Quantitative spatial analysis of thermal infrared radiation temperature fields by the standard deviational ellipse method for the uniaxial loading of sandstone

Previous studies focused mainly on the temporal analyses of thermal infrared radiation variations based on statistical parameters for rocks under loading conditions, and the spatial features were qualitatively obtained by visual interpretation. Hence, quantitative studies on the infrared radiation temperature fields on rock surfaces caused by stress variations and fracture activity remain scarce. Therefore, the standard deviational ellipse algorithm was introduced into spatial statistical analysis based on a temporal analysis. First, the abnormal infrared temperature points with values exceeding three times the standard deviation were extracted according to the statistical results for the entire calculated region, and the spatial coordinates of those abnormal points at different loading times were obtained. Second, the standard deviational ellipse was plotted based on the spatial coordinates of the abnormal points, and the lengths of the axes parallel and perpendicular to the loading direction, the coordinates of the ellipse center, and the area and ellipticity of the ellipse can be calculated at a certain loading moment. Then, the continuous temporal curves of the ellipse parameters during the whole loading process can be plotted, and quantitative analysis can be carried out on the spatiotemporal characteristics. The ellipse parameters changed steadily in the elastic stage, and the inflection point on the curves of the ellipse parameters occurred earlier than the inflection point on the curves of the average infrared radiation temperature and standard deviation in the microfracture development stage. The length of the coordinate axis perpendicular to the loading direction exhibited a decreasing trend. In the fracture development stage, the area of the ellipse decreased, and the ellipticity increased; the coverage region decreased, and the shape of the ellipse changed from circular to elongated. The ellipse parameters can quantitatively describe the evolution trend of the infrared radiation temperature field on the rock surface from a uniform random distribution to a centralized distribution in the fracture area, and the moving direction of the ellipse center can roughly indicate the macrofracture location. These research results are expected to provide experimental data-based guidance for the comprehensive quantitative analysis of temporal-spatial characteristics for the monitoring of rock stress disasters by thermal infrared remote sensing.