Lab 4: Slope stability and landslide mapping

Transcription

1 Lab 4: Slope stability and landslide mapping Objectives In this lab, you will map landslides associated with hurricane Irene in the Adirondack Mountains of upstate New York, and compare your results to predictions based on an infinite slope-stability model. You will come out of this lab with a sophisticated understanding of how to generate and interpret landslide hazard maps in soil-mantled upland landscapes. P. Brown, timesunion.com Figure 1. Landslide scar on Wright Peak following Hurricane Irene on August 28, The typical slide involved approximately 1 m of soil failing at the interface between soil and competent bedrock. Background On August 28, 2011, the remnants of Hurricane Irene dumped 5-7 inches of rain on the high peaks of the Adirondacks in upstate New York, triggering dozens of shallow landslides throughout the region. We are going to take advantage of the excellent satellite imagery coverage in the area to map the spatial distribution of the resulting landslide scars, which stick out starkly in the otherwise densely forested landscape. The distribution of landslides throughout the landscape is not random, but varies depending on local topographic parameters such as slope and upstream drainage area. This enables us to test a range of slope-stability models that vary in their treatment of rainfall-induced changes in pore pressure. I have included a landmark paper that describes the methodology behind one of the models we will be using: Montgomery, D.R., and Dietrich, W.E. (1994). A physically based model for the topographic control on shallow landsliding, Water Resources Research 30(4),

2 4.0 Summary of provided datasets You have been provided with a map file lab_4.mxd that includes a number of layers that reflect the terrain, satellite imagery, and mapping of landslides and bedrock exposures in the high peaks region of the Adirondacks. These layers can all be found in the file geodatabase lab_4_data.gdb. Below is a brief summary of the pertinent data sets. Table 1. Summary of provided datasets Name Data type Grid size Description Source adk_dem raster 10 m Elevation (m) USGS NED adk_hillshade raster 10 m Hillshade adk_tan_slope raster 10 m Tangent of slope angle (m/m) adk_drainage_area raster 10 m Contributing drainage area (m 2 ) adk_d_over_h raster 10 m Modeled variable soil saturation (m/m) NAIP_2009 raster (3 band) 1 m Pre-Irene satellite imagery USDA NAIP NAIP_2013 raster (3 band) 1 m Post-Irene satellite imagery USDA NAIP adk_10m_contour line feat. class N/A Contours of elevation with 10m spacing pre_2009_landslides polygon feat. class N/A Outlines of pre-irene landslide scars R. mapping pre_2009_ls_heads point feat. class N/A Location pre-irene landslide heads R. mapping bedrock_polygons polygon feat. class N/A Outlines of persistent bedrock exposures R. mapping By this point you should be familiar with elevation, hillshade, and imagery rasters. In addition, there are a few new spatial data sets that will aid you in this lab: The raster dataset adk_tan_slope is the tangent of the slope angle at each cell (Fig. 2), and as a result will look nearly identical to the slope maps you are used to generating. Figure 2. Tangent of slope angle vs. slope angle in degrees. Note the linear relationship up until about 30. The raster dataset adk_drainage_area indicates the total upstream drainage area for each cell in units of square meters. This value will be lowest on the ridgelines, and increase as you move downstream into the river network. The minimum value of 100 m 2 indicates the area of a single 10 m x 10 m grid cell. We will go through the steps to generate maps of drainage area in a later lab, but for now, just note that this raster was calculated using the D-infinity flow-direction algorithm (Tarboton, 1997 Water Resources Research). 2

3 The raster dataset adk_d_over_h is the modeled degree of soil saturation during the rainfall event associated with Hurricane Irene. The degree of soil saturation, expressed as the ratio of the water table height d to soil thickness h, varies from d/h = 0 (completely dry) to d/h = 1 (completely saturated). This value was calculated according to the following equation: dd h = qq TT AA bb sin θθ (Equation 1) Where A is the drainage area, b is the grid size (10 m), θ is the local slope taken from the digital elevation model, q is the average rainfall rate, and T is the soil transmissivity, a metric of how efficient water can move through the soil layer (Montgomery and Dietrich, 1994). The specific values for each of these are listed below. Table 2. Parameters used in infinite slope-stability model for Adirondack high peaks. Parameter Value Units Description tan φ m/m Angle of internal friction ( = 30 ) C 2500 Pa Soil cohesion h 1 m Average soil thickness η Soil porosity ρ 1800 kg/m 3 Average bulk density of soil ρ w 1000 kg/m 3 Density of water g 9.8 m/s 2 Gravitational acceleration P m 24 hour rainfall total for Aug. 28, 2011 q 7.5 mm/hr Average rainfall rate K sat m/s Saturated soil hydraulic conductivity T m2/s Soil transmissivity (hk sat) 4.1 Mapping landslide scars The first task for this lab will be to map the distribution of landslide scars associated with Hurricane Irene. In a nutshell, you will switch back and forth between the 2009 and 2013 imagery, and assume that any visible landslide scars occurred during Hurricane Irene in August 2011 (Fig. 3). Figure 3. Before (left, 2009) and after (right, 2014) Hurricane Irene on Saddleback Mountain (Google Earth) 3

