DIFFERENTIAL EQUATION METHOD FOR SEMI-ANALYTIAL SOLUTION OF STRESS IN THICK-WALLED CYLINDERS CONSIDERING STRESS-DEPENDENT ELASTIC MODULI

A differential equation method is derived and validated for solving the stress in thick-walled cylinders which are continuous, isotropic, small deformation, linear elasticity, infinitely large, with the minimum principal stress-dependent elastic moduli, and under hydrostatic pressure stress. And combined with Griffith's strength criterion, the influence of the factors including burial depth h, radius r₀, and support stress p₀, to the distribution of tensile stress around a circular tunnel, quantified by σ_tmax (the maximum tensile stress) and d (the distance from the location of σ_tmax to the tunnel wall), is analyzed. The result shows that the differential equation method is reliable. σ_tmax ​remains unaffected by r₀​, monotonically increases with the increase of h, and exhibits a "constant-decrease" trend with the increase of p₀. d is proportional to r₀, demonstrates a "constant-increase-decrease" pattern with the increase of h, and first decreases and then remains unchanged as p₀​ increases.