Experimental and numerical simulation investigation of the deformation characteristics of vertical boreholes under non-uniform horizontal principal stress

To study borehole deformation under non-uniform horizontal principal stress in the deep strata, a prediction method for horizontal principal stress was developed based on the morphological parameters of boreholes, the deformation trajectory equation for the standard circular borehole was derived based on elasticity theory, and the morphological characteristics of boreholes were analyzed. Additionally, a quantitative relationship between the geometric parameters of elliptical boreholes and horizontal principal stress was established. Subsequently, uniaxial tests on borehole deformation were conducted to verify elliptical deformation under non-uniform horizontal principal stress. A combined deductive, experimental, and numerical simulation approach to borehole deformation analysis was adopted, and the impact factors of borehole deformation were obtained. The results indicated as following: (1) the deformation morphology of borehole under non-uniform horizontal principal stress was elliptical; (2) for the given lithology, the greater the difference in horizontal principal stress, the greater were the ellipticity and elliptical deformation of borehole; (3) for given stress background, rock strength was inversely proportional to ellipticity. Additionally, the smaller the Young’s modulus and compressive strength, the larger was the Poisson’s ratio and the larger was the ellipticity. For example, the ellipticity of mudstone and coal was greater than that of limestone and sandstone; (4) with an increase in load, the displacement of borehole wall exhibited three stages: initial micro-deformation, accelerated deformation, and stable deformation; (5) horizontal principal stress can be calculated by using the morphological parameters (long and short axes) of an elliptical hole. Furthermore, a horizontal principal stress method theory can be developed based on the morphological parameters of boreholes. The results of our study can provide new ideas and methods for the measurement of in situ stress in deep boreholes and a theoretical basis for the development of equipment for measuring elliptical boreholes.