## What is consolidation?

Consolidation is the process of expulsion of pore water present in the voids of soil solids under the pressure of the applied load. This is a quick process in the case of coarse-grained soils since the permeability is high due to the presence of more voids, while it is a slow and gradual process in the case of clayey soil as the permeability of clay is less. An example of consolidation is the settlement of soil under a building due to the load coming from the building.

## Stages of consolidation

### Initial consolidation

The initial decrease in the volume of the partially saturated soil is caused by the expulsion of air voids on the addition of load. In the case of fully saturated soil, the initial consolidation occurs due to the compression of the soil solids.

### Primary consolidation

When the volume of the soil is reduced due to the expulsion of pore water from the voids after the initial consolidation, all the applied stress is taken up by the excess pore water.

### Secondary consolidation

The gradual reduction in the volume of the soil after initial and primary consolidation is called as secondary consolidation. This process may take up years in fine-grained soils such as clay.

## Laboratory tests for consolidation

This laboratory test is also known as the standard odometer test. The consolidation test is used to measure the magnitude of consolidation and to determine the consolidation parameters such as coefficient of consolidation, coefficient of compressibility, coefficient of volume compressibility, and compression index. These consolidation parameters play a vital role in the field of construction.

Consolidometers is an instrument with loading frames to measure the consolidation of soil. Consolidometer Accessories include Consolidation Ring Porous Stones (enable the drainage of water from the fine-grained soil sample), Reservoir, filled with water to ensure that the soil remains essentially saturated. The interface of stone and soil surface is separated by a filter paper to prevent blockage of stone pores by soil particles. Consolidation cell, dial gauges, loading device are the apparatus used in this test.

On applying the load, the soil sample starts deforming along with the loading frame. The vertical deformation of the soil is measured using a dial gauge from which the values of deformation of loading frame and porous stones are subtracted. After positioning the dial gauge, the height, diameter, and weight of the confining ring are measured. The specimen is trimmed to the size of the ring.

The load is applied and is constantly maintained for 24 hrs and this loading time is increased to 48 hours for clayey soil. After this period, the load is increased by doubling the applied stress. During the test process, the soil sample is kept saturated by adding water to the consolidation cell. After application of each load, the reading of deformation from the dial gauge is noted at 0, 1/4, 1/2, 1, 2, 4, 8, 15, 30, 60 min, and 2, 4, 8, 24 hour(s) to plot the settlement curve. When the loading reaches its maximum stage, the unloading is done by reducing the load by a factor of 4 in each step. At the end of the test, the final height and water content of the sample are noted.

## Consolidation parameters derived from the Oedometric test

### Determination of Consolidation coefficient (C_{v})

#### Time-fitting method

This is a laboratory-based method for determining consolidation coefficient. In this method, the graph for the theoretical relationship between time factor and degree of consolidation is plotted and for a practical relationship, the dial gauge readings and the total time taken is plotted. Then those two parameters are correlated either by the square root of the time-fitting method or logarithmic of the time-fitting method.

${C}_{v}=\frac{{T}_{50}{d}^{2}}{{t}_{50}}$

where,

T_{50}= time factor for 50% consolidation,

d= length of the drainage path

t_{50}= time required for 50% consolidation

#### Square root of time fitting method

The theoretical curve is plotted between the square root of the time factor (âˆšTv ) at the X-axis and the degree of consolidation (U) at the Y-axis. The practical curve is plotted for the square root of elapsed time (âˆšt Â ) X-axis and dial gauge reading at Y-axis.

#### Logarithmic of time fitting method

Theoretical curve is plotted between the time factor on a logarithmic scale (log_{10}T_{v}) at X-axis and the degree of consolidation (U) at Y-axis. The practical curve is plotted for the square root of elapsed time in logarithmic scale (log_{10}t) at X-axis and dial gauge reading at Y-axis

### Determination of coefficient of compressibility (a_{v})

It is the ratio of change in void ratio to change in effective stress. It can be obtained from the slope of the graph plotted in-between void ratio on the Y-axis and effective stress on the X-axis. The minus sign indicates that for every increase in effective stress, the void ratio decreases.

${a}_{v}=-\frac{\xe2\u02c6\u2020e}{\xe2\u02c6\u2020\mathrm{\xcf\u0192}}$

$\xe2\u02c6\u2020e$- Change in void ratio

$\xe2\u02c6\u2020\mathrm{\xcf\u0192}$- Change in effective stress

### Determination of Volume compressibility (m_{v})

It is the volumetric strain per unit increase in the effective stress.

${m}_{v}=\frac{{a}_{v}}{1+{e}_{0}}$

${e}_{0}$- initial void ratio of the soil

${a}_{v}$- compressibility coefficient

### Determination of Compression index (C_{c})

${C}_{c}=\frac{{e}_{1}-{e}_{2}}{\mathrm{log}\left({\mathrm{\xcf\u0192}}_{1}\right)-\mathrm{log}\left({\mathrm{\xcf\u0192}}_{2}\right)}\phantom{\rule{0ex}{0ex}}$

where,

${e}_{1}=initialvoidratiobeforeconsolidation\phantom{\rule{0ex}{0ex}}{e}_{2}=finalvoidratioafterconsolidation\phantom{\rule{0ex}{0ex}}{\mathrm{\xcf\u0192}}_{1},{\mathrm{\xcf\u0192}}_{2}=successivevaluesofappliedeffectivestress$

## Context and Applications

Consolidation has a wide range of applications in the field of Geotechnics and foundation engineering.

- Bachelors of Technology in Civil Engineering
- Bachelors of Technology in Geotechnical Engineering
- Masters of Technology in Geotechnical Engineering

## Practice Problems

1. What is a pressure meter in soil mechanics?

- An instrument used to measure the porosity of soil
- An instrument used to measure the stress-strain response of the tested soil
- An instrument used to measure plasticity of soil
- An instrument used to measure the compressibility of soil

Answer: Option b

Explanation: A pressure meter is a device that is used to determine the stress-strain relations of in-situ soil by pumping it into a certain depth of the borehole.

2. What is soil modulus?

- A measure of the soil stiffness or elasticity
- A measure of effective stress of soil
- A measure of the void ratio of soil
- A measure of the soil consolidation process of subsoil stratum

Answer: Option a

Explanation: Soil Young's modulus (E), also known as soil elastic modulus, is a measure of soil stiffness. It is the ratio of the stress along an axis over the strain along that axis in the range of elastic soil behavior.

3. What do NCC and OCC soils stand for?

- Normally consolidated Clay and over-consolidated Clay
- Normally Compacted Clay and Over Compacted Clay
- Normally Compressible Clay and Over Compressible Clay
- Normally Consolidated Coarse soils and Over Consolidated Coarse soils

Answer: Option a

Explanation: Normally consolidated clay and over consolidated clay soils indicate the pre-consolidation or over consolidation pressure, the soil has undergone in the past.

4. What is subsidence of soil?

- Correction of uneven distribution of soil
- Increment of stress on undisturbed soil
- Movement of subsoil due to sudden expulsion of pore water
- Movement of subsoil due to uneven distribution of soil solids

Answer: Option c

Explanation: Movement of subsoil due to sudden expulsion of pore water due to various human activities.

5. What is DMT in geotechnical engineering?

- Test to determine deformation characteristics of fine-grained soil
- Test to determine deformation characteristics of coarse-grained soil
- Test to determine recompression of fine-grained soil
- Test to determine recompression of coarse-grained soil

Answer: Option a

Explanation: It is an on-field test used to determine the lateral stress and deformation of fine-grained soils.

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