Direct Shear Test Analyzer

A direct shear test drives failure across a horizontal plane in a split box while a known vertical stress is held on the specimen. Repeating the test at three or four normal stresses and plotting peak shear stress against normal stress produces the Mohr-Coulomb envelope tau = c + sigma * tan(phi). A least-squares line through those points gives the friction angle from the slope, arctan of the slope, and the cohesion intercept from the y-intercept, while the R-squared value reports how nearly linear the envelope really is. Standard shear boxes are 60 mm square, giving a 3600 square millimeter shear area, with 100 mm boxes used for gravelly material; ASTM D3080 requires the specimen to be at least ten times the maximum particle size across and six times that size in thickness. Realistic parameters help flag bad regressions. Clean sands give c close to zero and phi of roughly 28 to 32 degrees when loose and 38 to 45 degrees when dense, with the extra strength in dense material coming from dilation rather than from added friction. Drained clays typically show effective friction angles of 18 to 28 degrees with small effective cohesion, often under 15 kPa, and a fitted c above about 25 kPa in a granular soil usually means the envelope is curved or a data point is bad rather than that real bonding exists. The known limitations are that failure is forced onto a plane that may not be the weakest one, stress on that plane is non-uniform with concentrations at the box edges, principal stress directions rotate during shearing, and drainage cannot be controlled well enough to obtain reliable undrained parameters in fine-grained soil, which is why the test must be run slowly enough to keep excess pore pressures near zero.

The linear strength envelope predates the apparatus. Charles-Augustin de Coulomb, who had served as a military engineer on the fortifications of Martinique, presented an essay to the French Academy of Sciences in 1773, published in 1776, in which he described soil resistance as a sum of cohesion and a friction term proportional to normal load, which he applied to retaining wall design. Alexandre Collin, investigating deep-seated failures in French canal embankments, published Recherches Experimentales sur les Glissements Spontanes des Terrains Argileux in 1846 and used an early shearing device on clay. Christian Otto Mohr supplied the graphical stress-circle framework around 1900, and the combined Mohr-Coulomb criterion took the form used today. The modern shear box came out of the first generation of soil mechanics laboratories. Karl Terzaghi and Arthur Casagrande built and refined shear boxes at MIT and Harvard through the late 1920s and 1930s, and the test was a workhorse until Alan Bishop and others at Imperial College popularized the triaxial cell in the 1950s, which offered controlled drainage and pore pressure measurement. The direct shear test survived because it is fast, cheap, and uniquely suited to large-displacement work. Arthur Skempton drew attention to residual strength on pre-existing slip surfaces in his 1964 Rankine Lecture, and reversing shear boxes and the ring shear devices developed by Bishop and coworkers in 1971 and by Edward Bromhead in 1979 were built specifically to measure it. ASTM D3080 codified the consolidated drained procedure that most commercial laboratories follow.