## 1 Introduction  
The earth pressure problem dates from the beginning of the 18 th century, when [PERSON] [1] listed five areas requiring research, one of which was the dimensions of gravity-retaining walls needed to hold back soil. However, the first major contribution to the field of earth pressures was made several decades later by [PERSON] [2], who considered a rigid mass of soil sliding upon a shear surface. [PERSON] [3] extended earth pressure theory by deriving a solution for a complete soil mass in a state of failure, as compared with [PERSON]'s solution which had considered a soil mass bounded by a single failure surface. Mohr circles have also been used with great effect to derive solutions for the Rankine analysis. Originally, the [PERSON]'s theory considered the case of only cohesionless soils. However, this theory has subsequently been extended by [PERSON] [4] to cover the case of soils possessing both cohesion and friction. [PERSON]'s [5], on the other hand, gave a general solution for a purely frictional soil which allows for sloping backfill, sloping back of wall and a frictional wall. This solution has been obtained on the same basis as the Coulomb solution. [PERSON] and [PERSON] [6] modified [PERSON]'s equations to account for a nonplanar rupture surface. They used a logarithmic spiral to represent the rupture surface instead. This modification is important for passive earth pressure where there is soil-wall friction, however, for the active pressure coefficient, the logarithmic spiral rupture surface provides a negligible difference compared to Muller-Breslau. Despite of the fact the above solutions are, in essence, the earliest approaches to the problem, they are, undoubtfully, the main methods used in practice. The same also stands for [PERSON]'s method [7; 8; 9], which is an extension of [PERSON]'s method to horizontal-vertical pseudo-static conditions.  
Except for the above widely adopted solutions, numerous other evidential, closed-form, limit analysis, limit equilibrium, discrete spring model, and continuum model approaches have been proposed by various researchers for the calculation of the active and passive earth pressure. The concept of these approaches is described in [PERSON] et al.'s [10] excellent book, \"Earth Pressure and Earth-Retaining Structures\".  
The coefficient of earth pressure at rest has also received considerable attention over the years. Theoretical approaches considering static conditions and cohesionless soils have been proposed by [PERSON] [11], [PERSON] [12; 13], and [PERSON] [14], whilst empirical correlations, among others, by [PERSON] [15], [PERSON] and [PERSON] [16] and [PERSON] [17]. Among all, [PERSON]'s [11] coefficient of earth pressure at rest, \(K_{o}\), which is based on [PERSON]'s first law of motion, is by far the most widely used worldwide. Besides, its reliability has been tested and validated by numerous researchers (e.g., [18; 19; 20; 21; 22]).  
The present paper offers an extension of [PERSON]'s first law of motion to deformable bodies with internal resistance with application to earth pressures. In this respect, a unified continuum mechanics approach for deriving earth pressure coefficients for all soil states, applicable to cohesive-frictional soils and both horizontal and vertical pseudo-static conditions is proposed. In this framework, [PERSON]'s [11] soil heap hypothesis will be adopted, for the derivation of generalized coefficients of earth pressure for all soil states, i.e., at rest, active, and passive.