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  • 00:00

    In 2015, an unusual incident happened on the  construction site for a sewage lift station  

  • 00:05

    in British Columbia, Canada. WorksafeBC, the  provincial health and safety agency, posted a  

  • 00:10

    summary of the event on YouTube. A steel caisson  had been installed to hold back soil while the  

  • 00:15

    lift station could be constructed. One worker on  the site was suddenly pulled into a sinkhole when  

  • 00:20

    the bottom of the caisson blew out. The cause of  the incident was related to groundwater within the  

  • 00:24

    soils below the site. We don’t all have to live in  fear of the ground opening up below our feet, but  

  • 00:30

    engineers who design subsurface structures do have  to consider the impact that groundwater can have.  

  • 00:35

    The solutions to subsurface problems are almost  always hidden from public view, so you might never  

  • 00:40

    even know they’re there. This video is intended  to shed some light on those invisible solutions  

  • 00:45

    (including what could have been done to prevent  that incident in BC). I’m Grady and this is  

  • 00:50

    Practical Engineering. In today's episode, we’re  talking about how groundwater affects structures. 

  • 01:03

    This video is sponsored by HelloFresh,  America’s Number 1 meal kit. More on that later. 

  • 01:14

    Groundwater has always been a little mysterious  to humanity since it can’t easily be observed.  

  • 01:19

    It also behaves much differently than surface  waters like rivers and oceans, sometimes  

  • 01:24

    defying expectations, as I’ve shown in a few of my  previous videos. One of the most important places  

  • 01:29

    where groundwater shows up in civil engineering  is at a dam. That’s because groundwater flows  

  • 01:34

    from high pressure to low pressure, and a  dam, at its simplest, is just a structure  

  • 01:39

    that divides those two conditions. And what do  you know, I’ve got an acrylic box in my garage  

  • 01:43

    full of sand to show these concepts in real life. You can imagine this soil sits below the base of  

  • 01:48

    a dam, and I can adjust the water levels on either  side of the structure to simulate how groundwater  

  • 01:53

    will flow. Blue dye placed in the sand helps show  the direction and speed of water movement below  

  • 01:58

    the surface. A higher level on the upstream side  creates pressure, driving water in the subsurface  

  • 02:04

    below the dam to the opposite end of the model.  I’ll be the first to say it: this is not the most  

  • 02:08

    mind-blowing revelation. You probably could have  predicted it without the fancy model. But to a  

  • 02:13

    civil engineer, this is not an inconsequential  phenomenon, and for a couple of reasons. 

  • 02:18

    First, water seeping below a dam  can erode soil particles away,  

  • 02:22

    a phenomenon called piping. Obviously, you don’t  want part of your structure’s foundation to be  

  • 02:27

    stolen from underneath it, and piping can create  a positive feedback loop where failure progresses  

  • 02:33

    rapidly. I have a whole video on piping that  you can check out after this one. The second  

  • 02:38

    negative effect of groundwater is less obvious.  In fact, until around the 1920s, dam engineers  

  • 02:43

    didn’t even take it into account (leading to  the demise of many early structures in history). 

  • 02:49

    The engineering of a dam is largely an  exercise in resisting hydrostatic pressure.  

  • 02:53

    Water in the reservoir applies an enormous force  to the upstream face of a dam, and if not designed  

  • 02:58

    properly, that force can cause the dam to slide  downstream or overturn. The hydrostatic force is  

  • 03:04

    actually pretty simple to approximate. Pressure  in a fluid increases with depth, so you get a  

  • 03:09

    triangular distributed load. Once you know that  load, you can design a structure to resist it,  

  • 03:14

    and there are a lot of ways to do that. One of  the most common types of dam just uses its own  

  • 03:19

    weight for stability. Gravity dams are designed  to be heavy enough that hydrostatic forces  

  • 03:23

    can’t slide them backwards or turn them over.  But, to the dismay of those early engineers,  

  • 03:28

    pressure from the reservoir is not  the only destabilizing force on a dam. 

