Brillouin optical time-domain reflectometer（BOTDR） techniques have numerous advantages such as distributed measurement

long distance and real-time online

which are widely used in the structural engineering field and show extensive application prospects. However

the application of BOTDR is relatively limited in the field of geotechnical engineering

and thus some relevant technologies need to be improved. In this study

the relationship between strain measurements by the optical fiber distributed along the direction of axial tunnel and the deformation of tunnel roof subsidence is investigated based on the strain monitoring technology of BOTDR. Firstly

according to the deformation regularity of tunnel roof

three mathematical models

namely the circular arc model

the parabolic model and the triangle model

are established for the relationships between the strain along tunnel axial direction and the deformation of tunnel roof subsidence. Secondly

experiments are conducted to examine the relationship between the optical fiber strain and the deformation of tunnel roof subsidence. The final comparative analysis reveals that the theoretically calculated values show well agreement with experimental data. The optical fiber strain can be linked with the roof subsidence by using these three analytical models

which has theoretical significance and practical engineering value for the application and improvement of BOTDR technology.