Grey Correlation Analysis on the Sensitive Factors of Plastic Zone Extension of Surrounding Rock

Abstract

As lack of explicit analysis method on the sequence of many factors influencing the plastic zone extension of surrounding rock, the grey correlation analysis method is adopted to study the relationship between the plastic zone extension radius Rp and the six factors such as cohesive c, internal friction angle φ, deformation modulus E, unit weight γ, initial ground stress σ and the radius of chamber r. By dealing with dimensionless, the corresponding sequences composed with the sensitive factors as sub-sequence and the plastic zone extension radius as mother sequence are obtained. The gray correlation analysis model of sensitive factors which evaluates the results with grey correlation degree is built by the methods of dimensionless and extreme difference variation. Then, an engineering example is analyzed with grey correlation. Based on the analysis results, the sorting of sensitive factors is φ > σ > c > r > E > γ. It implies that the influences of internal friction angle φ and initial ground stress σ are the most prominent, and the sensitivities of deformation modulus E and unit weight γ are lowest. These are in good agreement with the analytical formula of classical theory, and can be used in guiding the further optimization and improvement of the analytical expression of the plastic zone extension radius Rp of surrounding rock.