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Rock Slope Engineering Transcript

This transcript describes the YouTube video "Rock Slope Engineering - Dr. Evert Hoek Lecture"


Rocscience logo appears on a black background followed by the word “presents”. Fades to black.

The text Practical Rock Engineering Lecture Series by Dr. Evert Hoek copyright 2016 appears on black background. Fades to black.

Text appears “Rock slope engineering Lecture 5.”

An image of a mountain which appears to have had a rockfall is shown on screen. There are trees in the foreground with grey rocks.

Dr. Hoek: Lecture number five deals with rock slope engineering and this is a large subject which certainly justifies more than one video

Dr. Evert Hoek is shown on screen standing in a room with green walls and gold accents speaking to a group of people sitting listening to him deliver the lecture.

Dr. Hoek: but I'm going to try and summarize everything to give you a general impression of how we go about designing rock slopes.

Transitions to the same image of the mountain. After a moment, the image moves to the top right-hand corner to show Dr. Hoek on screen again.

Dr. Hoek: The opening slide shows the Frank slide in southern Alberta in Canada. This occurred in 1903, a huge slide and the run out was almost a kilometer long and it was suspected that the cause was mining and for coal in the toe of the slope. It destroyed the village of Frank and there were a large number of fatalities. So, this is one end of the spectrum that we have to deal with, large natural landslides. In previous lectures in this series, I've mentioned the influence of scale

A slide is shown on screen with a photo in the top left of a dump truck with a rock slope in the background. Text below it reads “Small slope failures in open pit mine benches can be tolerated because ample catch facilities and equipment to clear the debris are readily available.” On the right, an image of a large open pit mine showing a road and the large benches. Text beside it says “Slope failures in large open pit slopes can have very serious operational and economic consequences.”

Dr. Hoek: and I repeat the slide showing 18-meter-high benches on the Chuquicamata open-pit mine in Chile where the failures are controlled by structure.

This image moves to the top right corner to reveal Evert on screen again.

Dr. Hoek: And the one-kilometer-high slope on the right-hand slide where we can treat the rock masses homogeneous on that scale. I'm going to show you two examples of the extremes of slope design because the essence of slope design is not only calculating the factor of safety or the mode of failure but looking at the risks and consequences of failure.

A new slide is shown on screen showing an aerial view of the Thissavros dam plunge pool in Greece.

Dr. Hoek: This is a very large dam in northern Greece and the dam is shown there, it's a fill dam. Spillway is going down into the plunge pool and these slopes around the plunge pool are critical because they will take fluctuating water levels, there's an underground powerhouse below them, and they have to remain stable for the duration of the project. So, the design of those slopes has to be very carefully carried out. You see the blasting has been very carefully done and that would be a high-risk project, where failure of any component would have very serious consequences.

A new slide appears in the top right corner showing two images of large rock masses with holes going through them with text reading “A difficult rock slope problem on a remote mountain road.” After a moment, the slide takes up the full screen.

Dr. Hoek: The other end of the scale is this one, which is a road in India which I passed through many years, for many years on the way to a Hydro project and I wouldn't even know how to begin to analyze the stability of that slope. and this is one of the things that we encounter, that sometimes in mountainous areas in the Himalayas, in the Andes, in the Alps, in the Rockies. We come across situations which just have to be done in order to get a road through and you have to accept the risk that goes with that. In order to understand the process of rock slope behavior, we have to look at a number of simple models and those are illustrated in this slide,

A new slide is shown on screen with four graphics. The top right shows Plane Failure, top left showing Wedge Failure, bottom left showing circular failure and bottom right showing toppling failure. Green is shown to represent the surface, and red to show the soil visible after failure. The screen alternates between the slide and Dr. Hoek speaking.

Dr. Hoek: which shows four of the typical failure mechanisms that we encounter. The plane failure on the upper left is typical of some types of granitic batholiths, where you have sheet jointing, and you get sliding of the material overlying the joints on a plane. So, it's the simplest type of failure we deal with. The one on the upper right, wedge failure, is more common where we have intersecting structural features that define wedges. And I'll show you an example of that in a moment. Circular failure, down on the lower left, is probably the most, we come across this most commonly in soil slopes or transported material slopes. But it can occur in rock masses where if the slope is very large such as the kilometer high slope, I showed you in Chuquicamata and where the failure surface finds the path of least resistance which might be on a whole number of structural features and perhaps some failure of the intact material. And then an unusual one on the lower right, which I'm really not going to deal with very much in this lecture, is toppling failure. Where you have vertical columns or slightly in dipping structures which allow the columns to topple.

