Abstract: The coefficient of earth pressure at rest is a critical parameter in the field of geotechnical engineering, which is the foundation of determining the stress state in horizontal site and the calculation of earth pressure at rest. However, at present the study of the coefficient of earth pressure at rest is not enough. The theoretical formula of coefficient of earth pressure at rest of normally consolidated soils is derived from the analysis of the internal stress state of sand prism with natural accumulation stayed in a critical state. Compared with the formula k0 =0.95-sin? (k0 stands for the coefficient of earth pressure at rest, ? stands for the inner friction angel of soil; the same as below) proposed for the coefficient of earth pressure at rest on sandy soil and with the formula k0= 1-sin? proposed for the coefficient of earth pressure at rest on clay; the results show that the formula for the coefficient of earth pressure at rest matches very well with the regular formula for sandy soil and has a little bias with the formula proposed for clay. The formula and its derivation of the coefficient of earth pressure at rest in this paper are scientific and reasonable to express its origin, which makes up the blank in this study area, provides the theoretical support and plays a certain role in the promotion of the derivation of the coefficient of earth pressure at rest of indoor, field test and empirical formula.

Key words: coefficient of earth pressure at rest, sand prism, parabolic hypothesis