Shear Strength of Soil Calculator
Compute shear strength soil using validated scientific equations. See step-by-step derivations, unit analysis, and reference values.
Reviewed by Daniel Agrici, Founder & Lead Developer
Formula
tau = c + (sigma - u) * tan(phi)
Shear strength tau equals the cohesion c plus the effective normal stress (total normal stress sigma minus pore water pressure u) multiplied by the tangent of the friction angle phi. This is the Mohr-Coulomb criterion in effective stress form. When excess pore pressure is present, the effective stress is reduced, lowering the available shear strength.
Worked Examples
Example 1: Sandy Soil with Low Cohesion
Problem:Calculate shear strength of soil with c = 10 kPa, phi = 30 degrees, normal stress = 100 kPa, and pore pressure = 20 kPa.
Solution:Effective normal stress = 100 - 20 = 80 kPa\ntan(30) = 0.5774\nEffective shear strength = 10 + 80 * 0.5774 = 56.19 kPa\nTotal shear strength = 10 + 100 * 0.5774 = 67.74 kPa
Result:Effective shear strength = 56.19 kPa
Example 2: Undrained Clay Analysis
Problem:A saturated clay has undrained cohesion cu = 50 kPa and phi-u = 0 degrees under undrained conditions.
Solution:Shear strength = cu + sigma * tan(0) = 50 + 0 = 50 kPa\nUndrained strength is constant regardless of normal stress.\nThis is the total stress approach for short-term loading.
Result:Undrained shear strength = 50 kPa (constant)
Frequently Asked Questions
What is the difference between drained and undrained shear strength?
Drained shear strength applies when pore water can freely drain during loading, so no excess pore pressure builds up. This condition uses effective stress parameters c-prime and phi-prime and governs long-term stability. Undrained shear strength (Su or cu) applies when loading is too fast for drainage, common in saturated clays under rapid loading. In undrained conditions, the friction angle is effectively zero, and all resistance comes from cohesion. The choice between drained and undrained analysis depends on the loading rate relative to the permeability of the soil.
What is soil composition and how is it measured?
Soil is composed of minerals (45%), organic matter (5%), water (25%), and air (25%). Texture is classified by percentages of sand (0.05-2mm), silt (0.002-0.05mm), and clay (less than 0.002mm) using the USDA soil texture triangle. Loam, an ideal garden soil, has roughly equal parts of each.
References
Reviewed by Daniel Agrici, Founder & Lead Developer · Editorial policy