Landslide Mechanics：滑坡力学.doc

EPSC 409: Surface Processes Assignment 3 Landslide MechanicsNote for using Excel file: DONT click on the chart, dont mess with the grey cell. If you mess something up, revert to the unchanged downloaded file.For a derivation of the equations go to /geo/faculty/lemke/geomorphology/lecture_outlines/17_slope_stability.htmlBased on the factor of safety equation:generate a formula for the cells under “driving force” and “resisting force” (outlined) that will calculate each force using the given parameters (e.g., density, thickness, etc.). c=cohesion, h=slab thickness, q=slope angle, g=unit specific weight slab material, gw=unit specific weight water f=angle of internal frictionNote 1: g, or unit specific weight, is SIMPLY density (r) * gravity. Note 2: Lets try to get this as accurate as we can: the effect of pore pressure on the normal force is incorporated into the resisting forces through inclusion of the gwm factor in the shear strength formula; but lets add in the changes to the driving force as well. To approximate the effect of having a partially saturated slab, modify the driving force equation so that the weight of the portion of the slab which is above the water table is calculated using the *dry* density of the material, while the weight of the portion of the slab below the water table is calculating using the *wet* density of the material.Note 3: Excels default when calculating trig functions is to presume the input angle is in radians; since both f and q are in degrees, you will have to deal with the conversion.1. Please write out the modified formulae you used. (You do not have to give me exactly what you typed- A2*B2etc.; just write out the formulae with the changes you made (e.g., rg substituted for g, etc.), including the conversion from degrees to radians.Next: set the following as default values (dry granular material, no cohesion):Dry density2000 kg/m3H1 mq15 degreesG9.8 m/s2f25C0M0And insert a formula for F into the appropriate cell (H3).The chart on the Excel sheet should show a comparison of the driving and resisting forces, give F, and tell you whether the slope is stable (safe) or not (SLIDE!). 2. What did you get for driving and resisting forces, and F? 3. With ALL OTHER parameters at their default values, vary EACH of the parameters below over the following ranges. Create graphs of your results both for driving and resisting force for each sensitivity test. Each test should include at least five values.f25-45 degreesH0.2 to 20 mq0 to 90 degreesYou should finish this part of the exercise with three sets of graphs relating driving and resisting force to changing input parameters. For each graph summarize in one sentence how changing a particular parameter affects the balance of driving and resisting forces, and thereby F. 4. Based on the graphs you just created, is there one single most important parameter controlling slope stability; if so, what is it? Explain your answer. _Now lets look at how water changes the picture.Set: Dry density1800 kg/m2Wet density2000 kg/m2H2mF30C0q20G9.8 m/s25. At what water table elevation above the failure plane (m*h) will the slope fail? 6. What are the driving and resisting forces at that point?7. What about cohesion: set cohesion at 10,000 pascals (10 kPa: weak sandy clay). Does the slope fail? Even if you saturate it completely?8. How important is cohesion to the overall balance? Note: 10 kPa is very low cohesion. Now lets try using these equations on whole regions using GIS.1. Open an empty map document and add the DEM and the polygon coverage “geol”.2. Using “PTYPE” as the join field, join the table “data”, within the geodatabase “db1” to “geol”.3. Now take a look at the attribute table for “geol”. Its got most of what you need (densities, cohesion, internal friction) to calculate F; but, the calculator functions require rasters, so we need to convert from vector to raster. Go to Spatial AnalystOptions. Click the Extent tab, and set the Analysis extent to “Same as layer “Calculation5”. This will effectively clip the new rasters you create to the size of the DEM.Now go to Spatial AnalystConvertFeatures to Raster. Input features should be “geol polygon”. For field, start with “data.DRYDEN”. For Cell Size, enter 30 (this is the size of the cells in the DEM, 30 m; this way the resolution of all your datasets will be the same). Save the output raster to your folder, call it “DRYDEN”. Click OK. Repeat this procedure for WETDEN, INTFR and COHES. Note: if you go to Spatial AnalystOptions and in the General tab, set the working directory to your folder, it will automatically store your calculations in that folder, you wont have to browse to it every time.4. You can remove “geol polygon” from the map document. OK, what next? You need slope angle. Use Spatial AnalystSurface AnalysisSlope to calculate the slope in degrees from your DEM.5. Now for the fun part. You should have everything you need, now, to calculate F except h and m, which well vary. You could automate this process using an ArcGIS extension called ModelBuilder, but were not going to go there for now (its even more of a pain than the rest to make work). First, in Spatial analysisOptionsExtent, set the analysis extent back to Union of Inputs (I was getting errors until I did this, but I dont know why). What I would suggest you do is do the calculation of F in several stages; you will be using Spatial AnalystRaster Calculator. Open the Raster Calculator window. If you dont see Trig Functions, click the right arrows in the lower right hand corner. Start by calculating q in radians; in the expressions box in the Raster Calculator window, type ( then doubleclick on “Slope of Calculation5”; that should put Slope of Calculation5 in the window. Then type “ * 3.14159) / 180” without the quotes, but *do* make sure to surround any operators (like the * or /) with spaces. Otherwise it wont work. Then click “Evaluate”. Look at the range of values in your new raster; does this look right? Go to Properties on your new calculation and rename it “ThetaRadians”.6. Now go to Raster Calculator again. This time hit the “Sin” button, then doubleclick “ThetaRadians” in the layers window. Click evaluate. Again, look at the range of values you get in the raster. Do they seem right? Do this with every calculation you make to be sure you have calculated the right thing. Calculate as many components of F (the modified version you developed in part 1) as you can without involving m or h, name each with what it is (e.g., sinXcos). List the rasters you have calculated. Note: to generate the square of something hit the “Sqr” button and then double click the layer you want to square.7. Lets start with a simple case; 1 m thick slab, fully saturated. Generate rasters for the driving and resisting forces. Copy the expressions you wrote into the Raster Calculator box for the driving force raster and the resisting force raster into your word document. Export the 2 maps as images, place them into your word document and label them. Make sure you include a legend for each. 8. Now calculate F. You will have a hard time displaying this because of the range of the data; however, we dont really care about the values of F, just whether or not its above or below 1. This brings us to another useful tool; Spatial AnalystReclassify; this allows you to take ranges of data from one raster and assign them a new value. Make sure your input raster is set to your F raster. By typing directly into the “Old values” column, set the ranges of data to “ xx 0.5” for new value 1, where “xx” is simply the minimum value given (leave it at what it is), “0.5 0.9” for new value 2, “0.9-1” for 3, “1-1.1” for 4, “1.1-1.5” for 5, and “1.5- yy” for 6, where “yy” is the given maximum. Click reclassify. In your new raster (Reclassify of CalculationX), go to PropertiesSymbology, and in the label field, type in “Very unstable” for 1, “Unstable” for 2, “Slightly