4 To get started, create a new feature class by navigating to and opening the tool \\Data Management\Feature Class\Create Feature Class\ (Fig. 4). Figure 4. Create feature class dialog box. Set your workspace to Lab_04_data.gdb, and give your feature class a name such as landslide_outlines. Make sure the geometry type is POLYGON, and then set the coordinate system to be the same as the other layers in your map (NAD_1983_UTM_Zone_18N). Once you have created a feature class, you can begin mapping individual features using the editor toolbar (Fig. 5). To start an editing session, click start editing from the drop-down menu on the editor toolbar. Select feature Vertices Editing Toolbar Create Feature Window Figure 5. Editor toolbar showing main tools used in this lab. Before starting, it will be helpful to turn off snapping. You can open the snapping toolbar through the drop-down menu on the editor toolbar. Make sure that use snapping is unchecked (Fig. 6). 4

5 Figure 6. Snapping toolbar options. To draw a polygon, click the create features button to bring up the create features window (Fig. 7). Here you can select which layer you want to edit, and choose the type of feature you wish to create. Be sure you are aware of which layer you are editing! To map a landslide, select the polygon shape, and start clicking out the boundaries of the scar, and double click to finish the shape. It is helpful to switch back and forth between the 2009 and 2013 imagery (Fig. 7) Imagery 2013 Imagery Mapped landslide scar Figure 7. Example of mapped landslide scar, showing create features window. To delete a feature you created, use the select feature tool (Fig. 5) to click and select the feature you wish to delete. Once it is highlighted, press delete to delete it. If you mistakenly delete a feature, you can always press Ctrl-Z to undo. 5

6 If you want to edit the vertices of one of the polygons you drew, simply double click on the outline of it to switch to vertex mode (Fig. 9). You can move around individual vertices, add new one, or delete them. Figure 9. Edit vertices toolbar. As you are mapping, be sure to periodically Save Edits through the editor toolbar menu. Some potentially helpful mapping tips: From the Window pull-down menu, you can open up the Imagery Window, where you can accelerate the drawing of individual image files, and also enable a cool slider button. I already mapped bedrock outcrops and old (pre-2009) landslides, which are included as polygon feature class layers in your map. Looking at the landslides associated with Hurricane Irene, I was able to map somewhere around 40 individual scars. You should shoot for a similar number. Remember to think about the expression of different zones of the landslide scars (i.e., erosion, transport, and deposition). We are mostly interested in mapping the erosional zone, where bedrock has been exposed. Once you are finished editing, select Stop Editing through the drop-down menu on the editor toolbar. Next, we want to estimate the total volume of material evacuated by these landslides. Open up the attribute table of your mapping layer, and you should see a few data columns. Right click the column titled Shape_Area, which reflects the planform area in square meters for each polygon, and select Statistics. Below, record the Sum of the Shape_Area column, including units. Total area of Hurricane Irene landslides (m 2 ): To convert this to volume, multiply the area by the average soil depth given in Table 2 (we are assuming that these landslides failed along the soil-bedrock boundary, which is likely the case based on photographs from the area). Total volume of Hurricane Irene landslides (m 3 ): We can convert this volume to a measure of landscape-averaged erosion by dividing by the total area of our mapping extent (roughly 40 km 2 or 4 x 10 7 m 2 ). It will be easiest to interpret if you convert to units of mm. Landscape averaged erosion (mm): 4.2 Plotting landslide initiation points on slope-area diagrams As mentioned in the introduction to this lab, the distribution of landslide scars is not random, but depends on local hydrologic and topographic conditions. In this section, you will extract this information from your landslide map and plot it up in Excel to assess where the landslide initiation points sit in a stability diagram of local slope versus upstream contributing area. 6

