Mass Wasting

2 – Slope Stability

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Slopes occur everywhere – steep ones, gentle ones, and in-between ones. Any slope may have objects on it that gravity can act upon, and every slope with any loose material on it has component pieces that are also under gravity’s influence. Most slopes are stable. That is, the downslope force (Fd) is more than balanced by the frictional force (Ff) In this case we will use the mathematical shorthand Ff > Fd (or Fd < Ff). Slopes that are metastable have Fd =~Ff. Unstable slopes move, and do so essentially instantly. In this case Ff > Fd (or Fd < Ff). When movement occurs we say that the slope fails or talk about its failure. If conditions change and one of the forces is either increased or decreased by those changes then the inequality can be thrown in the opposite direction. A stable slope becomes unstable or a metastable slope is stabilized. Let’s remind ourselves of the concept of changing mathematical inequalities. If two cars are on the interstate going 70 (car 1) and 68 (car 2) mph, then car 1 is either overtaking or leaving car 2 behind. We can express this V (car 1) > V (car2). If car 2 adds speed, so that it is going 75 mph, then the inequality changes to V (car 1) < V (car 2) and car 2 thus either stays ahead of car 1 or overtakes it. Anything that changes one or both of the forces on a slope can change the inequality of those forces.

Remember that: • Gravity (Fg) is not the force that pulls you down a slope, the downslope force (Fd) is. It derives from Fg but is not as strong (except in free-fall). • Friction (Ff) operates in exactly the opposite direction as Fd. • Ff depends upon two things: the coefficient of friction and some other contribution of gravity.

We need to see now what that contribution is.

Fg

Fd

Ff

ACME Anvil Co.

We’ll call this the “snug” force and label it Fn. The “n” is for “normal” in the sense of “perpendicular”. On a horizontal surface there is no Fd, so all of Fg is Fn (or Fg = Fn)

Fg = Fn

As always, don’t worry about understanding the math, just get the general idea that the math let’s us describe very precisely what the forces on an object are and how the object will move (or not move). Let’s do a thought experiment before moving on. Imagine we are in a warehouse. You are sitting above the floor looking down (map view) and you see Arnold Schwarznegger (when he made the first Terminator movie) and me (when I first saw the first Terminator movie) pushing on a box. It is heavy, but not so heavy that we can’t both move it across the floor. Arnie can push with 3x the force I can, so his vector is 3x longer. We begin. After a certain amount of time, where does the box end up?

Arnie

Me

If I were to push the box alone for some amount of time any point on that box would move a certain distance. We will focus our attention on the corner of the box as indicated by my distance vector, but the center, or another corner, or any other point would move in exactly the same way.

Me

If Arnie were to push the box by himself this would be the result. His force vector is three of mine, remember, so he would push the box 3x farther in the same amount of

time. (His distance vector would be 3x the length of mine.)

Arnie

If Arnie pushed the box by himself first, and then I pushed it from that position this would be the result.

Arnie

Me

If we both pushed simultaneously the result would be the same: the corner would end up in the same place as if Arnie pushed first and I pushed second (green vectors) or I pushed first and he pushed second (blue vectors). While I was moving it “my” distance, Arnie would be moving it “his” distance. The red vector is the resultant. That is “R” in the diagram. If we can measure x and y (beforehand) we can predict the length of R because x2 + y2 = R2. If we can measure the resultant (after the fact) we can figure out x and y because tan A = y/x.

Me

Arnie

y y

x

x

R

A

y y

x

x

R

A

x?

y?

Now you try it. Was person x or person y pushing harder on the box? About how much harder?

x x

y

y

R

A

x?

y?

The length vectors in the x direction are about 2x the length of those in the y direction so “x” must have pushed twice as hard as “y”.

Fg

(Fd)

(Fn)

Remember: On a slope the snug force is perpendicular (normal) to the slope itself. The downslope force is, of course, parallel to the slope. Fg is therefore the resultant of the vectors of these two forces.

A

Fg

(Fd)

(Fd) (Move Fd

vector to here)

(Fn)

Study the diagram and see that this makes a right triangle with a known hypotenuse length and one known acute angle (A). Though we will not do it, this means we can actually calculate the exact strengths of the two derived forces.

A

Controls on Slope Stability

1. The most obvious control on slope stability is the steepness of the slope.

As the angle increases the contribution of Fg to Fd increases and the contribution to Ff decreases. Study the diagram and make sure you see this. The vector lengths of the two derived forces change.

Fd vector longer / Ff vector shorter.

Steepening a slope BOTH increases downslope force and decreases friction.

CUT FILL

CUT FILL

Humans need flat places to build such things as houses and roads, and routinely oversteepen slopes by cutting and filling in order to make them. This example is in the town where I went to school. The dotted line shows the original natural slope, the solid line shows the present slope. There is evidence of gradual mass wasting on the slope, which we’ll come back to.

