Once again welcome back to the drawing board. In the last couple of videos we talked about the design of equipment and the resistances of that equipment. We looked at the props and we looked at the wailers. Now we will have a look a bit at the other side, where the forces come from.
Today we are going to look at Excavation Surcharges. Now what do I mean by surcharges? It’s an extra force that’s applied around the excavation that will add a little bit more load to the kit. For instance, excavators and heavy machinery moving around. You could have the force of a building, foundations or it could be rail or road or some of the traffic nearby. These will all add vertical pressure onto the ground which will eventually become a horizontal force which this kit will have to resist.
Surcharges come in all kinds of different flavors, the main four are written up on the board here. You have a blanket surcharge which is basically a uniform pressure which just applies to the whole area of ground around the excavation. You then have an area surcharge, similar to this but it’s all in one localized area. This might be a crane pad or a pad foundation or something similar. It just applies a concentrated force in that area. Two very similar ones at the bottom here, you have a line surcharge and a strip surcharge dealt with in very slightly different ways which we will look at on the other side of the board. But that’s basically a wall or a foundation that runs alongside you excavation.
The difference between this area and this strip is that this is assumed to just have infinite length, it just goes on for the whole length of your excavation. Where as this one has a finite end to it. We’ll look at a little bit of basic Rankine theory to work out these pressures. Generally speaking the pressure of ground level is going to be zero and then it increases according to this little equation here. Where you active pressure is Ka times by your vertical stress take away a little bit for cohesion. In this case, the vertical stress is equal to the density of the ground times by the depth of ground so you end up with this pressure at the bottom.
When we add the blanket surcharge, this is why it’s the easiest to deal with. Instead of starting with zero, you start with Ka times the value of that surcharge. So you basically are just adding a big block onto it so it’s nice and easy to deal with and then at the end you’ll end up with the same again Ka gamma Z plus Ka times your surcharge and then minus a bit for cohesion.
What happens with the others though? when you have a concentrated load you’re not going to have this nice easy uniform distribution to work with. Previously we may have used something like Boussinesq which will give you a good approximation. If you want to have a look at a technical blog from tony’s technical blog talking about let’s say the 45 degree of thumb and it goes into the boussinesq equations and that has a pretty good conversation about this 45 degrees and whether Boussinesq really represents what happens in real life. We’ve started using this, I’m going to say new but it’s back in 1998, Georgiadis and Anagnostopoulos. Came up with a system that is a little more empirically based and gives you more results that will reflect the kind of things you would really see on-site. You take a surcharge and you spread it out on a 45 degree angle until you hit your excavation line, there… and you get this q’. q’ is the reduced value of this pressure and it’s according to the ratio of that width to that width. So it will be slightly smaller, it has been spread out a bit. You then flip that around 90 degree against here and the value of pressure here is you Ka times by the pressure of that surcharge over the area that will be covered by that.
Let’s have a look at the line load. I said that was dealt with slightly differently. Well in this case we actually decided rather than using a line load which can be quite complicated you spread that line load out, you never really are going to get a knife edge load on the ground. At the very minimum we’ve taken 300 millimeters because you very well may get a 300 millimeter wide wall foundation but you can spread that across 300mm and then in the same way as a spread surcharge here you can spread that out so you have a slightly smaller q’ here. I’ve written this here, KA cos delta q’, the cos delta is involving our wall friction. What you want to be careful of, if you’ve already modified your Ka to take into account your wall friction you shouldn’t really apply this cos delta a second time. It’s kind of giving you the benefit twice. If you’re going to use the unmodified Ka without wall friction, feel free to apply a little bit of wall friction to that surcharge. If you’ve already modified your Ka take that cos delta out of that equation. You don’t want to be too optimistic with these.
How do you deal with the area surcharge then? It’s not got an infinite length. It’s very similar to this except you’re spreading out the 45 degrees into a horizontal direction and that just gives you an area of surcharge against the back of the sheets that will be influenced by this.
I hope that gives you a little bit of insight, it’s not the whole picture but you can have a look on tony’s technical blog there’s some bits and pieces. And if you want to download our version of GF safe that will give you a little bit of instruction in how to do some geotechnical designs so thank you very much and I hope you come back to the drawing board soon.
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