A slide is shown on screen with an image of an engineer looking up at a rock slope. Text below reads “Example of a probabilistic wedge failure analysis.” A graphic of a wedge failure is in the top right showing sliding planes 1 and 2 and a tension crack in red. The wedge slides along line of intersection of sliding planes 1 and 2. The bottom right is a chart showing the factor of safety in the horizonal and relative frequency in vertical and red bars up to 1 and green bars above 1 on the FS scale.

Dr. Hoek: I mentioned wedge failure in the previous slide, and this is an example under an open pit mine bench and the upper right-hand drawing shows the wedge analysis that we perform to understand this type of failure. And this although it's a fairly simple analysis, it does allow us to do probabilistic analysis. And so, the lower right shows a distribution of factors of safety calculated for this wedge failure and the red part of the plot indicates factors of safety of less than 1. In other words, those slopes would fail. And the probability of failure is defined as the total area of the red part of the histogram divided by the total area of the whole histogram. So, the factor of safety you see there is 1.13 and the probability of failure is 18.6%. And those are critical numbers, and they have different meaning in our decision-making on slope stability. Calculating the probability of failure itself is not adequate.

A colourful table is shown on screen. Risk = Hazard x Consequence. Very High Risk is red. High risk is orange. Moderate Risk; yellow and low risk is green. The columns from left to right: very high hazard, high hazard, moderate hazard, low hazard. The rows top down: very high consequence, high consequence, moderate consequence, low consequence. The colours are read from left to right. Top row the colours are red, red, orange, orange. Second row: red, orange, yellow, yellow. Third row: orange, yellow, yellow, green. Fourth row: orange, yellow, green, green. The screen alternates between the matrix and Dr. Hoek on screen.

Dr. Hoek: And this matrix here defines the question of risk. Risk is the product of hazard or the probability of failure and consequence, the consequence of the failure. So, you can imagine the dam and the slopes that I showed you would have very high consequences of failure. So, it would be in their upper column and the hazard might be high or moderate depending on how much confidence you have in the design. But the risk is defined as the product of these two factors and it's something that is integral to our understanding of the use of rock slope stability analysis in engineering design. Obviously, the roadway on the highway that I couldn't analyze is both very high hazard and very high consequence, but we have no remedial measures to offer for it. You just have to accept that if it fails, the road is going to be closed for a long time.

An image is shown on screen of a slope with machinery with text “Reinforcement of the toe of a slope by means of 20 m long 2 m diameter reinforced concrete piles penetrating a weak horizonal layer at the toe of the slope.” The screen alternates between this slide and Evert speaking.

Dr. Hoek: Here’s a very high hazard and a very high-risk situation. This is a rock slope behind a large powerhouse. The powerhouse in front of us here and behind the powerhouse are a number of columns that carry the powerlines and so you see there in the middle of the photograph the foundation of one of the columns and obviously you need to protect the slope against failure in order to ensure the stability of that column which would destroy the power line or runout onto the powerhouse below. And so, the solution adopted here, I should just go back for a moment and say that this is andesitic lava flow and it's underlined by weak marine sediments. So, there's a potential for failure at the bottom of the slope coming outwards. And so, in order to counter that, the design was to place 20 meter long 2-meter diameter reinforced concrete piles which go right through the weak zone at the bottom of the of the of the slope. Obviously a very expensive solution, very time-consuming to construct but necessary because of the high risk, the high-risk probability and consequence are both high in this situation.

A new slide is shown on screen with two images. In the bottom left, a slope that has failed and the top right the result of the remediation of the slope. Text in the top left “Clearing a critical access road to a large project by careful excavation at the toe of a rock slope failure.” Text in bottom right “The successful result of the very high-risk operation shown above.” The screen alternates between the slide and Dr. Hoek with the images in the top right corner.