CUT

Nature also oversteepens slopes by eroding them. This is a meander (bend) on the Alapaha River near Willacoochee, GA. The river bends from the back right part of the picture and continues its flow behind the photographer. The outside of that bend has faster currents than the inside, and is eroded. What evidence is there that that cutbank is eroding?

(All true river meanders are like this. The outside of the bend is a cutbank and the inside is a pointbar. We will come back to this when we talk about rivers.)

2. Mass

The mass on a slope is important because it increases both the downslope and frictional forces. It’s effect on the downslope force is greater. It does increase the snug force, but not the coefficient of friction.

Most natural slopes reach a metastable or stable configuration with all the masses on them as part of the equation. If additional mass is added, for example if a house is built, that equation changes and the slope

becomes less stable and may fail. In this case the force of gravity on the slope with the house is much greater than on the slope without the house, increasing Fd more than Ff on the overall slope.

If you’ve ever seen a movie with a snow avalanche in it (some James Bond movies, XXX) then you’ve see a natural example of an overloaded slope. In this case the problem rapidly accelerates and the result is chaos. A little snow falls and knocks a little more loose, and now there’s twice as much falling, which knocks some

more loose (4x), and so on. The weight accumulates exponentially to the bottom of the slope.

Fg Fg

3. Water

Water has two effects on a slope, neither of them good news for slope stability. The first one is straightforward and easy to understand. Water adds mass to the slope in the same way that adding anything else (a house, for instance) adds mass, and it has the same effect on Fd. The second thing requires a little explanation. The two photographs below are at the same scale.

If you take an inflated balloon from the surface (big photo) down into a pool (smaller photo) the volume changes. I assume you know the reason for this. The “water pressure” is higher in deeper water. The size of the balloon decreases (as the air is compressed) and the shape changes (as the air is forced by its low density into the upper part of the balloon.

The question is, if the pressure increases, why

doesn’t it simply collapse the balloon?

The answer, of course, is that the air inside the balloon pushes back on the water. It compresses until its internal pressure is equal to that of the surrounding water, but resists compressing any more. The twin facts that it is air inside a flexible, closed sheath that makes the compression (and resistance to further compression) obvious and easy to illustrate. What is not obvious is that every little package of water, in fact, every molecule of water in the pool does the same thing. They all push together until the pressure among them is “right” and then they resist any further compression. Barometric pressure in the atmosphere is the same thing. This is what we experience as the weather changes. Lithostatic pressure inside the Earth is the same thing. That is the pressure that causes C to collapse into the diamond crystal structure and the pressure that makes iron collapse into a solid in the inner core. The pressure in every case is equal to the weight of the overlying material – the overlying rock in lithostatic pressure, the overlying air in barometric pressure, and the overlying water in hydrostatic pressure. These are all confining pressures meaning that they are equal in every direction.

Now imagine a soil profile, or some loose sediment on a slope. The circles represent the soil grains and the blue represents the water. Rainwater can infiltrate the pores between the grains. Near the bottom of the soil the pore pressure, that is, the hydrostatic pressure within the pores, can vary quite a bit. In the left picture the soil is relatively dry and the pore pressure pushing outward on the soil grains is low. As the pores above fill with water (right picture) the hydrostatic pressure, and therefore the pore pressure increases. Imagine a 30 or 50 foot thick soil or sand. The pore pressure would be quite high near the base and the strength of the friction between individuals thereby reduced. This is why a sand castle at the beach actually collapses. The water lowers its internal friction and gravity pulls the sand into a more nearly flat configuration.

So water does two things to a slope. It increases the total mass on the slope, increasing Fd in proportion to Ff, and it decreases Ff. In a thick enough soil or sediment Ff can reach zero near the bottom as the grains literally lose contact with each other. In this case the material actually flows as a viscous liquid.

Fd

Ff

4 -- Vegetation

As a general rule vegetation adds stability to a slope. The reason is that the roots, including nearly microscopic root hairs, bind the soil together and find their way into cracks and weathered pockets in the bedrock, anchoring the upper part of the soil to the bedrock below. The effect is to increase the internal friction in the soil (binding) and the basal friction between the soil and bedrock (anchoring).

There are also potential down sides to vegetation. First, a vegetated slope retains more water after a rainfall, with all that entails (see above). Second, as the vegetation matures the weight of the vegetation is added to the slope. This is particularly problematic when a large tree dies because then the roots begin to decay, and they do so much faster than the above-ground wood. Thus there is a consequent reduction in the frictional force formerly provided in part by the tree. I have seen entire steep mountain slopes in Tennessee covered in large pines killed by bark beetles. That is a lot of weight on a slope with decreasing internal friction.

5 – Geologic Nature of the Slope

Sedimentary bedding, metamorphic foliation, joints, faults, and so on all impart a degree of weakness that does not occur in rocks without those structures. Furthermore the weakness is generally oriented in

some particular direction within the rock body, making it more likely to fail in that direction than in the other.