  • 03:32

    Take a look at this pipe I’ve included in the  model that shows the water level between the two  

  • 03:37

    boundaries. If the base of a structure was below  the water level shown here, the groundwater would  

  • 03:42

    be applying pressure to the bottom, counteracting  its weight. We call this uplift pressure. Remember  

  • 03:47

    that the only reason gravity dams stay put is  because of their weight, so you can see how having  

  • 03:52

    an unanticipated force effectively subtracting  some of that weight would be a bad thing. Many  

  • 03:58

    concrete gravity dams have failed because  this uplift force was neglected by engineers,  

  • 04:03

    including the St. Francis Dam in California that  killed more than 400 people when it collapsed in  

  • 04:08

    1928. Many consider this to be the worst American  civil engineering disaster of the 20th century. 

  • 04:14

    Unlike the hydrostatic force of a reservoir,  uplift pressure from groundwater is a much more  

  • 04:19

    complicated force to characterize. It exists  in the interface between the structure and  

  • 04:24

    its foundation, in the cracks and pores of the  underlying soil, and even within the joints of  

  • 04:29

    the concrete structure itself. The flow of  groundwater is affected by soil properties,  

  • 04:34

    the geometry of the dam, the water  levels upstream and downstream,  

  • 04:38

    and even the subsurface features. How these  factors affect the uplift pressure can be pretty  

  • 04:43

    challenging to predict. But engineers do have  to predict it. After all, we can’t build a dam,  

  • 04:49

    measure the actual uplift force, and add weight  if necessary. It’s gotta work the first time. 

  • 04:55

    One way to characterize groundwater flow around  structures is the flow net. This is a graphical  

  • 05:01

    tool used by engineers to estimate the volume  and pressure of seepage in the subsurface.  

  • 05:06

    In simple terms, you divide the flow area into  a curvilinear grid, where one axis represents  

  • 05:11

    pressure and the other represents flow. If this  looks familiar, you might notice that a flow  

  • 05:16

    net is essentially a 2D solution to the Laplace  equation, which also applies to other areas of  

  • 05:21

    physics including heat flow and magnetic fields.  Developing flow nets is almost an art as much as  

  • 05:26

    a science, so it’s probably a good thing that  groundwater problems are mostly solved using  

  • 05:31

    software these days. But, we can still use flow  nets to demonstrate a few of the ways engineers  

  • 05:36

    combat this nefarious uplift force on gravity  dams. And one common idea is a cutoff wall. 

  • 05:42

    If water flowing below a dam causes so many  problems, why not just create a vertical wall  

  • 05:46

    to cut it off? We do it all the time. But, how  deep does it need to be? Some dams might have a  

  • 05:52

    convenient geological layer into which a cutoff  can be terminated, creating an impenetrable  

  • 05:57

    envelope to keep seepage out. But, many don’t.  Cutoff walls can still reduce the volume of  

  • 06:03

    flow and the pressure, even if seepage can still  make its way underneath. Let’s take a look at the  

  • 06:08

    model to see why. I’ve added a vertical wall  of acrylic below the upstream face of my dam,  

  • 06:13

    and we’ll see how it affects the flow. The  groundwater flow lines adjust to go under the  

  • 06:18

    wall and back up to the other side of the model.  If you look closely you’ll see a slight decrease  

  • 06:23

    in the uplift measurement pipe below the dam. The  only thing I changed between this model and the  

  • 06:28

    last one was adding the cutoff wall. So why would  the pressure decrease on the downstream side? 

  • 06:35

    The flow of groundwater is described with a  fairly simple formula known as Darcy’s law.  

  • 06:40

    Besides the permeability of the soil, the only  other factor controlling the speed water flows  

  • 06:45

    is the hydraulic gradient, which consists of the  difference in pressure over the length of a flow  

  • 06:50

    path. By adding a cutoff wall, I didn’t change  the difference in pressure between one side of the  

  • 06:55

    model and the other, but I did increase the length  of the flow path water had to take below the dam,  

  • 07:00

    reducing the hydraulic gradient. I can sketch  a flow net over the model to make this clearer.  

  • 07:05

    The black lines are equipotentials; they connect  areas of equal pressure. The blue lines show the  

  • 07:11

    directions of flow. Without a cutoff, the flow  paths are shorter, and thus the equipotential  

  • 07:16

    lines are closer together. With the cutoff wall,  the equipotential lines are spread out. That means  

  • 07:21

    both the volume of seepage and the uplift pressure  at the base of the structure have been reduced. 

