1.2. One dimensional theory hypothesis

Assumptions:

• The soil medium is completely saturated
• The soil medium is isotropic and homogeneous
• Darcy’s law is valid for flow of water
• Flow is one dimensional in the vertical direction
• The coefficient of permeability is constant
• The coefficient of volume compressibility is constant
• The increase in stress on the compressible soil deposit is constant
• Soil particles and water are incompressible

One Dimensional Theory relies on specific assumptions to simplify analysis. First, it assumes the soil is saturated, meaning all voids are filled with water. This is crucial for calculating flow dynamics. Next, it assumes isotropy and homogeneity, indicating the soil behaves uniformly in all directions under the same conditions. Darcy’s law is essential as it describes how water flows through soil. The theory posits that flow is unidirectional (up or down), and that both the permeability of the soil and its volume compressibility do not change as pressure changes. Additionally, it assumes that any increases in stress on the soil will be consistent, and that both soil and water can be treated as incompressible for these calculations.

Imagine a sponge (the soil) that is soaked in water (the pore water). The assumptions are like saying that the sponge is made of a uniform material that behaves the same in every direction and can’t be squeezed. When you push down on it, the water will flow out from the same point where you are applying pressure without any twists or turns, making it easier to predict how it will respond.

One dimensional theory is based on the following hypothesis

1. The change in volume of soil is equal to the volume of pore water expelled.
2. The volume of pore water expelled is equal to change in volume of voids.
3. Since compression is in one direction the change in volume is equal to change in height.

This part of the theory outlines key hypotheses. First, it states that when soil consolidates, the volume change in the soil corresponds directly to the amount of pore water that has been expelled. This makes sense because as pressure increases, the water has to go somewhere. Additionally, it highlights that the volume of water expelled is equal to the change in volume of the voids (spaces in the soil). Finally, it asserts that because the compression of the soil is happening only in one direction (vertically), the change in the soil's volume can be equated to the change in its height.

Think of a jar filled with marbles (the soil) and water (the pore water). If you were to press down on the jar, it would compress the marbles together, forcing water out. The decrease in space between marbles (voids) directly relates to how much water you see spilling out. Here, the jar being compressed explains how the height of the jar changes as you push down.

The increase in vertical stress at any depth is equal to the decrease in excess pore water pressure at the depth.

This statement emphasizes the relationship between stress and pore water pressure in the soil. When additional weight or stress is applied to the soil surface, it generates excess pore water pressure at various depths within the soil. This theory asserts that as the vertical stress increases, there should be a corresponding decrease in pore water pressure, balancing the hydrostatic pressures within the soil layers.

Consider a sponge sitting in a bowl of water. When you press on the sponge (adding stress), you can feel the water squeezing out from the sponge, which represents the excess pore water pressure. As you apply more pressure, the sponge compresses further, and more water is expelled, reducing the internal pressure of the water in the sponge.

Limitations of 1D consolidation

1. In the deviation of 1D equation the permeability (Kz) and coefficient of volume compressibility (mv) are assumed constant, but as consolidation progresses void spaces decrease and this results in decrease of permeability and therefore permeability is not constant. The coefficient of volume compressibility also changes with stress level. Therefore Cv is not constant
2. The flow is assumed to be 1D but in reality flow is three dimensional.
3. The application of external load is assumed to produce excess pore water pressure over the entire soil stratum but in some cases the excess pore water pressure does not develop over the entire clay stratum.

Despite being a useful model, one-dimensional consolidation has key limitations. Firstly, the assumption that permeability and compressibility are constant fails with real-world consolidation because as soil compresses, voids decrease, affecting water flow. Additionally, while the theory simplifies flow to one dimension, actual water movement can occur in multiple directions, complicating calculations. Lastly, the theory supposes that loading creates uniform excess pore water pressure throughout the soil layers, which is often not the case, as this pressure may develop unevenly in practice.

Imagine trying to fit a balloon (the soil) into a tight box (the external load). If you keep pushing it in, the balloon may not compress evenly, and some areas may bulge out instead of pushing uniformly. The fact that air can escape in multiple directions represents the real-life complexity of fluid flow that the one-dimensional model cannot capture.

--