7 First, create a point feature class, following the same steps as shown above (Fig. 4), except give it a name like landslide_heads and be sure to select POINTS for the geometry type. Don t forget to select the appropriate coordinate system! Once you have created the point feature class, start editing, and create a point at the uppermost extent of each landslide you have mapped (Fig. 10). Be sure you know which direction is uphill! If in doubt, turn the contours on, or use the info button to spot-check elevations. Figure 10. Example of landslide head, or initiation point, locations (yellow dots). Once you have mapped all of the landslide heads associate with Hurricane Irene, don t forget to close your editing session by selecting Stop Editing. Next, we want to extract the value of the local slope and contributing area for each point. Open the tool \\Spatial Analyst\Extraction\Extract Multi Values to Points (Fig. 11). Figure 11. Extract Multi Values to Points dialog box. Be sure to change the output field name as shown. 7

8 For the Input point features, select the point feature class you just created. For the Input rasters, add the rasters adk_tan_slope and adk_drainage_area. You will need to shorten the Output field name as shown in Figure 10. Note that these will be columns in the attribute table of the point feature class containing the local values for the tangent of the slope angle and the contributing area. This has already been done for the older landslides, as you can see in the attribute table for the feature class pre_2009_ls_heads (Fig. 12). Figure 12. Attribute table showing the addition of two new data columns containing the local values for slope and area at each landslide head. Next, we want to bring this data into Excel for plotting. Navigate to and open the tool \\Conversion\Excel\Table To Excel (Fig. 13), and save your data to a folder location (not the geodatabase!) with a name like landslide_heads.xls. Figure 13. Table to Excel dialog box. Now, open up the newly created Excel spreadsheet, and copy and paste the data tables into the appropriate columns of the Excel file lab04.xlsx, which has been provided to you. You should be able to add your data to the existing plots that show the stability diagrams for the two pore pressure models you will explore later in the lab. The black symbols indicate the slope and area values for each of the pre-irene landslides. Do the landslides from Hurricane Irene fail in similar parts of the landscape? When you have added your data to both plots, save the charts as a.pdf file to include with your report. (Fig. 14). 8

9 Figure 14. Slope-area plot showing stability fields for a uniform pore pressure model (left) and a spatially variable pore pressure model (right), along with values for pre-2009 landslide heads. 4.3 Calculating Factor of Safety in ArcMap Now that we have generated a nice landslide map, we can compare our result with an estimate of slope stability using the infinite slope-stability model. Recall from class the factor of safety (FS) equation for the infinite slope stability model, which we can separate into three key terms: FFFF = FFFF ffffffffffffffff + FFFF ccccheeeeeeeeee FFFF pppppppp pppppppppppppppp (Equation 2) FFFF ffffffffffffffff = tan φφ tan θθ (Equation 3) FFFF ccccheeeeeeeeee = CC ρρρρh sin θθ FFFF pppppppp pppppppppppppppp = ρρ ww ρρ dd tan φφ h tan θθ (Equation 4) (Equation 5) Table 2 provides estimated values for many of these parameters, and we can extract tanθ from the raster dataset adk_tan_slope. We are now going to use the \\Spatial Analyst\Map Algebra\Raster Calculator tool to solve the above equations. You can click on the datasets to input them into the equation box (Fig. 15), and the Raster Calculator performs the algebraic expression on every grid cell in the raster. Because you will be generating a number of similar data sets, it is critical to stay organized. It will be easiest to follow along if you use the same file naming conventions as I do. First, calculate the term FS friction (Equation 3) by entering the following into the Raster Calculator and saving to the Output raster FS_friction (Fig. 15): 0.577/"adk_tan_slope" 9

10 Figure 15. Raster calculator dialog box, showing calculation for FS_friction. To estimate the FS cohesion term, we can repeat the process with a more complicated expression (Equation 4): FS_cohesion = 2500/(9.8*1800*1*Cos(ATan("adk_tan_slope"))*Sin(ATan("adk_tan_slope"))) Note that you only enter the right hand side of the equation into the Raster Calculator (Fig. 15), and set the left hand of the equation as your Output raster. You can copy and paste this equation in, or just be very careful about syntax, especially keeping parentheses balanced! Remember, rather than typing in the full raster dataset name (i.e., "adk_tan_slope"), you can simply click on the raster layer in the upper-left box when you wish to insert it (Fig. 15). We can now estimate the dry factor of safety by adding these two rasters together: FS_dry = "FS_friction" + "FS_cohesion" The output raster FS_dry now corresponds to the factor of safety estimate without any added rainfall trigger. Recall that for FS > 1, slopes are predicted to be stable, and for FS < 1, slopes are predicted to be unstable. Thus, we might expect some correspondence between areas where FS_dry < 1 and areas of persistent bedrock exposure, which I have included in your map as the layer bedrock_polygons. Change the classification of FS_dry to highlight areas of instability (I suggest FS<0.8 = highly unstable; = unstable; = stable; and >1.2 = very stable). How does this line up with the patterns of bedrock exposure? 4.4 Modeling the influence of rainfall on slope stability 1D Since we are interested in how Hurricane Irene influenced slope stability, we clearly need to include water into the picture. Equation 5 indicates that the pore pressure term is primarily controlled by the ratio d/h, which is a measure of the degree of saturation of the landslide material assuming parallel seepage (in this case the height of the water table divided by the soil thickness). We do not have direct measurements of soil moisture immediately preceding the landslides, so we must model this quantity. The simplest way we can do this is to treat it in one dimension, as if the rainwater is filling a bucket (or more precisely, a sponge). 10