  • 07:26

    Cutoff walls on dams have a long history of  use, and nearly all large gravity dams have  

  • 07:30

    at least some kind of cutoff. It can be as simple  as excavating a wide area of the dam’s foundation  

  • 07:36

    before starting on construction, and that’s  a popular choice because it gives engineers  

  • 07:40

    a chance to observe the subsurface conditions  and make sure there are no faults or problems  

  • 07:45

    before the dam gets built. Another option is to  excavate a deep trench and fill it with grout,  

  • 07:51

    concrete, or a slurry of impermeable clay. For  smaller or temporary structures, sheet piles can  

  • 07:57

    be driven into the subsurface to create a cutoff.  One final option is to inject high pressure grout  

  • 08:03

    to create an impenetrable curtain below the dam. The other way to deal with seepage and uplift  

  • 08:08

    pressure are drains. Drains installed below a dam  do two important jobs. First, they filter seepage  

  • 08:14

    using sand and gravel so that soil particles can’t  be piped out from the foundation. Second, they  

  • 08:20

    relieve uplift pressure by removing the water.  Let’s see how this works in my model. Upstream  

  • 08:24

    of my uplift monitor, I’ve added a hole through  the back of the model with a tube to drain seepage  

  • 08:29

    out. Instead of flowing all the way downstream,  now some of the seepage flows up to and through  

  • 08:35

    the drain, and you can see this in the streamlines  of dye flowing in the subsurface. Again, the  

  • 08:39

    effect is subtle, but the uplift pressure monitor  is showing a slight decrease in pressure compared  

  • 08:44

    to the original configuration. There is less  pressure on the base of the dam than there would  

  • 08:49

    be without the drain. Plotting a flow net over the  model, you can see why it behaves this way. The  

  • 08:54

    drain relieves the uplift on the base by creating  an area of low pressure below the dam. You can  

  • 08:59

    also note that the drain actually increases the  hydraulic gradient by shortening the flow paths,  

  • 09:04

    so there’s actually more seepage happening  than there would be without the drain. However,  

  • 09:08

    because the drains are installed with  filters to reduce the chance of piping,  

  • 09:11

    that additional seepage is often  worth the decrease in uplift pressure. 

  • 09:15

    Many concrete dams include a row of vertical  drains into the foundation, and some even use  

  • 09:20

    pumps to depress the groundwater level further,  minimizing the uplift. I can simulate this by  

  • 09:25

    lowering the downstream level as if a pump was  removing the water. Watch how the flow lines  

  • 09:30

    adjust when I make this change in the model. Like  drains, these relief wells create more seepage  

  • 09:35

    below a dam because of the greater difference  in pressure between the two sides, but they  

  • 09:40

    can significantly reduce the uplift pressure  and thus increase a structure’s stability.

  • 09:50

    I’ve been using dams as the main  example of managing groundwater flow,  

  • 09:54

    but lots of other structures have similar  issues. Retaining walls and temporary shoring  

  • 09:59

    have to contend with groundwater challenges,  including caissons, which are watertight chambers  

  • 10:04

    sunk into the earth to hold back soil during  construction. Remember the worker I mentioned  

  • 10:09

    in the intro? He was on a site near a caisson.  It’s typical to dewater a structure like this,  

  • 10:14

    meaning the water is pumped out, creating a  dry area for construction crews to work. Let’s  

  • 10:19

    take a look at how this works in the model. I’m  simulating the act of pumping water out of the  

  • 10:24

    caisson by draining out of the model at the bottom  of the structure. When a caisson is dewatered,  

  • 10:29

    it is essentially working like a dam, separating  an area of high pressure from low pressure within  

  • 10:34

    only a short distance between them. And, as  you know, distance matters when it comes to  

  • 10:38

    groundwater, because the shorter the flow paths,  the greater the hydraulic gradient, and thus the  

  • 10:43

    higher the volume and velocity of seepage. If you look closely, you can see the sand  

  • 10:48

    boiling up as the seepage exits the soil into the  bottom of the caisson. This elevated pressure in  

  • 10:53

    the subsurface and high velocity of flow means  that the soil particles themselves aren’t being  

  • 10:59

    strongly held together. All it takes is a little  agitation for the soil to liquefy and flow into  

  • 11:04

    the bottom of the caisson, creating a sinkhole  that can easily swallow anything at the surface.  

