3:45 PM - 4:00 PM
[SCG44-14] Motion of a sphere on a vibrated granular slope
Keywords:Granular slope, Sphere motion, Vibration
On the lunar surface, there are many boulder-fall trails that might be triggered by moonquakes. However, it is not very easy for boulders to roll down on the surface of regolith layers because the regolith layers could be very soft. On the surface of the Earth, landslides can be triggered by earthquakes. In natural landslides, large and small grains flow down complexly. Thus, a fundamental understanding of complex flow which includes small and large grains is crucial to reveal the occurrence conditions of boulder falls, landslides, etc.
In this study, we focus on a very simple experimental setup in which a large sphere is placed on the surface of a granular slope. Then, the entire system is vertically vibrated. In this experiment, the density ratio between the large sphere and granular bed, ρ*, is mainly varied. In addition, the maximum vibration acceleration normalized to the gravitational acceleration, Υ, is also systematically varied. Glass beads of typical grain diameter 0.4 mm are used to form the granular slope. The diameter of the large sphere used in this experiment is about 12 mm. At the initial state, the sphere is placed at the upper part of the granular slope. Then, the vibration is applied. The motion of the large sphere and the instantaneous gradient relaxation of the granular slope are measured by taking the movies of the vibrated entire system with 20 fps.
By the qualitative evaluation of the observed phenomena, we categorize the phenomena into 5 types of behaviors: (i) rolling, (ii) slide, (iii) static, (iv) sink, and (v) submerge. The details of the observed phases should be introduced in the presentation. While we observe various types of these behaviors, it is difficult to find the conditions to form boulder-fall-like behaviors in this experimental setup.
From the acquired movies, we measure the sinking depth of the large sphere, δ, and the relative velocity between the sphere and grains on the surface of the granular slope. We find that δ is scaled by ρ* and size of the large sphere. This scaling indicates the sinking depth can be governed by the effective buoyancy produced by the fluidized granular bed. However, the degree of fluidization depends on the vibration strength. Regarding the relative velocity, the sphere’s velocity is basically slower than the surface grains’ velocity, except for the very early stage. Namely, the sphere is pushed by the granular flow. Besides, the relative velocity approaches the asymptotic (almost steady) value, Vgap, in the late stage of sphere’s motion. In this stage, the driving force exerted on the sphere originates from the dynamic pressure created by the granular surface flow. To counter this pushing force, the effective friction force at the bottom of the sphere can be considered. At the bottom of the sphere, the degree of fluidization of the vibrated granular bed is minimal. Thus, the effective friction can create an effective drag force on the sphere. By assuming a certain relation between the degree of fluidization and the vibration strength, we can explain both δ and Vgap behaviors in the unified model. Specifically, we consider the degree of fluidization should be linked to the strength of inter-particle friction strength. Thus, the friction coefficient which varies depending on the vibration strength Υ is employed in this study.
In this study, we focus on a very simple experimental setup in which a large sphere is placed on the surface of a granular slope. Then, the entire system is vertically vibrated. In this experiment, the density ratio between the large sphere and granular bed, ρ*, is mainly varied. In addition, the maximum vibration acceleration normalized to the gravitational acceleration, Υ, is also systematically varied. Glass beads of typical grain diameter 0.4 mm are used to form the granular slope. The diameter of the large sphere used in this experiment is about 12 mm. At the initial state, the sphere is placed at the upper part of the granular slope. Then, the vibration is applied. The motion of the large sphere and the instantaneous gradient relaxation of the granular slope are measured by taking the movies of the vibrated entire system with 20 fps.
By the qualitative evaluation of the observed phenomena, we categorize the phenomena into 5 types of behaviors: (i) rolling, (ii) slide, (iii) static, (iv) sink, and (v) submerge. The details of the observed phases should be introduced in the presentation. While we observe various types of these behaviors, it is difficult to find the conditions to form boulder-fall-like behaviors in this experimental setup.
From the acquired movies, we measure the sinking depth of the large sphere, δ, and the relative velocity between the sphere and grains on the surface of the granular slope. We find that δ is scaled by ρ* and size of the large sphere. This scaling indicates the sinking depth can be governed by the effective buoyancy produced by the fluidized granular bed. However, the degree of fluidization depends on the vibration strength. Regarding the relative velocity, the sphere’s velocity is basically slower than the surface grains’ velocity, except for the very early stage. Namely, the sphere is pushed by the granular flow. Besides, the relative velocity approaches the asymptotic (almost steady) value, Vgap, in the late stage of sphere’s motion. In this stage, the driving force exerted on the sphere originates from the dynamic pressure created by the granular surface flow. To counter this pushing force, the effective friction force at the bottom of the sphere can be considered. At the bottom of the sphere, the degree of fluidization of the vibrated granular bed is minimal. Thus, the effective friction can create an effective drag force on the sphere. By assuming a certain relation between the degree of fluidization and the vibration strength, we can explain both δ and Vgap behaviors in the unified model. Specifically, we consider the degree of fluidization should be linked to the strength of inter-particle friction strength. Thus, the friction coefficient which varies depending on the vibration strength Υ is employed in this study.