Using P-wave propagation velocity to characterize damage and estimate deformation modulus of in-situ rock mass

As the actual jointed rock mass often does not behave elastically, its deformation modulus is typically used in practical engineering. In this study, an analytical equation for characterizing the damage variable of in-situ rock mass was investigated. This equation is primarily based on the P-wave propagation velocity, and its simplified form, which only considers the deterioration of the P-wave propagation velocity compared with intact rocks, is presented. Moreover, a novel approach for estimating the deformation modulus of in-situ rock mass, is proposed, based on the P-wave modulus and simultaneously modified by the damage variable, Poisson's ratio, and an empirical coefficient. A simplified equation comprising only two basic, easily obtainable parameters is also provided, which can approximate the deformation modulus of in-situ rock mass. Literature from in-situ databases was discussed to verify the applicability of the two proposed simplified equations. Back calculation analysis was further conducted to obtain a piecewise function, thereby improving the accuracy of the simplified equation. These validations demonstrate that the proposed estimation method can provide consistent prediction values for the deformation modulus of in-situ rock mass with the same lithology based on its damage variable. Based on observations of the field deformation modulus, the proposed method exhibites a satisfactory degree of accuracy.