  • 11:09

    One way of mitigating this hazard is dewatering  the soil outside the caisson. Construction crews  

  • 11:14

    use well points, small evenly spaced wells  and pumps, to draw water out of the soil so it  

  • 11:20

    can’t seep to areas of lower pressure. Caissons  can also be driven deeper into the subsurface,  

  • 11:25

    creating a condition similar to a cutoff wall  on a dam. They can even go deep enough to reach  

  • 11:30

    an impermeable layer, creating a better seal that  prevents water from flowing in through the bottom. 

  • 11:35

    Thankfully for the worker in BC, his  colleagues were able to rescue him before  

  • 11:40

    he was consumed by the earth. Next time  you see a dam, retaining wall, caisson,  

  • 11:44

    or any other subsurface construction, there’s a  good chance that engineers have had to consider  

  • 11:50

    how groundwater will affect the stability.  Even though you’d never know they’re there,  

  • 11:54

    some combination of drains and cutoffs were  probably installed to keep the structure  

  • 11:59

    (and the people around it) safe and sound. 

  • 12:02

    Speaking of sounds, here is the peaceful  sound of a napping toddler while my wife  

  • 12:06

    and I prepare a home-cooked meal from  the sponsor of this video, Hello Fresh. 

  • 12:10

    “What do you call that?” “Hot raisin water” 

  • 12:15

    HelloFresh has kid-friendly recipes for  picky eaters but this one is just for  

  • 12:19

    us. The meals take about 30 minutes to  prepare which is perfect for nap time  

  • 12:24

    because it’s really hard to film yourself  preparing lunch while chasing a toddler at  

  • 12:28

    the same time, especially when the  photographer is 9 months pregnant.  

  • 12:32

    But… our little helper just couldn’t stand to be  left out of the fun, so he woke up early anyway. 

  • 12:43

    They also have different plans to meet your  various nutritional or dietary goals, like  

  • 12:48

    pescatarian, Fit and Wholesome, or vegetarian  which is what we usually get. It’s a perfect way  

  • 12:54

    to make a change or try something new. And this  is not us being mean, he really loves lemons. 

  • 13:00

    And here’s the most important thing: Hello  Fresh meals are delicious. We’ve done this  

  • 13:04

    for quite a while now, and there isn’t a single  recipe that we haven’t enjoyed. Actually we got  

  • 13:09

    invited to a party at the last minute, so we  ended up combining the portions of this meal  

  • 13:13

    and bringing it to share, and it was a huge hit. “This might be the best one you’ve made yet” 

  • 13:20

    Go try it yourself at HelloFresh.com, and if you  use code PRACTICAL16, you’ll get up to 16 free  

  • 13:26

    meals plus 3 surprise gifts. I wouldn’t recommend  it if I didn’t think you would love it. That’s  

  • 13:32

    HelloFresh.com and use my code PRACTICAL16. Thank  you for watching and let me know what you think.

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The example sentences of CURVILINEAR in videos (1 in total of 1)

in preposition or subordinating conjunction simple adjective terms noun, plural , you personal pronoun divide verb, non-3rd person singular present the determiner flow noun, singular or mass area noun, singular or mass into preposition or subordinating conjunction a determiner curvilinear noun, singular or mass grid noun, singular or mass , where wh-adverb one cardinal number axis noun, plural represents verb, 3rd person singular present

Use "curvilinear" in a sentence | "curvilinear" example sentences

How to use "curvilinear" in a sentence?

  • Girls marry for love. Boys marry because of a chronic irritation that causes them to gravitate in the direction of objects with certain curvilinear properties.
    -Ashley Montagu-

Definition and meaning of CURVILINEAR

What does "curvilinear mean?"

/ˌkərvəˈlinēər/

adjective
Characterized by or following a curved line.