L12 Retaining Walls

追加: 2026-05-31

[00:00:00]okay so I hope that video was helpful for you to visualize the behavior of retaining walls now in this video we're going to dive a little bit deeper into retaining walls and answer some questions from the are so that video demonstrated how the retaining wall on the left here was actually more efficient when resisting overturning and sliding so from a structural engineer's perspective we would prefer to design retaining walls like the one on the left however as I mentioned in the previous video from a constructability standpoint the retaining wall on the right is preferred because we would be cutting back less soil so ultimately the location of the wall along the footing matters and just as with pretty much every element in a building there is some give and take pros and cons to where you place that wall and the discussion needs to take place regarding whether we want to prioritize efficiency or constructability now I've used the words overturning and sliding a few times in this video already and they were mentioned in the previous video as well now we are going to look at all three stability modes of failure for our retaining wall first as the previous video mentioned we have the lateral pressure of the wall that is causing an overturning moment about the point Q that lateral pressure is resisted by the soil pressure the vertical soil pressure on the backspan or the heel of the footing if the overturning moment exceeds the stabilizing moment then we have an overturning failure and as the video mentioned the main method for resisting overturning and footing is to extend this footing back further and gain more vertical soil pressure the next mode of failure is when we have a horizontal soil pressure that exceeds the frictional force underneath the footing and this causes a mode of failure called sliding and there are a couple of methods for mitigating sliding and a footing that I will mention in just a moment finally we have a third mode of failure that looks a lot like the first but it is quite different so as you can imagine just as with any footing there is weight to this structure that needs to be resisted by the bearing pressure the soil pressure underneath the soil pressure also tends to increase towards the toe of the pudding this side of the footing to resist the overturning moment that's generated by this horizontal pressure on the back if that maximum pressure that's applied at the toe of the footing exceeds the allowable bearing pressure of the soil you could have settlement occur and that pudding could start to sink so this would be a bearing pressure failure so with the first mode of failure we have adequate bearing pressure underneath and so the footing does not dip down at all however it overturns due to an insufficient stabilizing moment about the point Q with the bearing pressure failure the entire footing actually sinks below where it initially started so those are our three primary stability modes of failure for a retaining wall now it's important to note that retaining walls can also fail due to over stressing of the rebar or the concrete so in this example if we have insufficient reinforcing on this face of the retaining wall then we will end up having cracks in the concrete which of course is a huge problem because we could end up having water in those cracks which could rust this rebar that eventually lead to a full failure now this type of failure would be considered more of an internal overstressing failure and not a global stability failure like those listed above so with all of that in mind let's move on to some are example questions so this question asks what is the total lateral force exerted by the Earth against the retaining wall shown per lineal foot of wall assume the pressure of the retained Earth to be equivalent to a fluid weighing 30 pounds per cubic foot so 30 pounds per cubic foot that is our equivalent fluid pressure and what they mean by per lineal foot of wall is you can imagine that this section that they've cut is a section looking through a long piece of wall and for the purposes of analysis we choose to look at one unit strip the wall so in global terms all of these answers are actually in pounds per linear foot of wall and that's important to keep in mind as we start solving this problem and looking at our units so let's start with a diagram on the right so this is the equivalent fluid pressure that is applied to our wall and it has a depth of 10 feet so if the lateral fluid pressure is equal to 30 pounds per cubic foot that means that as we move down along this wall the pressure increases per foot until we reach the bottom this 10 foot where we have 30 pounds per cubic foot times 10 feet and so that maximum pressure at the bottom is equal to 300 pounds per square foot now the question is asking what is the total lateral force exerted by the Earth against the retaining wall we currently have a pressure in pounds per square foot and we want a force given in pounds per foot so what we're looking for is the equivalent Point load we'll call it that is acting against this wall so what does this Force F equal well as we've done with these distributed loads before this is a triangular distributed load so we will have that the force is equal to 300 pounds per square foot times 10 feet and since it's a triangular distributed load times one-half and we get 1500 pounds per unit strip foot and that is our final answer which is answer C now we can also take this question a few steps further by calculating the overturning moment and the resisting moment so this question doesn't actually provide enough information for us to know what the resisting moment would be but we can solve for the overturning moment and then I'm going to provide the remaining information that we need in order to solve for the resisting moment so starting with the overturning moment we know that our force is equal to 1500 pounds per lineal foot and in order to calculate the overturning moment about this point Q we need to know its perpendicular distance that distance we can of course obtain through geometry since it's a triangular distributed load we know that the force acts through the Center of this shape which happens to be one-third from the base so 1 3 times the height will give us that distance or we could take two-thirds times the height in this direction so if we take that Force f and multiply it by 1 3 times the height we get the overturning moment so if I plug in those variables I get 1500 pounds per foot times one-third times 10 feet and we get a value of five thousand moment is of course given in units of force times a distance and so this would be pound feet and since we're looking at a unit strip method it would be pound foot per foot for our overturning moment next we can solve for the resisting moment that's provided by the soil on the back of the footing or the heel of the footing and for that we first need to know the density of the soil so the density of the soil is not going to be the same value as this equivalent fluid pressure this 30 pounds per cubic foot in fact it's typically going to be much higher in fact the density of about 120 pounds per cubic foot is fairly typical for soils you can recall that the density of concrete if it's normal weight concrete reinforced it's typically 150 pounds per cubic foot so now that we have this value we can calculate a resisting moment so we need to First find this equivalent Point load on the backspan of the pudding that is equal to the weight of the soil so that weight of soil is going to be equal to the density of the soil times the depth here we have nine feet of depth of soil given that the depth of the footing is one foot and so that would be the weight of the soil in terms of pounds per foot along the length of this footing and as before when we solve for equivalent Point loads given a uniformly distributed load like this we need to multiply by the width and so overall the weight of soil on the back of that footing is going to be 120 times 9 times 8.

