4. You are at a spa and are presented with a mud mask. Being a very particular e

Question

4. You are at a spa and are presented with a mud mask. Being a very particular engineering geologist, you say that you only use mud masks that have a saturated unit weight (?m) that is less than 20 kN/m3. The esthetician tells you that the mask has a moisture content (w) of 43%.he specific gravity of the solid matter is 2.70. Do you apply it? Also, calculate the void ratio (e), and the volumetric water content (?). (Hint: you will have derived the expressions for Gs and Gm in terms of n and w from problem 2).

Explanation / Answer

Saturated unit weight means total density of the material when it is saturated.So we will calculate the total density of the given mask material first and then compare it with 20kN/m3.

So let us take 100 g of the given material. Then as per question it has 43% moisture i.e. water content. And we know that density of water is 1g/cc. So in 100 g of sample 43g is water which gives the the density of the 43% of the sample as 43g/cc.

Now the density of the solid part i.e (100-43)% = 57% . Its specific gravity is 2.70. Hence it will contribute as (2.70*57)g/cc =153.9g/cc.

finally we have total density of 100 g of the material as { 43g/cc (moisture) + 153.9g/cc (solid part) } = 196.9g/cc

it is for 100 g of the sample. So for 1 g of the sample it will be 196.9/100 =1.969g/cc

Now to convert 1.969g/cc in kg/m3 it should be multiplied by 1000. It gives the value 1969kg/m3.

Converting it again into kN/m3 we will multiply it by 9.8m/s2 (acceleration due to gravity) as 1kg*9.8m/s2 = 9.8N

So 1969*9.8= 19296.2 N/m3 = 19.2962 kN/m3 (1kN=1000N)

As 19.2962kN/m3 < 20 kN/m3 therefore that mud mask can be used.

For Void ratio we will have to calculate the volume of voids i.e. vol of water and vol of solid part.

vol of water=43cc as density of water is 1g/cc.

As specific graviy of solid is 2.70 means 2.7 g is present in 1 cc. So in 57 g (as calculated above) will be available in (1/2.7)*57 cc= 21.11cc

Void ratio = (volume of water containg voids) / (vol. of solid) =43/21.11 = 2.03

volumetric water content = (Vol of water) / Total Volume = 43/(43+21.11) =43/64.11 = 0.67

(as vol of water = 43cc and that of total =21.11cc i.e. for solid plus 43cc)

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