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Material cracking is one of the key mechanisms contributing to structural failure. Distributed fiber optic sensing (DFOS) can measure the strain profile along optical fiber distributively. However, the conventional strain measurement using a Brillouin-DFOS system (Brillouin optical time-domain analysis/reflectometry (BOTDA/R)) has a decimeter-order spatial resolution, making it difficult to measure the highly localized strain generated by a sub-millimeter crack. This paper introduces a crack analysis method based on decomposing the Brillouin scattering spectrum to overcome the spatial resolution induced crack measurement limitation of the BOTDA/R system. The method uses the non-negative least squares algorithm to back-calculate the strain profile within the spatial resolution around each measurement point. The performance of this method is verified by a four point bending test of a brittle slag cement-cement-bentonite beam. The crack width estimation error is improved to ±0.005 mm for a crack as narrow as 0.76 mm. 

Biogeochemical reactions occurring in soil pore space underpin gaseous emissions measured at macroscopic scales but are difficult to quantify due to their complexity and heterogeneity. We develop a volumetric-average method to calculate aerobic respiration rates analytically from soil with microscopic soil structure represented explicitly. Soil water content in the model is the result of the volumetric-average of the microscopic processes, and it is nonlinearly coupled with temperature and other factors. Since many biogeochemical reactions are driven by oxygen (O 2 ) which must overcome various resistances before reaching reactive microsites from the atmosphere, the volumetric-average results in negative feedback between temperature and soil respiration, with the magnitude of the feedback increasing with soil water content and substrate quality. Comparisons with various experiments show the model reproduces the variation of carbon dioxide emission from soils under different water content and temperature gradients, indicating that it captures the key microscopic processes underpinning soil respiration. We show that alongside thermal microbial adaptation, substrate heterogeneity and microbial turnover and carbon use efficiency, O 2 dissolution and diffusion in water associated with soil pore space is another key explanation for the attenuated temperature response of soil respiration and should be considered in developing soil organic carbon models.