Mohr-Coulomb Equation formula |
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\( \tau \;=\; c + \sigma \cdot tan( \varphi ) \) (Mohr-Coulomb Equation) \( c \;=\; \tau - \sigma \cdot tan( \varphi ) \) \( \sigma \;=\; \dfrac{ \tau - c }{ tan( \varphi ) } \) |
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| Symbol | English | Metric |
| \( \tau \) (Greek Symbol tau) = Shear Stress of the Soil | \(lbf \;/\; ft^2\) | \(Pa\) |
| \( c \) = Cohesion of the Soil | \(lbf-sec\;/\;ft^2\) | \(Pa-s \) |
| \( \sigma \) = Normal Stress on the Plane | \(ft\;/\;sec\) | \(m\;/\;s\) |
| \( \varphi \) = Angle of Internal Friction | \(deg\) | \(rad\) |
Mohr-Coulomb equation, abbreviated as \(\tau\), is a relationship used in soil mechanics and geotechnical engineering to describe the shear strength of soils and other granular materials. It expresses the maximum shear stress that a soil can resist before failure occurs, based on both the internal friction and cohesion of the material. The equation is where \( \tau \) is the shear strength, \(c\) is the cohesion (the inherent bonding between soil particles), \( \sigma \) is the normal stress acting on the failure plane, and \( \varphi \) is the angle of internal friction, which represents the soil’s resistance to sliding due to interparticle friction. This model combines both cohesive and frictional properties, making it applicable to a wide range of soils, from cohesive clays to cohesionless sands. The Mohr-Coulomb criterion is often represented graphically by a straight line (the failure envelope) tangent to the Mohr’s circle, which illustrates the state of stress at failure.