[00:12:45]which equals eight thousand six hundred and forty pounds per linear foot along the length of the footing going in and out of the page now to calculate the resisting moment we take that weight at 8640 pounds per foot and we multiply by the perpendicular distance to Q I'm gonna add one more Dimension here two feet so that perpendicular distance is eight feet divided by two plus two feet and we get a resisting moment equal to 51 840.

[00:13:42]pound feet per foot and as you can see this footing has no issues with overturning as the resisting moment is much much greater than the overturning moment and if we wanted to we could calculate the factor of safety which is equal to the resisting moment divided by that overturning moment in our case it would be 51 840 divided by five thousand so the factor of safety would be equal to 10.3 which is a very large factor of safety and so this footing could easily be trimmed back provided of course that we have no issues with either soil bearing pressure or sliding it's possible that we would have to keep this footing this large even though we have such a high factor of safety for overturning if we either had very low soil bearing capacity or a very low coefficient of friction now moving on to the next example question this question asks all of the following may increase the sliding resistance of a retaining wall except and we have four possible choices so if you can recall a sliding failure occurs when our lateral pressure of soil exceeds the friction that's provided beneath the floating surface so let's look at our options option A provides an additional integral key to the footing which I've shown below here of course this key would provide a lateral pressure going in the opposite direction of the pressure that's applied and so yes this would be a good option for providing additional sliding resistance next we have making the footing wider or increasing its length in this direction and here we are providing more surface area underneath and therefore a larger frictional force to resist our lateral soil force and so again yes this would be a good option for increasing the sliding resistance next we have increasing the depth of the footing and while this doesn't increase the amount of surface area underneath the pudding for friction what it does is it provides more weight on top and as you may recall from your physics courses a heavier object is going to provide more frictional force then a lighter object with the same coefficient of friction and so this is also a possible option for increasing the sliding resistance of the retaining wall the only option that is remaining is increasing the amount of reinforcing Steel in the footing and as I mentioned above reinforcing doesn't have anything to do with the global stability failures of a retaining wall and so this would not be a good option for increasing the sliding resistance of the wall and therefore D is our answer now speaking of reinforcing our final question asks for the retaining wall shown below which faces are in tension noted as T and which are in compression noted as C when considering questions like this regarding the behavior of a structure the first thing you should try to consider is what does the deflected shape look like as you can recall from the foam demonstration when you bend that piece of foam it becomes very clear which side is in compression and which side is in tension by looking at the stretching of the fibers that same thought process can be applied here if we think about how the soil is pushing against this retaining wall and we draw its deflected shape this stem here can be considered as a cantilevered wall so this joint here at the base since it's integral with the footing is a fixed condition and up here there's nothing bracing the top portion of this wall so it is a cantilever condition and so it's deflected shape will start perpendicular to the footing and then it will lean to the right as it's being pushed by the soil and so when we look at this deflected shape we can see that there is tension along the back face so from that we can eliminate answer C next if we consider the forces that are applied to the footing underneath namely the soil bearing pressure underneath the footing and the weight of the soil on top we can see that the force pushing up from underneath is greater at the toe and the soil pressure pushing down is much smaller and so the toe will want to bend in this direction and therefore there is tension on the bottom face so from that we can eliminate answer a lastly for the heel of the footing you can see we have less pressure pushing up from the bottom and more pressure pushing down from the top and so the heel of the footing has a tendency to deflect that and therefore there's tension along the top face and therefore we eliminate answer B and choose t now given what we've just learned from this question we can also answer where we would want to place reinforcing in our retaining wall detail of course reinforcing will go along the tension phase of the wall and so for I cantilever retaining wall like this we would have reinforcing designed along the back face touching the soil here that would turn and go along the bottom face of the toe of the footing and then we would also have reinforcing along the top face of the heel that extends through like that and so that would be our primary reinforcing depending on the thickness of this wall we would likely also Place some simple minimum reinforcing or shrinkage and temperature Steel along these faces as well but the primary reinforcing would be what's shown in purple so I hope you found that helpful that's all that I have for you regarding retaining walls so with that good morning good afternoon and good night and I'll see you next time