Mohr-Coulomb Shear Strength Calculator
Soil & rock constitutive mechanics: Compute Mohr-Coulomb failure envelopes, principal stresses (σ'₁, σ'₃), shear plane angle (θ_f), and mobilized safety factor.
Strength Parameters & Confining Stress
Failure Envelope & Stress State
Recommended Tools & Equipment
Tested hardware and components for high reliability
Frequently Asked Questions
What is the Mohr-Coulomb failure envelope?
The Mohr-Coulomb failure envelope represents the maximum shear stress (tau) a soil or rock can sustain as a function of normal effective stress (sigma'): tau_f = c' + sigma' * tan(phi'). In principal stress space, it forms a straight tangent line to the Mohr circles at failure, defining the boundary between stable elastic states and plastic failure.
Why do shear planes form at an angle of (45° + ϕ/2)?
In a triaxial compression specimen, the maximum shear stress occurs at 45° to the principal axes. However, because soil shear strength increases with normal stress (friction), the critical combination of highest mobilized shear stress relative to available frictional resistance occurs on planes inclined at theta_f = 45° + (phi / 2) from the horizontal minor principal plane.
What is the difference between peak and residual friction angle?
Dense sands and overconsolidated clays exhibit a high peak friction angle (phi_peak) caused by particle interlocking and dilatancy (expansion during shearing). Once significant shear displacement occurs, the particles align and dilatancy disappears, reducing shear strength to the lower constant-volume critical state or residual friction angle (phi_res), which is vital for long-term slope stability.