Shear Strength of Soil Calculator

Shear strength is the maximum shear stress a soil element can carry on a given plane before particles slide past one another. The Mohr-Coulomb criterion expresses it as a straight-line envelope, tau = c + (sigma - u) tan(phi), where c is the cohesion intercept in kPa, phi is the angle of internal friction, sigma is the total normal stress acting on the plane, and u is the pore water pressure. The subtraction of u reflects Terzaghi effective stress: water carries pressure but no shear, so only the grain-to-grain contact stress mobilises friction. Clean sands typically show phi of 30 to 40 degrees with essentially zero effective cohesion; normally consolidated clays give phi-prime of 20 to 28 degrees with c-prime near zero, while overconsolidated clays retain a small intercept of roughly 5 to 20 kPa. The main caveat: c and phi are not fixed material constants. The real envelope is curved, flattening at high confining stress, so parameters fitted over 50 to 200 kPa should not be extrapolated to 1000 kPa. Dense soils show a peak strength driven by dilatancy that drops toward a critical-state value at large strain, and pre-sheared surfaces fall further to a residual angle that can be under 10 degrees in plastic clays. Under undrained loading of saturated clay the friction angle is taken as zero and strength equals Su, from about 12 kPa in very soft clay to over 200 kPa in hard clay. The derived bearing capacity factors Nc, Nq and N-gamma and the Rankine coefficients Ka and Kp assume this same envelope.

The frictional half of the criterion dates to 1773, when Charles-Augustin de Coulomb presented an essay to the French Royal Academy of Sciences on problems of statics applied to architecture. Working from his experience on fortifications at Martinique, Coulomb proposed that resistance along a rupture surface in earth combined a cohesion term independent of load with a friction term proportional to normal force, and used a trial-wedge method to size retaining walls. Just over a century later Christian Otto Mohr, a German structural engineer and professor at Dresden, published his graphical stress-circle construction and argued around 1900 that failure occurs when the stress circle touches an envelope characteristic of the material. Combining the two ideas produced the linear envelope now universally called Mohr-Coulomb. The decisive correction came from Karl Terzaghi, whose 1925 book Erdbaumechanik introduced the principle of effective stress and showed that soil strength responds to sigma minus u rather than total stress, which finally explained why saturated clays behave so differently under fast and slow loading. Laboratory practice was standardised over the following decades: Alan Bishop and Laurits Bjerrum published an influential 1960 account of triaxial testing that clarified the unconsolidated-undrained, consolidated-undrained and consolidated-drained procedures. In the late 1950s and 1960s Kenneth Roscoe and colleagues at Cambridge developed critical state soil mechanics, which explains peak, critical and residual strengths within one framework. The direct shear test is codified today as ASTM D3080.