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

Assuming the rock as an isotropic nonlinear elastic body, the rock 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 of the rock during the compaction-elastic stage under uniaxial compression are established and verified. The model of the rock secant modulus (Eg) 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 high correlation. The parameters of the model between Eg and σ1, σ3, including the initial modulus, the limiting modulus, and the 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 spalling observed in the tests, which is enlightening for understanding the mechanism of spalling.