Shear Strength of Soil
The shear strength of a soil is its resistance to shearing stresses. It is a fundamental property required to analyze the stability of slopes, the bearing capacity of foundations, and the lateral earth pressure on retaining walls.
Mohr-Coulomb Failure Criterion
The shear strength () is typically described by the Mohr-Coulomb Failure Criterion, which states that failure occurs when the shear stress on any plane reaches a critical value dependent on the normal stress on that plane.
Shear Strength Equation
Effective Stress Analysis (Drained)
$$
\tau_f = c' + \sigma' \tan \phi'
$$Total Stress Analysis (Undrained):
For saturated clays loaded rapidly, pore pressures do not dissipate.
Total Stress Analysis (Undrained)
$$
\tau_f = c_u + \sigma \tan \phi_u
$$Interactive Mohr's Circle
Visualize the state of stress and the failure envelope. Adjust the principal stresses () and soil properties () to see when failure occurs.
Mohr-Coulomb Failure Criterion
Stable
Major Stress (σ₁)100
Minor Stress (σ₃)40
Cohesion (c)10
Friction Angle (φ)30 °
If the circle touches or crosses the red failure envelope, the soil fails in shear. The radius of the circle represents the maximum shear stress ().
Pore Pressure Parameters (Skempton)
To predict how pore water pressure () will change in a saturated clay when subjected to changes in total principal stresses (), engineers use Skempton's Pore Pressure Parameters ( and ).
Skempton's Equation
The change in pore water pressure () during undrained loading is given by:
Skempton's Pore Pressure Equation
$$
\Delta u = B [ \Delta \sigma_3 + A (\Delta \sigma_1 - \Delta \sigma_3) ]
$$Laboratory Tests
To determine the shear strength parameters (), several laboratory tests are used.
Direct Shear Test
A sample is placed in a split box and sheared along a predetermined horizontal plane.
- Procedure: Apply normal load (), then apply shear force () until failure. Repeat for different normal loads.
- Advantages: Simple, inexpensive, good for sands.
- Disadvantages: Failure plane is forced, stress distribution is non-uniform, drainage is hard to control.
Triaxial Test
A cylindrical sample is encased in a rubber membrane and subjected to confining pressure (). An axial load () is increased until failure.
- UU (Unconsolidated-Undrained): Quick test. Simulates end-of-construction stability for saturated clays. ().
- CU (Consolidated-Undrained): Sample consolidated under , then sheared undrained. Pore pressure () is measured to get effective strength parameters ().
- CD (Consolidated-Drained): Slow test. Excess pore pressure dissipates completely. Simulates long-term stability. ().
Unconfined Compression Test (UCT)
A special case of the triaxial test where confining pressure .
- : Unconfined compressive strength.
- : Undrained shear strength.
- Suitable only for cohesive soils (clays).
Field Tests
Vane Shear Test (VST)
Used for soft to stiff clays. A four-bladed vane is pushed into the soil and rotated.
Vane Shear Strength
$$
c_u = \frac{T}{\pi \left( \frac{d^2 h}{2} + \frac{d^3}{6} \right)}
$$Key Takeaways
- Shear Strength depends on cohesion () and friction angle ().
- Mohr's Circle is used to represent the stress state at a point. Failure occurs when the circle touches the Failure Envelope.
- Effective Stress Parameters () govern long-term stability and drained conditions.
- Total Stress Parameters () govern short-term stability in saturated clays (End-of-Construction).
- Skempton's Parameters ( and ) are essential for predicting undrained pore pressure responses to loading.
- Triaxial Tests (UU, CU, CD) provide the most comprehensive data on soil strength and pore pressure behavior.