INTRODUCTION 



Beginning with Rankine more than a century ago, scientists and engineers alike have 

 sought to improve techniques for calculating soil pressures beneath the earth's surface. 

 This capability has been important not only for predicting soil pressures against 

 structures such as retaining walls and foundations, but also for predicting the depths 

 and pressures at which soil masses will fail when disturbed by either man or nature. 



This paper, based on Rankine 's classic assumptions and the contributions of others, 

 offers some additional refinements for calculating soil pressures. The equations have 

 particular relevance to much of the steep, mountainous lands managed by the USDA Forest 

 Service, particularly the Idaho Batholith, where Intermountain Station engineers and 

 scientists are studying slope stability and erosion problems. 



In 1860, Rankine presented the original theory for calculating lateral earth pres- 

 sures within a slope of infinite extent. Rankine 's development was based on a conjugate 

 stress relationship between vertical stresses and stresses on a vertical plane and consid- 

 ered a dry cohesionless material with either a sloping or a horizontal surface. During 

 the latter part of the nineteenth century, the Mohr circle of stresses was presented for 

 the graphic representation of the state of stress. The analytical work of Rankine was 

 subsequently adapted to a graphical method using the Mohr circle of stresses. 



In 1915, Bell extended Rankine's work to include cohesive soils. Bell's graphical 

 procedure made use of Mohr's stress circle, but in an inconvenient manner. Martin (1961) 

 derived an analytical expression that extends Rankine's work to include cohesive soils, 

 but it includes neither seepage conditions nor a variable plan of investigation. 



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