BI - Bare Index

Bare Index or Bare Soil Index (BSI) are a numerical indicators that combines blue, red, near infrared and short wave infrared spectral bands to capture soil variations. These spectral bands are rather used in a normalized manner than their simple formula. The short wave infrared and the red spectral bands are used to quantify the soil mineral composition, while the blue and the near infrared spectral bands are used to enhance the presence of vegetation 

Generic Formula (R is the reflectance at the wavelengths (nm) denoted by the subscripts): 

Formula by Sentinel-2 bands: 

References:

Loi, Duong & Chou, Tien-Yin & Fang, Yao-Min. (2017). Integration of GIS and Remote Sensing for Evaluating Forest Canopy Density Index in Thai Nguyen Province, Vietnam. International Journal of Environmental Science and Development. 8. 539-542. 10.18178/ijesd.2017.8.8.1012.