Effective Stress And Permeability Civil Engineering GATE Notes

Effective Stress and Permeability are crucial concepts in soil mechanics for Civil Engineering GATE preparation. Effective stress controls the strength and deformation behaviour of soil, influencing its stability and load-bearing capacity. 

Permeability, on the other hand, defines the ability of soil to transmit water, which impacts drainage and settlement in structures. Understanding these topics is essential for designing foundations, retaining walls, and analyzing embankment stability. Mastery of Effective Stress and Permeability is vital for GATE aspirants aiming to excel in soil mechanics and tackle related questions in the exam, as well as in real-world civil engineering applications.

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Effective Stress And Permeability Civil Engineering GATE Notes

Effective Stress

Effective stress (σ') is the stress carried by the soil skeleton. It is the inter-granular pressure. It controls soil strength and volume change. Total stress (σ) is the sum of effective stress and pore water pressure (u).

• Total Stress (σ): Total load per unit area. It includes the weight of soil and any applied external loads.

• Pore Water Pressure (u): Pressure exerted by water in the soil voids. It acts equally in all directions.

• Effective Stress (σ'): The stress transmitted through grain-to-grain contacts. It determines how soil behaves.

The principle of effective stress states:

Therefore,

Factors Affecting Effective Stress

Effective stress changes with groundwater level fluctuations.

• Rising Water Table: Increases pore water pressure, decreasing effective stress. This reduces soil strength.

• Lowering Water Table: Decreases pore water pressure, increasing effective stress. This increases soil strength.

• Applied Loads: Directly increase total stress, thus increasing effective stress (if pore pressure remains constant).

Permeability

Permeability is a soil's ability to transmit water through its interconnected pores. It is a key parameter for seepage analysis. Hydraulic conductivity (k) quantifies this property.

Darcy's Law

Darcy's Law describes fluid flow through porous media. It states that the flow rate is proportional to the hydraulic gradient.

Where:

• Q = Total discharge (volume per unit time)

• k = Coefficient of permeability (hydraulic conductivity)

• i = Hydraulic gradient (h/L)

• A = Cross-sectional area of flow

Coefficient of Permeability (k)

The coefficient of permeability depends on soil properties and fluid properties.

• Soil Properties: Particle size, void ratio, soil structure, shape of particles.

• Fluid Properties: Viscosity, density, temperature.

Factors Affecting Permeability

• Particle Size: Larger particles mean larger voids and higher permeability.

• Void Ratio: Higher void ratio means more space for water to flow, increasing permeability.

• Degree of Saturation: Unsaturated soils have lower permeability due to air pockets.

• Soil Structure: Flocculated structures usually have higher permeability than dispersed structures.

Below are typical permeability values for different soil types:

• Gravel: Typical Permeability k > 10^-1 cm/s

• Sand: Typical Permeability k from 10^-1 to 10^-3 cm/s

• Silt: Typical Permeability k from 10^-3 to 10^-7 cm/s

• Clay: Typical Permeability k < 10^-7 cm/s

Check: GATE Civil Engineering Notes

Key Rules of Effective Stress And Permeability

The Principle of Effective Stress

The principle of effective stress, established by Terzaghi, states that soil's engineering properties depend on effective stress, not total stress. Any change in total stress or pore water pressure directly impacts effective stress. This principle is fundamental for predicting soil behaviour under various loading conditions. For example, consolidation settlement is primarily due to changes in effective stress.

Darcy's Law for Permeability

Darcy's Law is crucial for understanding water movement through soil. It applies under laminar flow conditions, common in most soils. The law connects flow rate, hydraulic conductivity, and hydraulic gradient. It is widely used in seepage calculations, groundwater flow modelling, and dewatering designs in civil engineering projects. Its validity depends on the Reynolds number of the flow.

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