The coefficient of lateral subgrade reaction of a pile is generally given in proportion to −1/2 to −1 power of the pile width. However, since this relationship has been obtained from the experimental results of piles with relatively small diameters, its applicability to piles with large diameters is unclear. The influences of pile width and pile stiffness on lateral subgrade reaction are investigated by centrifugal model experiments. When the pile diameter is considerably large, the lateral subgrade reaction converges to a constant value. The validity is confirmed in comparison with the results of the in-situ horizontal load tests.

Frequency independent stress–strain relationships for the complex moduli used in a seismic response analysis of ground are discussed. In addition, a new complex modulus for the seismic response analysis of ground, named YAS (Yoshida–Adachi–Sorokin) model, is proposed. This model is designed so that the maximum stress and the hysteretic absorption energy agree with those of the cyclic shear test. It is shown that the complex modulus, in which the maximum stress and the damping ratio agree with the test result, is possible only when the damping ratio is less than 0.5. Then, three complex moduli, the Sorokin model used in the original SHAKE, the Lysmer model proposed to improve Sorokin model and used widely in the equivalent linear method, and the YAS model, are compared and discussed. The obtained conclusions are as follows. The Sorokin model overestimates the maximum shear stress. The Lysmer model gives the same maximum stress as the cyclic shear test result, but it underestimates the hysteretic absorption energy. Underestimation of the energy absorption is less than 5% for damping ratio less than 0.3 which is the maximum important damping ratio in practical use.

During the 2016 Kumamoto Earthquake, many special belt-like subsidences called “grabens” occurred in the Aso Caldera, and houses were severely damaged. According to the measurement results of SAR, a horizontal displacement of 2 to 3 m was generated in the area where the grabens occurred. A lake was formed in this area around 9,000 years ago. A soil investigation showed that the bottom of the old lake was bowl-shaped, and a special clay was deposited there. A residual deformation analysis showed that the soft clay flowed due to the earthquake, causing the grabens at the ground surface.