Please answer #5 only and plot the excel graph. Grain sizes: forces1. Let's look at our profile again. Let's say that you dug 2m into the profile and extracted asample of gravel; enough to fill a soda can.5mGravelV 1.5m6mClay3mSandBedrockYou take this sample to the lab and pour it on a tray. Yes, it looks like gravel, because it isgravel. It looks like the gravel that you find at the bottom of a fish tank. Clearly, you noticethat the particles do not have the same size. Some particles are the size of a rice grain,whereas others span the sizes of beans, and others are as large as a gum ball.Now you go back to the site and dig deeper, and extract a sample of clay from a depth of8m. You go back to the lab and extrude the clay from the can-of-soda-size sampler. It isdefinitely wet, saturated in fact. It stands cylindrically by itself, in contrast to the gravel,which flowed as you poured it on a tray. You squeeze the cylinder of clay with your barehand and it feels like you stuck your hand into a large can of peanut butter that was leftovernight in the fridge. You look closely at your hand, which is covered in clay smears, andtry to identify a single particle, but you cannot, as this is impossible for the human eye.Gravel and clay: two soils, but two totally different materials.2. Perhaps the most important aspect of a soil, as it pertains to the engineering behavior ofthe soil, is the sizes of the grains. This is because the forces that grains feel are dependenton their size.3. The two primary particle-level forces associated with soil grains are buoyant weight (FB)and van der Waals electrical attraction (FvDw). The buoyant weight is the weight of agrain when submerged in a fluid (i.e., water). Let's assume that grains can be representedas spheres. The buoyant weight of a spherical grain of diameter d composed of a mineralwith density ps (the 's' stands for solids) submerged in a fluid with density pf is:(p,-p, nd'gS%3D6. For minerals that compose soil grains, ps is typically 2.65 gm/cm³ (remember this).For water, pf = Pw = 1 gm/cm³ (remember this).%3D4. The van der Waals attraction is an electrical force that arises from the temporary polarityof surfaces in proximity. In general, any two objects that are very close to each otherexperience van der Waals attraction. For two grains that are spaced a very short distanced apart, the van der Waals force isA,H.%3DVDWd128where AH is the Hamaker constant, which captures the 'strength' of the polarization andis dependent on (1) the minerals that make up the two surfaces in proximity and (2) thefluid that lies between the surfaces. For silica mineral surfaces (common in soils) in thepresence of water, AH is 6.4 x 10-21 N-m. Generally, an inter-particle distance of separation8 = 30 x 1010 m can be used to approximate FyDw with the equation above.%3D5. Why are these forces important? Answer this question by creating a graph. On the x-axis,plot particle diameter d (in mm). Scale the x-axis from 0.001 mm to 10 mm. On the y-axis,plot both FvDw and FB. For clarity, change both axes to log-scale. This plot reveals that FvDw> FB for grains with d < 0.08mm, whereas FvDw < FB for grains with d > 0.08mm.6. Have you ever wondered why dust sticks to your computer screen and to other objects,in doing so defying gravity? Or why chalk sticks to the blackboard? The reason is that dustparticles are very small, and for them, FvDw > Fw. In this case, Fw is simply the weight of adust particle (not the buoyant weight).7. The competition between FVDw and FB, captured by the plot associated with item 4(above) is at the heart of the system that we use to characterize soil grains according totheir size. There are four sizes:If a grain is smaller than "0.01 mm, then it is called a clay particle.If a grain has a size between ~0.01mm and 0.075mm, then it is called a silt particle.If a grain has a size between 0.075mm and 4.75mm, then it is called a sand grain.If a grain is larger than 4.75mm, then it is called a gravel grain. /

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Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Please answer #5 only and plot the excel graph.

Transcribed Image Text:Grain sizes: forces 1. Let's look at our profile again. Let's say that you dug 2m into the profile and extracted a sample of gravel; enough to fill a soda can. 5m Gravel V 1.5m 6m Clay 3m Sand Bedrock You take this sample to the lab and pour it on a tray. Yes, it looks like gravel, because it is gravel. It looks like the gravel that you find at the bottom of a fish tank. Clearly, you notice that the particles do not have the same size. Some particles are the size of a rice grain, whereas others span the sizes of beans, and others are as large as a gum ball. Now you go back to the site and dig deeper, and extract a sample of clay from a depth of 8m. You go back to the lab and extrude the clay from the can-of-soda-size sampler. It is definitely wet, saturated in fact. It stands cylindrically by itself, in contrast to the gravel, which flowed as you poured it on a tray. You squeeze the cylinder of clay with your bare hand and it feels like you stuck your hand into a large can of peanut butter that was left overnight in the fridge. You look closely at your hand, which is covered in clay smears, and try to identify a single particle, but you cannot, as this is impossible for the human eye. Gravel and clay: two soils, but two totally different materials. 2. Perhaps the most important aspect of a soil, as it pertains to the engineering behavior of the soil, is the sizes of the grains. This is because the forces that grains feel are dependent on their size. 3. The two primary particle-level forces associated with soil grains are buoyant weight (FB) and van der Waals electrical attraction (FvDw). The buoyant weight is the weight of a grain when submerged in a fluid (i.e., water). Let's assume that grains can be represented as spheres. The buoyant weight of a spherical grain of diameter d composed of a mineral with density ps (the 's' stands for solids) submerged in a fluid with density pf is: (p,-p, nd'g S %3D 6.

For minerals that compose soil grains, ps is typically 2.65 gm/cm³ (remember this).
For water, pf = Pw = 1 gm/cm³ (remember this).
%3D
4. The van der Waals attraction is an electrical force that arises from the temporary polarity
of surfaces in proximity. In general, any two objects that are very close to each other
experience van der Waals attraction. For two grains that are spaced a very short distance
d apart, the van der Waals force is
A,
H.
%3D
VDW
d
128
where AH is the Hamaker constant, which captures the 'strength' of the polarization and
is dependent on (1) the minerals that make up the two surfaces in proximity and (2) the
fluid that lies between the surfaces. For silica mineral surfaces (common in soils) in the
presence of water, AH is 6.4 x 10-21 N-m. Generally, an inter-particle distance of separation
8 = 30 x 1010 m can be used to approximate FyDw with the equation above.
%3D
5. Why are these forces important? Answer this question by creating a graph. On the x-axis,
plot particle diameter d (in mm). Scale the x-axis from 0.001 mm to 10 mm. On the y-axis,
plot both FvDw and FB. For clarity, change both axes to log-scale. This plot reveals that FvDw
> FB for grains with d < 0.08mm, whereas FvDw < FB for grains with d > 0.08mm.
6. Have you ever wondered why dust sticks to your computer screen and to other objects,
in doing so defying gravity? Or why chalk sticks to the blackboard? The reason is that dust
particles are very small, and for them, FvDw > Fw. In this case, Fw is simply the weight of a
dust particle (not the buoyant weight).
7. The competition between FVDw and FB, captured by the plot associated with item 4
(above) is at the heart of the system that we use to characterize soil grains according to
their size. There are four sizes:
If a grain is smaller than "0.01 mm, then it is called a clay particle.
If a grain has a size between ~0.01mm and 0.075mm, then it is called a silt particle.
If a grain has a size between 0.075mm and 4.75mm, then it is called a sand grain.
If a grain is larger than 4.75mm, then it is called a gravel grain. /

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