Coefficient of compressibility:
The coefficient of compressibility is defined as the decrease in void ratio per unit increase in effective stress. It is equal to the slope of the pressure void curve as shown in the figure.
`a_v=-(triangle e)/(triangle sigma')`......(i)
Fig:pressure void ratio curve
The above equation shows that the coefficient of compressibility decreases with increase in effective stress. The above question gives the slope of pressure void curve drawn to a natural scale. This curve has a negative slope which indicate that void ratio decreases as the pressure increases. The slope,`(triangle e)/(triangle sigma')` is called the coefficient of compressibility and is denoted by `a_v`. Thus,in other words the coefficient of compressibility represent the change in void ratio with the change in pressure .
Coefficient of Volume Change:
The coefficient of volume change or volume compressibility is defined as the volumetric strain per unit increase in effective stress.i.e,
`M_v=((triangle V)/V_0)/(triangle sigma)`
Where,
`M_v=`Coefficient of volume change
`V_0=` initial volume
`triangle V=` change in volume
`triangle sigma=` change in effective stress
Let `e_0` be the initial void ratio. let the volume of solid be unity. Therefore, the initial volume `V_0` is equal to `1+e_0`. If `triangle e` is the change in void ratio due to change in volume, we have `triangle V=triangle e`.Thus,
`(triangle V)/(V_0)=(triangle e)/(1+e_0)=`
Thus, the coefficient of volume change is
`m_v=-(triangle e)/(1+e_0)*1/(triangle sigma') `
`Or,m_v=a_v/(1+e_0)`
Compression Index:
The compression index `c_c` is defined as the slope of the linear portion of the void ratio versus `log sigma `plot as shown in the figure .
Thus,
`c_c=-(triangle e)/(log_(10)((sigma') /(sigma'_0)) `.....(i)
Where,
`sigma'=`Final effective stress
`sigma_0=`Initial efffective stress
`triangle e=`Change in void ratio
Or, `c_c=- (triangle e)/(log_(10)((sigma'_0+triangle sigma')/(sigma'_0))) `.........(ii)
Where,
`triangle sigma'=`Change in effective stress
The compression index is extremely useful for determination of the settlement in the field. the compression Index of a clay is related to its index properties, especially the liquid limit. Terzaghi and Peck gave the following empirical relationship for clay of low to medium sensitivity
For undisturbed soils,
`c_c=0.009(w_l-10)`
For remolded soils,
`c_c=0.007(w_l-10)`
Expansion Index:
The expansion or swelling index `c_e` is defined as the slope of the void ratio versus `log sigma `plot obtained during unloading (`BEC` in figure).
`c_e=(triangle e)/(log_(10)((sigma'+triangle sigma')/(sigma')))`
Recompression Index:
Recompression is the compression of a soil which had already been loaded and unloaded.The load during the recompression is less than the load to which the soil has been subjected previously. The slope of the recompression curve obtained during reloading (`CFD` in figure) when plotted as the void ratio versus `log sigma ` is equal to the recompression index. Thus,
`c_r=-(triangle e)/(log_(10)((sigma'+triangle sigma')/(sigma')))`
In above figure, the curve AB indicates the decrease in void ratio with an increase in the effective stress.After the sample has reached equilibrium at the effective stress of `sigma_2`, as shown by point B, the pressure is reduced and the sample is allowed to take up water and swell. The curve `BEC` is obtained in unloading. This is known as expansion curve or swelling curve. It may be noted that the soil cannot attain the void ratio existing before the start of the test, and there is always some permanent set or residual deformation.
If the specimen which has swelled to the point C is reloaded, the recompression curve `CFD` is obtained. As the load approaches the maximum value of the load previously applied corresponding to point B, there is reversal of curvature of the curve and then the plot `DG` continues as an extension of the first loading curve `AB`. However, the reloaded specimen remains at a slightly lower void ratio at point `D` than that attained at `B` during the initial compression for the same load.
Normally Consolidated and Over Consolidated Clays:
A clay is said to be normally consolidated if the present effective overburden in pressure is the maximum pressure to which the layer has ever been subjected at any time in its history. That is, if the clay has not been consolidated with stress greater than the present stress, it is called normally consolidated clay.
A clay layer is said to be over-consolidated if the layer was subjected at one time in its history to a greater effective overburden pressure than the present pressure. That is, if the clay has already been subjected to a stress greater than the present stress, it is called overconsolidated clay.
The reasons for over consolidation may be due to following factors:
Weight of an overburden of soil which has eroded.
Construction and unload through the demolition of structure.
Groundwater movement and increase in pore water pressure.
Due to melting of glaciers which covered the soil deposit in the past.
Due to tectonic forces caused by the moment of earths crust.
Due to this desiccation of clay deposit.
The portion `AB` of the above curve represents the soil in normally consolidated condition. The curve in this range is also called the virgin compression curve. The soil in the range CD when it is recompressed represents over-consolidated condition, as the soil had been previously subjected to a pressure `sigma_2`, which is greater than the pressure in the range `CD`.
The maximum pressure to which an overconsolidated soil had been subjected in the past divided by the present pressure is known as overconsolidation ratio (O.C.R).
`OCR=P_c/P_0=(sigma'_c)/(sigma')`
Where,
`P_c (sigma_c)=`maximum effective past pressure
`P_0 (sigma')=`present effective pressure
For normally consolidated clay, `OCR~~1`
For over consolidated clay, `OCR>1`
For example, the soil indicated by the condition at point C as an overconsolidation ratio of `(sigma_2)/(sigma_1)`.
It may be emphasized that normally consolidated soil and overconsolidated soils are not different types of soil but these are the condition in which a soil exists. The same type of soil can behave as a normally consolidated in a certain pressure range and an overconsolidated in some other pressure range. For example, in figure the soil which behaves as overconsolidated In the range `CD` would again behave as normally consolidated in the range `DG`.
The liquidity Index of a normally consolidated clay is generally between 0.6 and 1.00, where is that for Innova consolidated clay is between 0.0 and 0.60.
As the recompression index is very small as compared with the compression index, the soil in the overconsolidated state have smaller compressibility.
If the clay deposit has not reached equilibrium under the applied overburden loads, it is said to be under-consolidated. It is the one which is still to be fully consolidated under the existing overburden pressure. This normally occurs in areas of recent landfills.
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