A new suggestion that complexity increases over time, not just in living organisms but in the nonliving world, promises to rewrite notions of time and evolution. The post Why Everything in the Universe Turns More Complex first appeared on Quanta Magazine

[Note that this article is a transcript of the video embedded above.] Even though it’s a favorite vacation destination, the beach is surprisingly dangerous. Consider the lifeguard: There aren’t that many recreational activities in our lives that have explicit staff whose only job is to keep an eye on us, make sure we stay safe, and rescue us if we get into trouble. There are just a lot of hazards on the beach. Heavy waves, rip currents, heat stress, sunburn, jellyfish stings, sharks, and even algae can threaten the safety of beachgoers. But there’s a whole other hazard, this one usually self-inflicted, that usually doesn’t make the list of warnings, even though it takes, on average, 2-3 lives per year just in the United States. If you know me, you know I would never discourage that act of playing with soil and sand. It’s basically what I was put on this earth to do. But I do have one exception. Because just about every year, the news reports that someone was buried when a hole they dug collapsed on top of them. There’s no central database of sandhole collapse incidents, but from the numbers we do have, about twice as many people die this way than from shark attacks in the US. It might seem like common sense not to dig a big, unsupported hole at the beach and then go inside it, but sand has some really interesting geotechnical properties that can provide a false sense of security. So, let’s use some engineering and garage demonstrations to explain why. I’m Grady and this is Practical Engineering. In some ways, geotechnical engineering might as well be called slope engineering, because it’s a huge part of what they do. So many aspects of our built environment rely on the stability of sloped earth. Many dams are built from soil or rock fill using embankments. Roads, highways, and bridges rely on embankments to ascend or descend smoothly. Excavations for foundations, tunnels, and other structures have to be stable for the people working inside. Mines carefully monitor slopes to make sure their workers are safe. Even protecting against natural hazards like landslides requires a strong understanding of geotechnical engineering. Because of all that, the science of slope stability is really deeply understood. There’s a well-developed professional consensus around the science of soil, how it behaves, and how to design around its limitations as a construction material. And I think a peek into that world will really help us understand this hazard of digging holes on the beach. Like many parts of engineering, analyzing the stability of a slope has two basic parts: the strengths and the loads. The job of a geotechnical engineer is to compare the two. The load, in this case, is kind of obvious: it’s just the weight of the soil itself. We can complicate that a bit by adding loads at the top of a slope, called surcharges, and no doubt surcharge loads have contributed to at least a few of these dangerous collapses from people standing at the edge of a hole. But for now, let’s keep it simple with just the soil’s own weight. On a flat surface, soils are generally stable. But when you introduce a slope, the weight of the soil above can create a shear failure. These failures often happen along a circular arc, because an arc minimizes the resisting forces in the soil while maximizing the driving forces. We can manually solve for the shear forces at any point in a soil mass, but that would be a fairly tedious engineering exercise, so most slope stability analyses use software. One of the simplest methods is just to let the software draw hundreds of circular arcs that represent failure planes, compute the stresses along each plane based on the weight of the soil, and then figure out if the strength of the soil is enough to withstand the stress. But what does it really mean for a soil to have strength? If you can imagine a sample of soil floating in space, and you apply a shear stress, those particles are going to slide apart from each other in the direction of the stress. The amount of force required to do it is usually expressed as an angle, and I can show you why. You may have done this simple experiment in high school physics where you drag a block along a flat surface and measure the force required to overcome the friction. If you add weight, you increase the force between the surfaces, called the normal force, which creates additional friction. The same is true with soils. The harder you press the particles of soil together, the better they are at resisting a shear force. In a simplified force diagram, we can draw a normal force and the resulting friction, or shear strength, that results. And the angle that hypotenuse makes with the normal force is what we call the friction angle. Under certain conditions, it’s equal to the angle of repose, the steepest angle that a soil will naturally stand. If I let sand pour out of this funnel onto the table, you can see, even as the pile gets higher, the angle of the slope of the sides never really changes. And this illustrates the complexity of slope stability really nicely. Gravity is what holds the particles together, creating friction, but it’s also what pulls them apart. And the angle of repose is kind of a line between gravity’s stabilizing and destabilizing effects on the soil. But things get more complicated when you add water to the mix. Soil particles, like all things that take up space, have buoyancy. Just like lifting a weight under water is easier, soil particles seem to weigh less when they’re saturated, so they have less friction between them. I can demonstrate this pretty easily by just moving my angle of repose setup to a water tank. It’s a subtle difference, but the angle of repose has gone down underwater. It’s just because the particle’s effective weight goes down, so the shear strength of the soil mass goes down too. And this doesn’t just happen under lakes and oceans. Soil holds water - I’ve covered a lot of topics on groundwater if you want to learn more. There’s this concept of the “water table” below which, the soils are saturated, and they behave in the same way as my little demonstration. The water between the particles, called “pore water” exerts pressure, pushing them away from one another and reducing the friction between them. Shear strength usually goes down for saturated soils. But, if you’ve played with sand, you might be thinking: “This doesn’t really track with my intuitions.” When you build a sand castle, you know, the dry sand falls apart, and the wet sand holds together. So let’s dive a little deeper. Friction actually isn’t the only factor that contributes to shear strength in a soil. For example, I can try to shear this clay, and there’s some resistance there, even though there is no confining force pushing the particles together. In finer-grained soils like clay, the particles