Terzaghi-Wegman Equation

Definition

The Terzaghi-Wegman Equation is a mathematical expression used in geotechnical engineering to analyze infinite slope stability by determining the factor of safety against sliding. This equation incorporates various factors such as soil properties, slope geometry, and external forces acting on the slope, making it essential for understanding the stability of slopes in soil mechanics. It aids engineers in predicting potential failures in slopes, allowing for better design and safety measures.

5 Must Know Facts For Your Next Test

1. The Terzaghi-Wegman Equation can be expressed as $$FS = \frac{c + (\gamma \cdot h \cdot \cos(\theta))}{\gamma \cdot h \cdot \sin(\theta)}$$, where FS is the factor of safety, c is cohesion, \gamma is unit weight, h is height of the slope, and \theta is the slope angle.
2. It accounts for both effective stress and pore water pressure in saturated soils, making it crucial for assessing the stability of slopes under varying groundwater conditions.
3. The equation is particularly useful in analyzing landslides and slope failures in natural terrains as well as in engineered slopes like embankments and cuttings.
4. The Terzaghi-Wegman Equation can be adjusted for different conditions by modifying input parameters such as cohesion, angle of internal friction, and slope height.
5. This equation emphasizes that both soil properties and external factors like rainfall or seismic activity significantly influence slope stability.

Review Questions

• How does the Terzaghi-Wegman Equation help assess slope stability in geotechnical engineering?
  • The Terzaghi-Wegman Equation assists engineers in evaluating slope stability by providing a quantitative measure of the factor of safety against sliding. By considering factors such as soil cohesion, slope height, and angle, the equation helps predict whether a slope will remain stable under various conditions. This analysis is essential for preventing landslides and ensuring the safety of structures built on or near sloped terrains.
• In what ways can changes in pore water pressure affect the calculations made using the Terzaghi-Wegman Equation?
  • Changes in pore water pressure directly impact the effective stress within soil layers, which is a key component in the Terzaghi-Wegman Equation. As pore water pressure increases—due to rainfall or saturation—the effective stress decreases, potentially lowering the factor of safety against sliding. Therefore, understanding groundwater conditions is vital when applying this equation to ensure accurate assessments of slope stability.
• Evaluate the importance of incorporating both cohesion and angle of internal friction in the Terzaghi-Wegman Equation for accurate slope stability analysis.
  • Incorporating both cohesion and angle of internal friction into the Terzaghi-Wegman Equation is crucial because these parameters reflect different aspects of soil strength. Cohesion represents the adhesive forces between soil particles that contribute to stability, while internal friction accounts for resistance due to particle interactions during shear stress. An accurate analysis of slope stability requires balancing these two forces; neglecting either can lead to misjudgments about a slope's safety and potentially catastrophic failures.

Related terms

Factor of Safety: A measure used to determine the stability of a slope, defined as the ratio of the maximum resisting forces to the driving forces acting on the slope.

Infinite Slope: A theoretical model in slope stability analysis where the slope is considered to extend infinitely in both horizontal directions, simplifying calculations.

Mohr-Coulomb Failure Criterion: A mathematical model that describes the response of materials under shear stress, often used to determine failure conditions in soil and rock mechanics.