Dr. Hoek: Here's another situation of extremely high risk and extremely high consequence and it involves a landslide on a highway in the Himalayas. And you'll see on the upper right the landslide just after it occurred. And the only solution there was to have somebody mine out the toe of the slope. And so, the arrow shows a little backhoe working its way gingerly across the slope and taking out the failure. That is an extremely high hazard occupation and it's one you wouldn't normally do but think how else would you do it? Normally we - we take a slope down from the top and you get up there on extremely steep slopes. And it was successful you see in the lower photograph. The highway has been cleared, the landslide mass has been reduced in size, and the traffic is passing through. So, it was a successful operation but certainly an extremely high-risk one. Now if we go through an analysis of slope stability as we will later on in the in the lecture, what we have to - the next step is if we detect that there is an unacceptable stability situation or in an unacceptably high risk, what can we do?

A slide is shown with text titled “Possible remedial measures for unstable slopes.” The content of this slide is explained verbally by Dr. Hoek.

Dr. Hoek: And so, we have a range of options which involves changing the geometry of the slope, unloading the top of the slope, adding a buttress to the toe of the slope, drainage of the slope is a very important and very usually very effective, reinforcement of the slope. We could put cables or bolts or retaining walls piles through weak layers as in the recent example. And we also have the question of rockfalls because if the slope is unstable, it's likely that pieces of rock can become loose at the surface and come down and you have to deal with that in a variety of ways.

Dr. Hoek is shown on screen speaking to the audience members.

Dr. Hoek: So, I'm going to run through a series of analyses showing examples of these different remedial options. And I'll start with a hypothetical slope, this has no connection to any particular project.

A slide is shown with a chart in the top left of the probabilistic analysis results and a slope model in the bottom right with text “example of a marginally stable slope showing groundwater and failure surfaces.”

Dr. Hoek: But I've chosen a slope 60 meters high, a fairly steep face with benches on it in highly jointed rock mass. So, it can fail both by internal structural failure and by failure of the material. And what you see there is a slope profile. The blue line is the groundwater surface, or the phreatic line and the red line is the calculated failure surface with a tension crack at the top and a non-circular failure surface through emerging at the toe. And a probabilistic analysis of this gives us a factor of safety very close to one. The red block on the left is pretty much half the area so the probability of failure in this case is 40%. That has an unacceptable situation, we have to do something about it.

The slide changes to the same chart and model, however the red portion on the chart is quite low and the model shows partial drainage of the slope. Alternates between the slide and Dr. Hoek on screen.

Dr. Hoek: So, the first option I'm going to look at is drainage and this would involve putting a tunnel or a drain of some kind behind the toe of the slope as you see by the red arrow there. And you'll see from the histogram that this is enormously effective. It reduces the probability of failure down to about 1.2 percent, increases the factor of safety to about 1.2 and that has to be judged a very effective solution. What this has done in effect is to reduce the pore pressures along the failure surface, the shear strength on the surface increases. It's not always possible to do this. As you can imagine there are situations where it might work better than others and as I said just now these are individual, each slope is unique, and these are individual solutions which you would have to do for each example.

A slide of similar layout with the histogram in the top left and model in the bottom right with text “Flatten overall slope 5 degrees.”

Dr. Hoek: The next possibility is to flatten the overall slope angle this is a solution that's often looked at. And in this case, it surprisingly doesn't do any good. In fact, it makes the situation very slightly more dangerous. The probability of failure increases to 42% as opposed to 40% factor of safety is almost the same very close to one. And you might be surprised at that but what it has done is it's reduced the weight of the rock mass sitting on the failure surface and therefore the shear strength decreases but the pore pressure remains high, and the slope fails.

Transitions back to Dr. Hoek speaking, looking at the projector which is off screen.

Dr. Hoek: Again, an unacceptable solution but there are situations where flattening the slope can be very effective. Another option commonly used is to unload the top of the slope.

A new slide is shown similar to the previous slides with the histogram in the top left and model in the bottom right with text “Unload top of slope by widening upper bench.” After a moment, Evert is shown on screen again.

