Effective Stress in Soil Mechanics Cheat Sheet

Effective stress is the stress carried by the soil skeleton, crucial for understanding soil behavior, strength, and deformation. It's calculated by subtracting pore water pressure from total stress.

Core Principles

• Total Stress (σ): The total force per unit area acting on a plane within the soil mass.
• Pore Water Pressure (u): The pressure of water within the soil voids, acting equally in all directions.
• Effective Stress (σ'): The stress transmitted through the soil skeleton via grain-to-grain contacts.
• Terzaghi's Principle: σ = σ' + u, fundamental for saturated soils.
• Seepage Force: Water flow through soil creates a force that can reduce effective stress.
• Quick Condition: Occurs when upward seepage pressure cancels effective stress, leading to loss of shear strength.
• Critical Hydraulic Gradient (icr): The gradient at which effective stress becomes zero.
• Factor of Safety (FS): Ratio of critical gradient to actual gradient (FS = icr / i) for heave failure.

Action Steps

• Identify soil layers and their properties (unit weights).
• Determine the water table level.
• Calculate total vertical stress (σv) at different depths.
• Calculate pore water pressure (u) based on depth below the water table.
• Calculate effective vertical stress (σ'v) using σ'v = σv - u.
• Analyze seepage effects if flow is present.
• Determine the critical hydraulic gradient (icr) for the soil.
• Calculate the actual hydraulic gradient (i) in the scenario.
• Compute the Factor of Safety (FS = icr / i) against heave failure.

Formulas

• $ \sigma = \sigma' + u $
• $ \sigma' = \sigma - u $
• $ \sigma_v = \gamma \cdot z $ (for uniform soil, vertical stress)
• $ u = \gamma_w \cdot z_w $ (hydrostatic pore-water pressure)
• $ j = i \gamma_w $ (seepage pressure)
• $ i_{cr} = \frac{\gamma'}{\gamma_w} = \frac{G_s - 1}{1 + e} $ (critical hydraulic gradient)
• $ \gamma' = \gamma_{sat} - \gamma_w $ (effective/buoyant unit weight)
• $ FS = \frac{i_{cr}}{i} $ (Factor of safety against heave failure)

Key Terms

• Total Stress: The total load per unit area acting on a soil element.
• Pore Water Pressure: The pressure exerted by the water within the voids of the soil.
• Effective Stress: The stress carried by the soil particles, controlling soil strength and deformation.
• Seepage: The flow of water through the pores of a soil mass.
• Quick Condition: A state where effective stress is zero due to upward seepage, causing liquefaction.
• Hydraulic Gradient: The change in total head per unit length of flow path.
• Critical Hydraulic Gradient: The hydraulic gradient at which the effective stress in a soil becomes zero.

Real World Examples

• Calculating stresses under a foundation.: Determining the load-bearing capacity and potential settlement of the soil.
• Analyzing slope stability.: Understanding how pore water pressure affects the shear strength of soil on slopes.
• Sheet pile wall design.: Assessing the risk of heave failure (boiling) at the toe of the excavation.
• Dam seepage analysis.: Evaluating the potential for internal erosion and instability due to water flow.

People

• Karl Terzaghi: Pioneer of Soil Mechanics, formulated the effective stress principle.