Vu Van Duong
Hirofumi Toyota
Study on similarity rule for model tests concerning ground vibration problems
Various experimental studies have been conducted to solve the ground vibration problems. In the model tests, the similarity rule is very important to predict the actual behaviour of the real ground. Therefore, two types of similarity rules were discussed in the study.
The first similarity rule is assumed that stress and shear stiffness have the same similitude ratio because they have the same dimension. In the previous study, the experiment was conducted using a material (e.g. agar-agar) except soils. However, there is a big gap in the characteristics between the soils and other materials. Those are the soil is frictional material and has larger shear stiffness G in deeper part. Moreover, it is doubt whether damping energy in wave propagation is the same between granular material such as the soil and elastic continuum material. Therefore, a diatomaceous soil, which consists of fossilized remains of diatoms, a type of hard-shelled algae and has large void (porous medium), was used in the experiments. In this similarity rule, when the model is 1/10, G also becomes 1/10. Then, it was examined that shear wave velocity Vs becomes 1/3.2 in the model because of relation of G = ĪVs2.
The second similarity rule consists of assumption, where the same soil with real ground is used in the model test. According to the previous research, it has been suggested that the G in the model should be in proportional to the square root of the model dimension. Although those were concluded from experimental results of triaxial tests, the data is insufficient under low confining stress level such as small model ground. Therefore, Vs was measured in soil container using two methods that are bender element and plate hitting to verify that Vs is in proportional to the fourth root of the model dimension because of relation of G =ĪVs2 @(referred to as the fourth root of Vs rule).
From the experiments, two main points were confirmed. The first, when the model ground is created using the diatomaceous earth, model ground can have small G to satisfy the first similarity rule. However, it is not suitable for large-scale model tests because the cost of diatomaceous earth is high. The second, the fourth root of Vs rule is satisfied not only in the case of high confining stress but also in the case of low one.
In the future, the fourth root of Vs of similarity rule will be used to perform the model tests concerning the ground vibration problems.