Question

Geotechnical Engineering

5. Describe the dipole structure of water molecules in detail.

6. Describe the Gouy-Chapman theory of diffuse-double layer in detail.

7. Describe Atterberg limits in detail.

8. What is PI and describe its impact on the properties of soil.

Answer 1

ANSWER:

5 . Dipole structure of water molecules:

The water molecule forms an angle, with hydrogen atoms at the tips and oxygen at the vertex. Since oxygen has a higher electronegativity than hydrogen, the side of the molecule with the oxygen atom has a partial negative charge. A molecule with such a charge difference is called dipole.

Water is a unique compound that is essential to life on Earth. In the pedosphere, the physical and chemical properties of water regulate the flow of energy and solutes, making soil water a crucial component of terrestrial ecosystems. Many of the familiar properties of water that result in its behavior in soils can be directly related to its molecular structure.

6 . Gouy-Chapman theory of diffuse-double layer :

Gouy suggested that interfacial potential at the charged surface could be attributed to the presence of a number of ions of given sign attached to its surface, and to an equal number of ions of opposite charge in the solution. In other words, counter ions are not rigidly held, but tend to diffuse into the liquid phase until the counter potential set up by their departure restricts this tendency. The kinetic energy of the counter ions will, in part, affect the thickness of the resulting diffuse double layer. Gouy and, independently, Chapman developed theories of this so called diffuse double layer in which the change in concentration of the counter ions near a charged surface follows the Boltzman distribution.

n = n_oexp(-zeY/kT)

where n_o = bulk concentration
z = charge on the ion
e = charge on a proton
k = Boltzmann constant

Already, however, we are in error, since derivation of this form of the Boltzman distribution assumes that activity is equal to molar concentration. This may be an OK approximation for the bulk solution, but will not be true near a charged surface.
Now, since we have a diffuse double layer, rather than a rigid double layer, we must concern ourselves with the volume charge density rather than surface charge density when studying the coulombic interactions between charges. The volume charge density, r , of any volume, i, can be expressed as

r_i = Sz_ien_i

The coulombic interaction between charges can, then, be expressed by the Poisson equation. For plane surfaces, this can be expressed as

d²Y/dx² = -4pr/d

where Y varies from Y_o at the surface to 0 in bulk solution. Thus, we can relate the charge density at any given point to the potential gradient away from the surface.
Combining the Boltzmann distribution with the Poisson equation and integrating under appropriate limits, yields the electric potential as a function of distance from the surface. The thickness of the diffuse double layer:

l_double = [e_rkT/(4pe²Sn_ioz_i²)]^1/2

at room temperature can be simplified as

l_double = 3.3*10⁶e_r/(zc^1/2)

in other words, the double layer thickness decreases with increasing valence and concentration.

The Gouy-Chapman theory describes a rigid charged surface, with a cloud of oppositely charged ions in the solution, the concentration of the oppositely charged ions decreasing with distance from the surface. This is the so-called diffuse double layer.

7 .  Atterberg limits:

The Atterberg limits are a basic measure of the critical water contents of a fine-grained soil: its shrinkage limit, plastic limit, and liquid limit.

Depending on its water content, a soil may appear in one of four states: solid, semi-solid, plastic and liquid. In each state, the consistency and behavior of a soil is different and consequently so are its engineering properties.

Thus, the boundary between each state can be defined based on a change in the soil's behavior. The Atterberg limits can be used to distinguish between silt and clay, and to distinguish between different types of silts and clays.The water content at which the soils changes from one state to the other are known as consistency limits or Atterberg's limit.

Shrinkage limit:

The shrinkage limit (SL) is the water content where further loss of moisture will not result in any more volume reduction. The test to determine the shrinkage limit is ASTM International D4943. The shrinkage limit is much less commonly used than the liquid and plastic limits.

Plastic limit:

The Plastic Limit (PL) is determined by rolling out a thread of the fine portion of a soil on a flat, non-porous surface. The procedure is defined in ASTM Standard D 4318. If the soil is at a moisture content where its behavior is plastic, this thread will retain its shape down to a very narrow diameter. The sample can then be remolded and the test repeated. As the moisture content falls due to evaporation, the thread will begin to break apart at larger diameters.

The plastic limit is defined as the moisture content where the thread breaks apart at a diameter of 3.2 mm (about 1/8 inch). A soil is considered non-plastic if a thread cannot be rolled out down to 3.2 mm at any moisture possible.

Liquid limit:

The liquid limit (LL) is conceptually defined as the water content at which the behavior of a clayey soil changes from the plastic state to the liquid state. However, the transition from plastic to liquid behavior is gradual over a range of water contents, and the shear strength of the soil is not actually zero at the liquid limit. The precise definition of the liquid limit is based on standard test procedures.

8 . what is PI:

The plasticity index (PI) is a measure of the plasticity of a soil. The plasticity index is the size of the range of water contents where the soil exhibits plastic properties. The PI is the difference between the liquid limit and the plastic limit (PI = LL-PL). Soils with a high PI tend to be clay, those with a lower PI tend to be silt, and those with a PI of 0 tend to have little or no silt or clay.

Impacts and properties of soil PI:

The soils are classified and identified based on index properties. Main index property for coarse grained soil are particle size and relative density and for fine grained, they are attenbeg's limits and the consistency.

Plastic Index properties are the simple physical properties of the soils, which are used for classification of soils for various engineering applications. They indicate a qualitative behaviour of soil when subjected to various types of load. They can be listed as given below:

1. Water content
2. Specific gravity
3. Grain size distribution
4. Plasticity properties popularly known as Atterberg limits (Liquid limit, Plastic limit and Shrinkage limit) and their indices like plasticity Index, Liquidity Index, Consistency Index, Shrinkage Index.
5. In-situ density
6. Relative density.