Assumption made in Terzaghi's consolidation theory:

Terzaghi's consolidation theory is a widely used theory in geotechnical engineering to analyze the settlement of saturated cohesive soils. The theory makes several assumptions to simplify the analysis. The correct answer is option 'D', which means that all of the following assumptions are made in Terzaghi's consolidation theory:

1. Soil is saturated: The theory assumes that the soil is fully saturated with water. This assumption is necessary because the consolidation process is primarily driven by the flow of water within the soil.

2. Compression is one-dimensional: Terzaghi's theory assumes that the consolidation and settlement of soil occur only in the vertical direction. This assumption simplifies the analysis by considering the soil as a one-dimensional system.

3. The coefficient of permeability is constant: The theory assumes that the coefficient of permeability (hydraulic conductivity) of the soil remains constant throughout the consolidation process. This assumption allows for a simplified analysis of the flow of water through the soil.

Explanation:

1. Soil is saturated: The assumption of soil saturation is crucial because it allows for the flow of water through the soil during the consolidation process. The presence of water in the soil affects its mechanical behavior and plays a significant role in the settlement process.

2. Compression is one-dimensional: The assumption of one-dimensional compression simplifies the analysis by considering the soil as a series of vertical layers. This assumption allows for the use of one-dimensional consolidation equations, which are easier to solve compared to three-dimensional equations.

3. The coefficient of permeability is constant: The assumption of a constant coefficient of permeability allows for a simplified analysis of the flow of water through the soil during consolidation. It assumes that the soil's permeability properties do not change significantly during the consolidation process.

These assumptions are made to simplify the analysis and make it more manageable. While they may not capture all the complexities of real-world soil behavior, they provide a reasonable approximation for many engineering applications. It is important to note that these assumptions may not hold true in all cases, and engineers should consider the specific conditions and properties of the soil being analyzed.