Dr. Hoek: In order to decrease the driving force driving the wedge down and this would involve widening the upper bench as you see with the red arrow there. And this is effective. It increases the factor of safety to about 1.1 and reduces the probability of failure to about 19 percent but it's not sufficient on its own. You have to do it in conjunction with something else, but it is an effective solution that can be considered if you have the possibility of doing that.

A new slide is shown with the same elements. The histogram in the top right shows little red in the curve. The model in the bottom right has a green portion indicating the buttress which changes the red line to exit just above the top of the green portion. After a moment, Dr. Hoek is shown on screen again.

Dr. Hoek: And finally the application of a toe buttress which in this case is simply a dump of waste rock placed at the toe of the slope and this could be very effective because what it does sometimes as it has here is to change the profile of the failure surface so that the failure surface actually emerges now above the toe the slope passing marginally through the waste dump and the factor of safety is increased to almost 1.2 and the probability of failure reduced to about 2 percent. So that's a very effective solution, and in each situation, you have to go through this kind of scenario analysis and determine what is possible in your situation and what is most effective and most economical.

An image is shown of a large hillside with a red line zigzagging up the slope on the left-hand side. A river flows through the bottom of the image. Text at the bottom of the slide reads “The 1.5 billion cubic metre Downie slide located upstream of the Revelstoke dam on the Columbia River in British Columbia, Canada.” Transitions back to Dr. Hoek after a moment.

Dr. Hoek: Here's an example of the use of drainage in an extremely large slide. This is a 1.5 billion cubic metre slide that called a Downie slide, which is located above the Revelstoke dam in British Columbia on the Columbia River. And it was generated during the last ice age when glaciers came down the valleys and scoured them out and so this failure occurred on a shear surface fairly low down in the rock. And it was moving very slowly but BC Hydro, the owners of the project, decided that some remedial measures were required before the reservoir was impounded and the toe of the slope flooded. And so, this was done by drainage.

A slide is shown in the top right corner. The previous image is in the top left of the slide. A new image is in the bottom right showing a man in a drainage gallery with water pouring in below the Downie slide. After a moment, the slide moves to fullscreen.

Dr. Hoek: A drainage gallery was started from where the red arrow is there and entered into the rock mass. In fact, there was another one slightly upstream and these went in maybe half a kilometer or so and from them upholes were drilled into the rock mass above. And in the slide at the bottom there, you see the flow from the drainage holes into containment vessel there and drainage was very effective indeed.

Two diagrams are shown on screen. One side section based on drawings and in the bottom right, the top-down view. The screen alternates between Dr. Hoek speaking and the slide.

Dr. Hoek: Here's an analysis of the situation, which was done by Moore and company of BC Hydro. And it shows a cross section through the slope at the top and a plan of the slope at the bottom and the blue line, the dotted blue line there is the phreatic surface before impoundment and before any drainage. So, its high in fact, it's artesian in places, it actually is above the surface. And so, water would flow out in as springs on the surface. And that was what was causing movement or that was helping movement in addition to the geography of the slope along the lower shear surface, which is the is the lower red line, red dotted line there. And after drainage, the green dotted line there is the phreatic surface that was monitored. So, it's been brought down significantly, and the movement was effectively halted in its checks. It wasn't zero, but it was way lower than it had been before this action was taken. And in the plan there, you can see that at the center of the drainage trough, the water head had been reduced 120 meters. So, this is a very very effective solution. It's the only economical solution you could even consider here because for 1.5 billion tons of material, there's no possibility of stripping the slope or reinforcing it and drainage is the only possible solution.

Dr. Hoek is shown in fullscreen talking to the audience.

Dr. Hoek: It's interesting that over the 10 years, first 10 years or so of operation of the system, the drainage efficiency decreased about 10 percent. So, the water levels rose slightly and that is due to clogging of the drain holes. So, it means that this drainage system has to be maintained. You have to go back perhaps every 20 or 30 years and perhaps redrill the holes or try in some way to flush them out, which is very difficult. Typically, it would be better to go in and redrill the drain holes to bring the efficiency back up.

A new slide is shown on screen. An image on the left shows water coming out of a vertical borehole with a man looking down at it. Text beside the image reads “Artesian flow from a vertical borehole.” The image on the bottom right shows four engineers watching water flow from a horizontal drain hole in an open pit mine slope.

