Question

The soil in a polder consists of a clay layer of 5 meter thickness, with a porosity of \(50 \%\), on top of a deep layer of stiff sand. The water level in the clay is lowered by \(1.5\) meter. Experience indicates that then the porosity of the clay is reduced to \(40 \%\). What is the subsidence of the soil?

Short answer

Answer: The subsidence of the soil is 2.5 meters.

Step-by-step solution

Calculate initial volume of voids in the clay layer

The porosity (\(n\)) is the ratio of the volume of voids to the total volume of the soil. In this case, the initial porosity is \(50\%\). To find the initial volume of voids in the clay layer, we can use the following formula: Initial volume of voids = Initial porosity × Initial total volume of the clay layer Since the initial thickness of the clay layer is \(5\) meters, we can assume that the initial total volume of the clay layer is \(5V\), with \(V\) being the volume corresponding to a depth of \(1m\). Initial volume of voids = \(0.50 \times 5V = 2.5V\)

Calculate final porosity of the clay layer

Now that we know the initial volume of voids in the clay layer, we can calculate the final porosity of the clay layer. The exercise indicates that the final porosity is \(40 \%\). Thus, the final porosity is \(0.40\).

Calculate the final volume of the clay layer

Since the initial volume of voids decreases when the water level is lowered, we can calculate the final volume of the clay layer using the relation: Final volume of voids = Final porosity × Final total volume of the clay layer Additionally, due to the conservation of the soil solid particles: Initial total volume - Initial volume of voids = Final total volume - Final volume of voids Then, we can write the equation as: \(5V - 2.5V = (Final\ total\ volume) - 0.40 \times (Final\ total\ volume)\) We can now solve for the final total volume of the clay layer: \(2.5V = (Final\ total\ volume) × (1 - 0.40)\) \((Final\ total\ volume) = \frac{2.5V}{0.60} = \frac{5}{2}V\)

Calculate final thickness of the clay layer

Having found the final total volume of the clay layer, we can now calculate the final thickness. Since we are assuming the same volume \(V\) for every meter of clay layer thickness, the final thickness can be found by dividing the final total volume by the volume \(V\) corresponding to a depth of \(1 m\). Final thickness = \(\frac{(\frac{5}{2}V)}{V} = \frac{5}{2}\) meters

Calculate the subsidence

Now that we know the final thickness of the clay layer, we can calculate the subsidence by subtracting it from the initial thickness: Subsidence = Initial thickness - Final thickness Subsidence = \(5 - \frac{5}{2} = \frac{5}{2}\) meters Hence, the subsidence of the soil is \(2.5\) meters.

Key concepts

Soil Mechanics

Soil mechanics is a vital branch of civil engineering that involves evaluating the physical properties of soil and its behavior under different conditions. Central to understanding soil mechanics is the concept of stress and strain, where soil is observed under the effects of weight, pressure, and shifts within its structure.

For instance, when discussing the subsidence of soil as referenced in the exercises, it's crucial to note that soil structure becomes compacted when the water level decreases. This changes the stress distribution within the clay's mass, leading to a change in volume, and hence, subsidence occurs. Subsidence is particularly prevalent in clay soils because they are more compressible than sandy soils or gravel due to their fine grains and the way they absorb water.

Clay Layer Porosity

Porosity is a measure of how much void space is contained within a material, such as a layer of clay. A high porosity means a large amount of space is available for water and air, which can affect both the density and the stability of the material.

When we talk about the porosity of a clay layer, we're referring to the percentage of the clay's volume that is made up of these voids. For engineers, understanding and calculating this factor is critical, especially when predicting how the soil will respond to environmental changes, such as water table fluctuations. As seen in the exercise example, a change in porosity from 50% to 40% has a significant impact, resulting in soil consolidation and ultimately, causing subsidence.

Volume of Voids in Soil

The volume of voids within soil is the total space that exists between the soil particles. Comprehending this space is key for various applications such as understanding saturation, soil compaction, and the settlement potential.

The volume of voids is closely linked to the porosity of a soil layer. As porosity decreases, the volume of voids is reduced, indicating that the soil particles are closer together, increasing the soil's density. This is precisely what happens in the provided exercise when the water level drops and the porosity decreases. The calculation of initial and final volumes of voids is fundamental to ascertain the level of subsidence that will occur due to lowering of the water table in the clay layer.