e=Vvoid/Vgrain PHYS 2133: Engineering Physics I ws01: Measurements: SP1.02 Objec
ID: 1524235 • Letter: E
Question
e=Vvoid/Vgrain
PHYS 2133: Engineering Physics I ws01: Measurements: SP1.02 Objectives: Appreciate the problem as a physics problem where mathematical methods are used in a critical way. Practice how to use parameters in physics mass density, ratio. Set up the right formula by using the definitions of parameter. SP1.02: Density and liquefaction, p7, H&R;,W A heavy object can sink into the ground during an earthquake if the shaking causes the ground to undergo liguefaction, in which the soil grains experience little friction as they slide over one another. The ground is then effectively quicksand. The possibility of liquefaction in sandy ground can be predicted in terms of the toid ratio e for a sample of the ground: Vernin Here, Vkrain is the total volume of the sand grains in the sample and V, is the total volume of spaces between the grains (void). (1) From the description above, a sand is modeled as a combination of Grains' and voids'. What would the mass and volume of a sand, Mand and Vand, be in terms of Moain, Mwid, Varain and Void? San Mara t (2) If e exceeds a critical value of 0.80, liquefaction can occur during an earthquake. What is the corre- sponding sand density ne? Solid silicon dioxide (the primary component of sand) had a density of psion 2.600 x 103 kg/m MAraw V sand varnio t V void It mm (3) In your answer from (2), discuss how many digits are significant. (Check the answer in the textbook. Is it correct?) Homework A sample of sand of 5.0 kg has a volume of 3200 cm3. obtain the void ratio, e to find out whether it would be safe against liquefaction. Get the significant figures properly in your answer. (5 points)
Explanation / Answer
mass = 5.0 kg and volume = 3200 cm^3 = 3200x10^-6 m^3
we know VOID RATIO = Volume of Voids / Volume of Soil
VT=32x10-4m3; MT : 5.0 kg; Ms : not givenlet 0.0802 kg ; Gs = not given
Void ratio e :
d = Ms/VT = 0.0802/32x10-4 = 25.0625 kg/m3
d = [Gs/(1+e) ]xw
then 25.0625 = [2.65/(1+e) ]x1000
1+e = ??
thus, e = ??
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