Analyze the data in Tables 1-1 and 1-2 to determine the consolidation properties

Question

Analyze the data in Tables 1-1 and 1-2 to determine the consolidation properties of the soil, and to reconstruct the field consolidation curve. Compute the void ratio at the "end of consolidation" for each increment. Table 1-1: Soil specimen properties from consolidation test specimen Water content s weights Consolidation specimen ies Vertical Wet soil &Dry; soil &ContainerDiameterHeightWeight; Specific effective container container (in) (in) (lb)gravity stress 75.9 64.2 12.6 2.5 0.362 2.72 1900 Table 1-2: Effective stress and corresponding "height at the end of consolidation" values Effective stress Specimen height in 0.603 0.597 0.579 0.550 0.491 0.499 0.512 0.503 0.485 0.452 0.403 0.393 0.406 1/2 4 4 16 4

Explanation / Answer

For consolidation to occur the soil must be saturated and hence degree of saturation S = 1

Also for soils eS = wG ; where e is void ratio , w is water content and G is specific gravity

From table 1-1

Weight of wet soil = 75.9- 12.6 = 63.3 g

Weight of dry soil = 64.2 - 12.6 = 51.6 g

Weight of water = 63.3- 51.6 = 11.7 g

Thus w = 11.7*100/ 51.6 = 22.67 or 0.2267 %

Thus e = 0.2267* 2.72 = 0.616

Now also e/ 1+e = H/ H

Thus for effective stress 0.25 tsf or 500 psf e1-e0 / 1.616 = 1-0.603 /1 =0.397

Thus e1-e0 = 0.397*1.616= 0.6415 ; thus e1= 0.6415+ 0.616 = 1.26 (rounded off to two decimal)

On similar grounds e2 corresponding to effective stress 1000 psf = 1.24

e3= 1.17

e4 = 1.06

e5 = 0.84

e6 = 0.869

e7 = 0.917

e8 = 0.883

e9 = 0.816

e10 = 0.692

e11 = 0.508

e12 = 0.47

e13 = 0.518

e14 = 0.585

Thus e1 to e14 are the values of void ratio at end of every effective stress increment or decrement as per table 1-2 above

Consolidation curve can be plotted between void ratio and effective normal stress and various consolidation parameters can be calculated

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Coeffecient of compressibility = - e/ effective stress = 1.26 -0.616 / (2000- 500 ) = 4.293 x 10^-4

Note that the negative sign in the formula of coeffecient of compressibility or av is to have a positive value .

Coeffecient of volume compressibility = mv = av / 1+e0 = 4.293x 10^-4 / 1+0.616 = 2.656 x10^-4

If coeffecient of permeability or K is known , coeffecient of consolidation could be calculated using relation

K= Cv mv Yw ,where Yw is unit weight of water

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