Abstract: A normal loading/unloading test were conducted out on the Silurian Luoreping Formation sandstone samples with discontinuities. The results indicate that, under the low normal stress conditions, the discontinuities deformation curves are in convex, and a concave shape is obtained on the discontinuities with the residual deformation under the normal unloading. The obvious stress strain hysteresis loops can be observed in the result. Currently, the normal deformation constitutive models of discontinuities are all empirical relations from laboratory test results. However, due to the difficulties in the determination of both the initial normal stiffness and maximum closure deformation at the discontinuities, the accuracy of these models is limited. A semilogarithmcircular arc constitutive model for predicting the normal deformation at the discontinuities is proposed in this paper based on the characteristics of low confining stress of the shallow rock mass. The loading curve is described by the semi-logarithm model and can be obtained from the regression analysis of the loading test results. The circular arc is used to represent the unloading process and it can be determined from the coordinates of three points: initial loading, final loading and the end of unloading. The calculated results were consistent with the laboratory test results.

Key words: Sandstone Discontinuities, Normal Loading/Unloading, Constitutive Models, Normal Stiffness