themselves have molecular-level attractions that make them, basically, sticky. The geotechnical engineers call this cohesion. And it’s where sand gets a little sneaky. Water pressure in the pores between particles can push them away from each other, but it can also do the opposite. In this demo, I have some dry sand in a container with a riser pipe to show the water table connected to the side. And I’ve dyed my water black to make it easier to see. When I pour the water into the riser, what do you think is going to happen? Will the water table in the soil be higher, lower, or exactly the same as the level in the riser? Let’s try it out. Pretty much right away, you can see what happens. The sand essentially sucks the water out of the riser, lifting it higher than the level outside the sand. If I let this settle out for a while, you can see that there’s a pretty big difference in levels, and this is largely due to capillary action. Just like a paper towel, water wicks up into the sand against the force of gravity. This capillary action actually creates negative pressure within the soil (compared to the ambient air pressure). In other words, it pulls the particles against each other, increasing the strength of the soil. It basically gives the sand cohesion, additional shear strength that doesn’t require any confining pressure. And again, if you’ve played with sand, you know there’s a sweet spot when it comes to water. Too dry, and it won’t hold together. Too wet, same thing. But if there’s just enough water, you get this strengthening effect. However, unlike clay that has real cohesion, that suction pressure can be temporary. And it’s not the only factor that makes sand tricky. The shear strength of sand also depends on how well-packed those particles are. Beach sand is usually well-consolidated because of the constant crashing waves. Let’s zoom in on that a bit. If the particles are packed together, they essentially lock together. You can see that to shear them apart doesn’t just look like a sliding motion, but also a slight expansion in volume. Engineers call this dilatancy, and you don’t need a microscope to see it. In fact, you’ve probably noticed this walking around on the beach, especially when the water table is close to the surface. Even a small amount of movement causes the sand to expand, and it’s easy to see like this because it expands above the surface of the water. The practical result of this dilatant property is that sand gets stronger as it moves, but only up to a point. Once the sand expands enough that the particles are no longer interlocked together, there’s a lot less friction between them. If you plot movement, called strain, against shear strength, you get a peak and then a sudden loss of strength. Hopefully you’re starting to see how all this material science adds up to a real problem. The shear strength of a soil, basically its ability to avoid collapse, is not an inherent property: It depends on a lot of factors; It can change pretty quickly; And this behavior is not really intuitive. Most of us don’t have a ton of experience with excavations. That’s part of the reason it’s so fun to go on the beach and dig a hole in the first place. We just don’t get to excavate that much in our everyday lives. So, at least for a lot of us, it’s just a natural instinct to do some recreational digging. You excavate a small hole. It’s fun. It’s interesting. The wet sand is holding up around the edges, so you dig deeper. Some people give up after the novelty wears off. Some get their friends or their kids involved to keep going. Eventually, the hole gets big enough that you have to get inside it to keep digging. With the suction pressure from the water and the shear strengthening through dilatancy, the walls have been holding the entire time, so there’s no reason to assume that they won’t just keep holding. But inside the surrounding sand, things are changing. Sand is permeable to water, meaning water moves through it pretty freely. It doesn’t take a big change to upset that delicate balance of wetness that gives sand its stability. The tide could be going out, lowering the water table and thus drying the soil at the surface out. Alternatively, a wave or the tide could add water to the surface sand, reducing the suction pressure. At the same time, tiny movements within the slopes are strengthening the sand as it tries to dilate in volume. But each little movement pushes toward that peak strength, after which it suddenly goes away. We call this a brittle failure because there’s little deformation to warn you that there’s going to be a collapse. It happens suddenly, and if you happen to be inside a deep hole when it does, you might be just fine, like our little friend here, but if a bigger section of the wall collapses, your chance of surviving is slim. Soil is heavy. Sand has about two-and-a-half times the density of water. It just doesn’t take that much of it to trap a person. This is not just something that happens to people on vacations, by the way. Collapsing trenches and excavations are one of the most common causes of fatal construction incidents. In fact, if you live in a country with workplace health and safety laws, it’s pretty much guaranteed that within those laws are rules about working in trenches and excavations. In the US, OSHA has a detailed set of guidelines on how to stay safe when working at the bottom of a hole, including how steep slopes can be depending on the types of soil, and the devices used to shore up an excavation to keep it from collapsing while people are inside. And for certain circumstances where the risks get high enough or the excavation doesn’t fit neatly into these simplified categories, they require a professional engineer be involved. So does all this mean that anyone who’s not an engineer just shouldn’t dig holes at the beach. If you know me, you know I would never agree with that. I don’t want to come off too earnest here, but we learn through interaction. Soil and rock mechanics are incredibly important to every part of the built environment, and I think everyone should have a chance to play with sand, to get muddy and dirty, to engage and connect and commune with the stuff on which everything gets built. So, by all means, dig holes at the beach. Just don’t dig them so deep. The typical recommendation I see is to avoid going in a hole deeper than your knees. That’s pretty conservative. If you have kids with you, it’s really not much at all. If you want to follow OSHA guidelines, you can go a little bigger: up to 20 feet (or 6 meters) in depth, as long as you slope the sides of your hole by one-and-a-half to one or about 34 degrees above horizontal. You know, ultimately you have to decide what’s safe for you and your family. My point is that this doesn’t have to be a hazard if you use a little engineering prudence. And I hope understanding some of the sneaky behaviors of beach sand can help you delight in the primitive joy of digging a big hole without putting your life at risk in the process.

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