Relationship models between secant modulus and maximum and minimum principal stresses of nonlinear elastic rocks

Stress-dependent elastic modulus (SDEM) of rocks is an important factor affecting the stress distribution of deep surrounding rocks. To quantitatively describe the rock SDEM, assuming rock as an isotropic nonlinear elastic body, its strain is decomposed into linear elastic strain and nonlinear pore strain. A hyperbolic model and a negative exponential model of the stress(σ)-strain(ε) relationship during the compaction-elastic stage under uniaxial compression are established and verified. The model of the rock secant modulus (E_g) and σ₁, σ₃ is derived and used to calculate the stress of the surrounding rock of deeply buried straight wall arch tunnel. The results show that the correlation coefficients between the calculated values of the hyperbolic and negative exponential models and the measured data are all above 0.999, indicating a level of high correlation. The parameters of the models, including initial modulus, limiting modulus, and limiting pore strain, can be determined by uniaxial tests. And the shapes and positions of the tensile stress concentration bands in the surrounding rock of the tunnel are basically consistent with those of the slabbing observed in the tests, which is enlightening for understanding the mechanism of slabbing in deep surrounding rock.