Dr. Hoek: Sometimes if you have artesian water as shown on the upper left or you put a horizontal drain hole in as shown on the lower right, you say why don't we just put horizontal drains in, and you see those very often in slopes. Unfortunately, they tend to clog up very quickly and so in a big situation like that they are completely ineffective.

Transition to show Dr. Hoek on screen speaking.

Dr. Hoek: They're quite useful if you have a fairly small rock slope where the joints would be clean, you wouldn't have too much material flowing through the structural features and where you might get good drainage for perhaps 10 or 20 years. But in a slope with a lot of clay or soil present, the drains clog up. Whatever you try to do to protect them, they clog up too quickly. And we also have to worry about the surface drainage because a lot of the water ingresses from stream flow and so on or rainfall on the top of the slope and very often I see attempts to put concrete drainage ditches in, which are way too rigid. And as you see on the left, they simply don't work.

A slide appears on screen with two images. On the left, engineers are standing on a hillside with a concrete ditch. The right image is another example of a concrete ditch. Text reads “Concrete ditches for surface water control are not sufficiently flexible to withstand slope deformation. Interlocking ditch segments or flexible membranes, such as used wide conveyor belting, are more effective.” After a moment, Dr. Hoek is shown speaking on screen.

Dr. Hoek: We have a mobile slope. The design on the right is a nice one I saw in Greece where you use interlocking segments which are basically flexible. I've also seen old conveyor belt. Mines tend to have very wide conveyor belts and sometimes they take the old conveyor belts and line the drains of those which is very effective.

A new slide is shown with two images. The top left image shows a smooth surface. The image on the bottom right shows rougher surface with a wedge. Transitions back to Dr. Hoek and then back to the slide.

Dr. Hoek: Blasting is very important, and the top slide shows a comparison between what we call controlled blasting, where you see the blasting has been. The drill hole alignment has been very carefully controlled. Drill holes close together, and these are detonated simultaneously so they effectively split the face off in what we call a smooth blast. And that gives you a very steep slope which has the advantage that any rocks falling will fall straight down the slope, they won’t bounce. And much better stability than the uncontrolled blast that you see on the right of that picture. A huge difference. Unfortunately, it's not always possible to do this for a variety of reasons and the slide on the right shows the slope where they tried controlled blasting, but a wedge came out in the middle of that and so sometimes in strongly jointed rock masses you simply can't control, you can't produce a nice clean blast face.

Transitions to show Dr. Hoek on screen with a slide in the top corner with three images. The top left image is of a dump truck at the bottom of a slope in a mine. The top right is of a bulldozer moving soil and the bottom right is of a man looking up at a slope. Text on the slide reads “In very closely jointed hard rock slopes, trimming the slope face with a dozer can sometimes result in smoother and more stable faces than by using controlled blasting.” After a moment, the slide moves to fullscreen.

Dr. Hoek: This was a very unusual attempt to develop smooth faces. This was done on a mine called Bougainville in Papua New Guinea and where the rock mass was very very heavily jointed, very small interlocking blocks of rock and it was very difficult to get a good blast face. And so, they decided to try doing it with the dozer once they'd done their production blast to take the ore out, they cleaned up as much as they could with a front-end loader and then just using a large bulldozer as you see on the top right there they came along and just trim the surface material off. And you see in the picture in the middle of the picture a very smooth face created by just bulldozer trimming. And that was a very effective solution.

Transitions to Dr. Hoek on screen.

Dr. Hoek: I've not seen it applied elsewhere and that mine was closed down for a variety of reasons. So, it hasn't found its way into general practice yet, but something worth considering. I quite often see shotcrete applied to slopes and this has to be done very carefully.

A new slide is shown on screen with two images. Top left: a slope with shotcrete that has failed. Bottom right: Engineers installing grouted cables into a rock face from a ledge. Transitions to show Dr. Hoek on screen momentarily and then back to the slide.

