Mass Wasting (Downslope Movement of Sediment by Gravity Alone)

1 – The Forces Involved

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If you’ve ever found yourself in this situation, or in a similar situation, what force was acting on you?

Gravity, of course. We will symbolize this “Fg” (force

of gravity).

Gravity operates directly toward the ground. We

illustrate this with an arrow pointing in the direction of

action. The size of the arrow is proportional to the

strength of a force – smaller arrows mean

weaker forces. This arrow symbol used in this way is

called a vector. Fg

ACME Anvil Co.

There is another force we need to explore before we think about mass movements of sediment down slopes. What is the force that keeps you from pushing a box of anvils like this? Where does it come from?

ACME Anvil Co.

This, of course is friction or the frictional force (Ff). You can only push the box across the floor if the force you apply (small red arrow) is greater than the frictional force (big red arrow). In this case the push vector is smaller than the friction vector and so the box stays put. The friction vector is drawn pointing in the opposite direction from the push vector because friction is a direct resistance to the applied force. Where does the frictional force come from?

Ff

ACME Anvil Co.

ACME Anvil Co.

Here is a clue. Assume that the same force is being applied by the workmen in both pictures. Which one of the boxes is empty and which has anvils in it?

ACME Anvil Co.

ACME Anvil Co.

The man pushing the empty box actually pushes it; he doesn’t just push on it. Why? Well, examine the vectors in each picture. There is a smaller frictional force in the upper diagram, symbolized by the smaller Ff arrow. It is smaller in fact than the applied push force. Why?

Ff

Ff

The obvious answer is that the full box weighs more than the empty one. We can’t push it because it’s too heavy. This time assume that both boxes are full. Why is one movable and the other not? If a full box were on a surface of low or zero gravity – a well-waxed floor, a bunch of ball bearings on the floor, or a huge air-hockey table – we’d have no trouble pushing it. We would have a hard time stopping it. It’s force of motion would be greater than any force we could apply to it.

ACME Anvil Co.

ACME Anvil Co.

Artificially lowered friction

So the weight of the box is the key. Without some way of decreasing friction a heavy box is harder to push than an empty one. But what is weight? Weight is just a value we assign to how the gravitational force affects a particular mass. On Earth you weigh a certain amount because there is a certain amount of mass in you. On the Moon you’d weigh less because Fg is lower on the moon, but the amount of mass in you doesn’t change, just Fg. (The Moon has less mass than Earth so the attraction between it and some other mass (like you) is proportionally lower.) So the root cause of the difficulty in pushing a heavy box is the force of gravity.

Fg

ACME Anvil Co.

Fg

If we summarize we find out something interesting. In some circumstances (falling) gravity makes things move, but in others (sliding) it is an important part of the frictional force that keeps things from moving.

Study the picture and make sure you get this. Gravity can have opposite effects in different situations.

Gravity causes motion.

Gravity impedes motion.

Why is it difficult to stay on a high-pitched roof like this? Why do you stay on and not slide off uncontrollably?

If gravity (which we’ll abbreviate Fg) is pulling you straight down, why do you feel as if you are sliding sideways? If whatever it is that’s pulling (or pushing) you is real, and if you’ve been here you know it is, why don’t you slide?

Fg

?

Gravity is pulling you straight down, as it always done, but the slope interferes with its action. So you are being pulled by gravity, but not down the slope. Instead, a derived force acts on you. It is derived from gravity, but it is not gravity – not Fg itself. In some sense it is not “real” in the same way that Fg is real. We can calculate its strength. This force we will call the downslope force (Fd). Of course the reason you don’t slide off the slope is the same reason you can’t push a box of anvils across the floor: friction (Ff). Notice that in this diagram Ff has a larger vector than Fd (Ff > Fd). You are stable on a slope like this.

Fg

Fd

Ff

Fg

ACME Anvil Co.

Fg

Let’s review, recalling the TWO things that gravity can do. It can make you fall, if there’s nothing under you (like a roof) to stop you. It also creates friction between two objects when a force is applied to one (or both) to make it move. In freefall only one of these things is evident (Fg = Fd). On a flat slope only the other thing is apparent (Ff = Fg + some other variable).

On a slope, BOTH things are operating.

Even though the roof on the left is less steep than the one on the right it is harder to stay on. (I know this from exhausting personal experience). What is the difference? The material, of course. The pliable, textured shingles on the one roof provide more friction that the metal on the other roof. They have a higher coefficient of friction. That is the other factor in the frictional force – the nature of the surfaces of the slope and the object on it. Soft-soled climbing shoes have a higher coefficient than cowboy boots. (Maybe the rust increases the coefficient of the sheet metal roof, but I’m not going back up there to find out.)

What does somebody on a roof have to do with mass wasting?

Fd

Ff (So far)

Rocks exfoliating from Stone Mountain eventually slide and/or fall off the side.

Those rocks at the bottom of the mountain were at the top of the mountain until Fd > Ff. A pile of rocks like this is called talus or scree.

At one place the Appalachian Trail traverses a scree field of enormous boulders. My brother and I took over 3 hours to cover this “hardest mile on the A.T.”). Part of the slowdown was that it was raining and the rocks were very wet. And slick. Their coefficient of friction was much reduced by the lubrication of the rain. (Everybody takes a long time to “walk” this mile.)

Mahousac Notch, ME Photo by David Carter

Fd

Ff

Fg

Never step on a rock that looks like its vectors might be unlike these.

Fd

Ff

Fg

Mt. Lincoln, NH with Mt. Lafayette in the background

Internal Friction

One Last Thing: If you pile dry sand onto a flat surface it will form a mound with a very specific shape. Viewed from the top it will be roughly round. Viewed from the side it will be roughly an isosceles triangle. In 3-D it will be conical, point up. If you add more sand the pile will get higher and bigger around, but it will maintain essentially the same shape. The sides will always slope at almost exactly the same slope. That angle is called the angle of repose. That angle exists because each grain is subject to the same forces as a rock on the side of a mountain. If the slope on the side is too much (Fd > Ff ) each grain moves down until (Fd = Ff ). In this way the slope becomes stable at some overall angle – the angle of repose. We can apply the same logic to a slope of loose material as to a rock on the side of Stone Mountain, but instead of a basal friction between a rock and a mountain there is an internal friction among all the grains on the slope. This is harder to calculate, but we can often estimate it by paying attention to the angle of slopes on similar materials when they fail.

Angle of Repose

Summary • Gravity (Fg) contributes two derived forces to objects on slopes. If the object moves, it is

NOT gravity (Fg) that causes it to move, but one of the derived forces.

• That force is the downslope force (Fd). It operates directly down the slope.

• Gravity (Fg) also contributes to the frictional force (Ff). Fg therefore keeps the object on the slope if it stays. For a solid object on a slope this is called a basal friction.

• The other contributing factor (or variable) to Ff is the coefficient of friction. There’s a reason people play basketball in sneakers and not wingtips.

• Slopes made of loose material behave in the same way as hard slopes with solid objects on them, but do so at a much finer and more complicated way. Each particle experiences both derived forces. The slope stabilizes when all particles are individually stable. Here we are dealing with an internal friction rather than a basal one.