Arches and contact forces in a granular pile

Area of Science:

• Physics of granular materials
• Statistical mechanics
• Mechanical engineering

Background:

• Mechanically stable granular assemblies under self-weight inherently form arches.
• Arches, defined as sets of mutually stable grains, are traditionally assumed to bear the majority of the system's stress.
• This study investigates the stress distribution within these granular structures.

Purpose of the Study:

• To test the hypothesis that grains within arches bear the most stress in granular assemblies.
• To quantify and compare the stress experienced by grains inside and outside of arches.
• To analyze the contact force distributions in relation to arch structures.

Main Methods:

• Experimental or computational study of granular particle assemblies.
• Identification and isolation of arch structures within the assembly.
• Measurement and analysis of stress (isotropic and anisotropic components) on individual grains.
• Examination of contact force distributions between grains.

Main Results:

• Particles within arches demonstrably withstand larger stresses compared to out-of-arch particles.
• In-arch grains exhibit significantly higher isotropic stress.
• The anisotropic stress component shows minimal difference between in-arch and out-of-arch grains.
• Contact force distributions differ: out-of-arch contacts follow an exponential tail, while in-arch contacts align with a Gaussian distribution.

Conclusions:

• The findings support the hypothesis that arches play a critical role in stress bearing in granular materials.
• The stress distribution is anisotropic, with in-arch particles experiencing greater isotropic stress.
• The contact force distributions provide insights into the force-balance constraints governing granular structures, particularly within arches.