This has a pronounced effect on the slopes that form on tilted (or otherwise oriented) rocks. Mass movements are more likely to involve rocks sliding in the direction of tilt (the dip direction) and to do so

quite readily. The opposite slope ( the scarp slope) is generally steeper (depending on the tilt angle) because mass movements are less common, and usually involve rocks falling after they have been

somewhat undercut by erosion.

Dip Slope Scarp Slope

Dip Slope Scarp Slope

Lookout Mt. Pigeon Mt. Shankle Ridge

Harpe Ridge

Dip Slope Scarp Slope

Dip Slope Scarp Slope

Dip Slope Scarp Slope

Dip Slope Scarp Slope

Incidentally, the same processes act at various scales. At large scales mass wasting processes may underlie much of the landscape of a region. This photograph is from the northwest corner of Georgia, where the Valley and Ridge province meets the Cumberland Plateau. The scarp and dip slopes of four ridges in the Chickamauga/Chattanooga Valley region are indicated. Notice the mirror symmetry centered between Hankle and Harpe Ridges (dotted line). (Harpe Ridge is difficult to see, being small and close to Lookout Mt.) The scarp slopes on both sides face this midpoint.

Schematically, this is what you see in the photograph. The dip angles are highly exaggerated to make the structure clear. The originally continuous layers have been eroded away where the dotted lines indicate their original locations. The erosion has created the main valley and also the smaller internal valleys by leaving more of the particularly resistant rocks (sandstone and chert) and removing more of the less resistant ones (shale and limestone). Compare the dip (DS) and scarp (SS) slopes of the various ridges here with the previous photograph. (Middle Ridge is barely visible in the photograph. Why do you think it got that name?) Why is there no scarp slope on Middle Ridge?

Lookout Mt Pigeon Mt

Harpe R. Shankle R.

(Middle Ridge)

DS

DS

DS DS DS

DS

SS SS

SS SS

These slopes have evolved as the material on them has become weathered and has either slid (dip slopes) or fallen (scarp slopes) into the adjacent valleys. There, the streams in the bottoms of those valleys have removed it and sent it down the Tennessee River system, and ultimately to the Gulf of Mexico. This happened more slowly on the resistant sandstone beds than on the more easily eroded other rocks, so the sandstone ridges stand proud and clearly show their dip and scarp slopes.

When someone tells you that the Colorado River cut the Grand Canyon that is only part of the story. The river deepened the canyon but the widening was mostly accomplished by mass wasting. The sides of the canyon are, in effect, scarp slopes facing each other. The dip slope angle is virtually 0°.

5 – Weathering

Weathering influences primarily the frictional force on the slope, and specifically the coefficient of friction. It does this by causing internal loosening of the material on the slope. Chemical weathering of minerals in a rock, of feldspar to clay, for example, clearly changes the cohesiveness of the rock. Solid granite turns into mushy clay, which is far easier to break apart than the original feldspar. Mechanical weathering can also change the cohesiveness of material as the diagram illustrates.

Slope Evolution

Any slope you see in the natural world is the current version of the slope’s constant requirement to equilibrate the downslope and frictional forces. In other words, there is the constant drive, because of gravity, to ensure that Ff > Fd or Ff = Fd. If at any time this inequality is reversed (Ff < Fd) then the slope will move until the equilibrium is re-established, or until friction overbalances the downslope force. Slopes are constantly evolving, even if humans are not involved. erosion may cut away at the foot of a slope, oversteepening it. A mass wasting event farther upslope may bring material to a lower part, both overloading and oversteepening it. Porous slopes are forevermore filling with rainwater and emptying. Slopes are constantly weathering. Trees and other vegetation grow on a slope and bind it deeper and deeper; then they die and their weight becomes an increase in Fd as their roots decay. So remember. As long as Ff > Fd the slope is fine. As the slope approaches Ff = Fd the slope becomes metastable. Once Ff < Fd the slope will fail.

Let’s quantify this just a little to make sure we see how it works. We’ll assign some hypothetical values to the slope forces without worrying about what the units are. Let’s start with a stable slope.

1) Fd < Ff Anything we or nature do to this slope that increases Fd or decreases Ff or both will change the slope dynamic, leading to failure.

2) Fd < Ff We’ll symbolize that with arrows. failure

3) 10 < 12 Suppose that we’ve measured the forces in some units and found them to have these values. The slope is stable.

7) 14 > 13

If the downslope force is increased by 3 units, the inequality changes and the slope fails.

5) 10 > 9 If the frictional force is decreased by 3 units, the inequality changes and the slope fails.

If the downslope force is increased by 2 units and the frictional force is decreased by 2 units, the inequality changes and the slope fails. 6) 12 > 10

4) 13 > 12

If both forces increase, but by different amounts, the inequality changes and the slope fails.