Dr. Hoek: On the top left there, you'll see shotcrete layer on a slope which is inherently unstable in a deep-seated circular failure. And the shotcrete is of absolutely no value there at all. In the early days, on the Egnatia highway in Greece, when they started this is a highway that runs 680 kilometers across northern Greece, they applied shotcrete to many slopes, and they subsequently went back and took it off because they found it was unsightly on the one hand and b) it wasn't very effective. And what they did was develop a series of meshing solutions and even little plant boxes which were held up along with slope and grew plants and stabilizing material of that sort. So, shotcrete was actually taken out of operation there. In some cases, it can be used, and the lower photograph is a slope in Taiwan, where they've used very heavy anchors to stabilize the rock slope and you see them being drilled in there. And the shotcrete is used to keep the surfaces stable. The shotcrete in that case would have probably a heavy mesh and the shotcrete would be applied on top of the mesh and integrated into it. So, in many cases it can be effective, but a thin layer of shotcrete just sprayed on the slope is not very much use. There are cases where it becomes essential to control the stability of a large slope, you don't have the option.

A new slide is shown on screen showing a concrete buttress being installed at the toe of a slope. Many engineers are working on a large platform on the right side of the slide with multiple layers of concrete. Text reads “Stabilization of the toe of a critical slope by means of a heavy buttress.”

Dr. Hoek: This is an outlet to a power tunnel and so that profile has to be maintained. And so, in this case it's a granitic slope with good rock behind you but many failure planes and so it was decided to stabilize a slope with a heavy concrete buttress and cables drilled into it.

Two images are shown. Top left long, high-capacity cable anchors are prepared for installation in a concrete buttress at a toe of the slope. Bottom right image shows many men carrying cable on a platform towards the concrete wall with machinery beside them. After a moment, it transitions back to Dr. Hoek speaking on screen.

Dr. Hoek: And here you see on the top left, the cables, these were 30 meter long hundred-tonne cables laid out on a bench. The sharp end if you like in the front of the picture. And on the bottom photograph you see an army of people, they're carrying one of these cables along and feeding it into a hole, next to a hole which is being drilled. So that's an unusual operation because in general it's not economical to try and stabilize large slopes like this but sometimes you have to. A very effective solution for small slopes is what we call a gabion, which is basically a wire basket filled with rock.

A slide is shown with two photos. On the top left, two engineers construct a Gabion wall behind some fencing. On the right, two Gabions, (wire mesh with rocks filled inside) one on top of each other are shown buttressing the toe of the slope. Transitions to Dr. Hoek speaking again.

Dr. Hoek: And you see one being constructed there and the lower right shows a gabion in place. And this has the advantage of being flexible and porous. So, it's a good weight, it's flexible, it allows the water to flow out and for small slopes these can be very very effective. And it's something you see all over the world as a solution to small slope stability problems. And then we come to the question of rockfalls.

A slide is shown with two images of Rockfall hazards. Both show a steep rocky slope directly next to a roadway with green hills in the background. After a moment, the screen transitions to show Dr. Hoek speaking.

Dr. Hoek: Rockfalls are a hazard in all mountain highways and there are various ways to control them. I'm sure if you've driven around the Rocky Mountains in North America, you've seen these rockfalls, rockfall hazards or at least hopefully haven't seen one but you've seen the potential for one. And even a small rock can be very dangerous. One of the slopes that I worked on has the potential for very big failures. The only fatality they've ever had was from a small boulder about the size of a baseball that bounced out and came through a windscreen and killed him, a person in the car. So, the size of the, don't be alarmed if you don't see big, big blocks. They’re still rockfall hazards and one of the ways we had examined this is by doing rockfall analyses.

A model is shown on screen of a slope with a boulder shown in blue and the path it will take as it falls down the slope. On the left there is a flat asphalt roadway. To the right is clean hard bedrock, then bedrock outcrops, followed by clean hard bedrock and then talus cover on the far right shown in green. A simulation occurs where the boulder falls from the Talus cover and rolls down the hard bedrock over the outcrops and bounces from the lowest clean hard bedrock onto the roadway.

Dr. Hoek: Now, this is a model in which boulders of various shapes can be sent tumbling down the slope and you see exactly what happens there. What becomes clear when you look at a model like that is that there are two controlling features. The first one most importantly is the geometry of the slope. If you have a slope that has the potential for outward facing dipping slopes, that effectively become ski jumps for the boulder and you'll notice how that boulder tumbled down and occasionally hit something and bounced outwards.

Transitions to show Dr. Hoek on screen.

