. 17.
It can be seen from Fig. 17 that under the same seismic wave, the ratio R at each measuring point of FBJF is generally lower than that of TBJF. At the same time, the ratio R at the measuring point rises with the increase of the peak acceleration of the seismic wave, and the gap between the two foundations also increases. This shows that FBJF has a more significant effect on the liquefaction resistance of sandy soil foundation than TBJF, and this effect will increase with the intensity of seismic. This is because FBJF has a larger self-weight, which makes the soil inside and around the bucket foundation bear the stronger compaction, and the shear shrinkage is weaker, thus its liquefaction resistance improved; In addition, compared with TBJF, FBJF has the advantages of symmetry, and the larger contact area with the soil, and the more stable structure. When subjected to earthquake, it is not easy to topple down in a single direction. When the large earthquake occurs, TBJF is prone to tilt in a single direction, the soil is disturbed and the excess pore pressure rises sharply, and the ratio R also increases. Therefore, when the input acceleration increases, the gap between the peak values of the R ratio for two bucket foundations increases.