Normal Stress given Shear Strength of Cohesionless Soil Calculator

Normal Stress Formula:

\[ \sigma_{nm} = \frac{\tau_s}{\tan(\phi)} \]

Normal Stress (σₙₘ):

1. What is Normal Stress in Cohesionless Soil?

Definition: Normal stress (σₙₘ) is the stress component acting perpendicular to the shear plane in a soil mass, calculated from shear strength and internal friction angle.

Purpose: This calculation helps geotechnical engineers analyze soil stability and design appropriate foundations or retaining structures.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \sigma_{nm} = \frac{\tau_s}{\tan(\phi)} \]

Where:

\( \sigma_{nm} \) — Normal stress (MPa)
\( \tau_s \) — Shear strength (MPa)
\( \phi \) — Angle of internal friction (degrees)

Explanation: The shear strength is divided by the tangent of the internal friction angle to determine the normal stress acting on the failure plane.

3. Importance of Normal Stress Calculation

Details: Accurate normal stress determination is crucial for slope stability analysis, bearing capacity calculations, and earth pressure determination.

4. Using the Calculator

Tips: Enter the shear strength in MPa, internal friction angle in degrees, and optional tolerance percentage (default ±5%). All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is a typical angle of internal friction for soils?
A: For cohesionless soils: 28-42° for sand, 30-45° for gravel. Higher values indicate more frictional resistance.

Q2: Why include a tolerance percentage?
A: The tolerance accounts for measurement uncertainties and natural variability in soil properties.

Q3: Can this calculator be used for cohesive soils?
A: No, this formula is specifically for cohesionless soils. Cohesive soils require additional parameters like cohesion.

Q4: How is shear strength determined?
A: Typically through direct shear tests or triaxial tests in a geotechnical laboratory.

Q5: What if I get negative normal stress?
A: This indicates invalid input values. Both shear strength and friction angle must be positive.