Dr. Hoek: It's the outward velocity imparted by those slopes that is dangerous because that is what pushes the boulder out into the highway or whatever you have below you. And so, the geometry in the slope is by far the most critical component and these models however simple or complicated they are, have a huge utility in simply looking at the consequences of the geometry that you have and giving you the opportunity of either changing the slope geometry if you can, or putting barriers in appropriate places. That particular slope was an actual project.

A slide is shown on screen of the probabilistic analysis. Spherical boulders in red and rectangular in blue and their paths are shown on the same geometry described in the previous slide.

Dr. Hoek: And you see there the probabilistic analysis was done for two boulder shapes: one was a spherical boulder and the other rectangular boulder. And they have different trajectories, the rectangular boulder actually goes out further because it's doing more rotations and tends to bounce further out. And you'll see that the bottom there was a highway and there's no way that that's an acceptable solution. In fact, that project had to be drastically changed.

Transitions to Dr. Hoek on screen looking at the projected slides on the screen speaking.

Dr. Hoek: If the situation exists, then you have to consider what kind of remedial action you can take, one of them is changing the shape of the slope but that's not always in fact, it's not usually possible to do that. One of the simplest solutions is to ensure that you have a catch ditch.

A slide is shown with an image of a catch ditch on the left at the base of a rock slope. A diagram is shown on the right.

Dr. Hoek: And this is a little diagram produced way back by the federal highways Department in the United States by a man called Ritchie, who simply stood on rock slopes and threw rocks down and watched where they bounced. Which is simple enough and produced a series of charts, so that for a vertical slope you have a relatively narrow catch bench with a back facing slope, so that tends to throw the boulder back into the slope. And as the slope rolls instead of drops you have to change the geometry of the catch ditch at the bottom.

Transitions back to showing Dr. Hoek on screen.

Dr. Hoek: So that's a very simple and very effective solution and you see it on hundreds of kilometers of highway around the world. Barriers are a very important aspect of rockfall control and there are hundreds of different types of designs. Again, this is a problem that's unique to each slope.

A slide is shown with two images. On the left is a steep slope with a path below it with a fence installed. The right image shows a light mesh along the slope face.

Dr. Hoek: On the top there you see a very steep slope constructed by careful blasting and normally there would be very little rockfall hazard but it's above, it's part of a benched very steep benched face. And so, you have to ensure that if a rock fall does occur you don't create a hazard for those working below you. And so, in that case a robust catch fence has been put up along the edge of the bench to prevent any small boulders from rolling.

Transitions back to Dr. Hoek on screen. After a moment, the slide is once again shown on screen.

Dr. Hoek: In many cases you will see very large structures, very large concrete structures and in order to ensure that you don't have this outward movement from a slope onto a road below or onto some feature below. This is in British Columbia through the Rockies. And it's a very light mesh but it's been placed in such a way that it's designed to simply kill the horizontal velocity of a boulder rolling down, small boulders obviously it wouldn’t withstand a large rock fall. But so, it's got a sort of funnel at the top that would catch the boulder and then the mesh would simply keep it close to the slope and drop it into the into the ditch.

Transitions back to Dr. Hoek on screen.

Dr. Hoek: So, there are many solutions of this type that can be considered. And the model that I showed you earlier on is a very valuable tool for placing these in the right locations and for calculating what capacity you need to resist the kind of boulders you're anticipating.

An image of a rock slope with two tunnels going in and out of the rock slope. A river is below the rock slope. Text reads “Rockfall and avalanche shelters over a railway line at the toe of a steep mountain slope.”

Dr. Hoek: And the final slide is one you see quite often in mountainous territory and particularly this is in British Columbia on a rail line through the Rockies where you have along the rail line there, you can see a couple of tunnels you might call them. Some of our real tunnels, some of them are cut and cover tunnels where you've got a very robust protection and usually the top of that is filled with rubble, so that any rock coming down slides off and in this case into the river.

Transitions back to Dr. Hoek.

Of course, what you don't want is to have it cascading down onto another highway below you but that's something you have to consider. But this is a very effective solution for both avalanches, snow avalanches and for rockfalls. So that brings us to the end of this lecture and thank you for your attention.

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