11 The total rainfall received was likely on the order of 150 mm, based on data from a nearby rain gage (Fig. 16). If we assume that the porosity η of the soil is 0.5, and the soil thickness is 1 m, then 150 mm of rain corresponds to a spatially uniform value of d/h = 0.3. Figure 16. Rainfall data from nearby weather station We can now calculate the term FS pore pressure (Equation 5) using the raster calculator (Fig. 14): FS_p_term_uniform = (1000*0.3*0.577)/(1800*"adk_tan_slope") And the corresponding factor of safety as: FS_wet_uniform = "FS_friction" + "FS_cohesion" - "FS_p_term_uniform" Change the symbology to classify the resulting factor of safety map the same as the dry case. How does the stability change with the addition of water? Are the patterns in stability consistent with the landslides you mapped? 4.5 Modeling the influence of rainfall on slope stability 2D The two-dimensional form of the landscape exerts a strong control on the spatial patterns of soil moisture and surface water. Areas of convergent topography tend to collect water and eventually form streams, while divergent ridges tend to drain water away. I have provided you with the raster adk_d_over_h, which indicates the output of a spatially variable model for the degree of soil saturation (Equation 1). This model accounts for the convergence or divergence of topography, and is calibrated for the soil conditions and rainfall events associated with Hurricane Irene. The full details of the model, which is called SHALSTAB, can be found in the attached 1994 paper by Montgomery and Dietrich. First, take a look at the map of d/h, and compare it to the map of contributing drainage area (Fig. 17). How are these two similar? Different? 11

12 Figure 17. Map of drainage area (left) compared to spatially variable d/h from SHALSTAB model (right). To incorporate this into the FS pore pressure term, open up the Raster Calculator again (Fig. 15), and calculate the following: FS_p_term_variable = (1000*"adk_d_over_h"*0.577)/(1800*"adk_tan_slope") and likewise calculate the new factor of safety accounting for spatially variable pore pressures: FS_wet_variable = "FS_friction" + "FS_cohesion" - "FS_p_term_variable" Again, classify this map with the same color scheme as the other two factor of safety calculations and compare the patterns to the locations of your mapped landslides. Note that the stability fields in slope-area space calculated from this model are plotted on Fig

13 Lab 4 deliverables, due Friday February 20 before lecture (50 pts total) Please submit as single PDF file to the Lab 4 drop box on Angel (10 pts) A map showing the distribution of landslides caused by Hurricane Irene The easiest base map to use is probably the 2013 air photo 70% transparent over the hillshade, but others are okay as well as long as they are not distracting. You only need to show the polygons for the landslides you mapped. There is no need to include the landslide heads, older mapped landslides, or bedrock polygons on this map. Be sure to include a legend, scale bar, north arrow, title you know the drill by now! (5 pts) 2 plots of slope vs. area showing landslide initiation points on top of slope-stability fields and the locations of pre-2009 landslide heads. This involves simply adding your data to the plots in the attached excel file Lab_04.xlsx, and saving as a.pdf. (see section 4.2) (5 pts) A map showing the dry factor of safety ( FS_dry ), with bedrock polygons overlain (see section 4.3) I highly suggest having the factor of safety map 50% transparent over the hillshade, with bedrock polygons as outlines (i.e., no fill color) Use an appropriate color scale (see suggestion in section 4.3) and keep it the SAME for all 3 factor of safety maps! (5 pts) A map showing the factor of safety using the 1-D soil moisture model ( FS_wet_uniform ) with landslide polygons overlain (see section 4.4) Same as the dry map, but include both the old landslide polygons, and the landslides you mapped from Hurricane Irene. (5 pts) A map showing the factor of safety using the 2-D soil moisture model ( FS_wet_variable ) with landslide polygons overlain (see section 4.4) Same as above, including both the old landslide polygons, and the landslides you mapped from Hurricane Irene. (20 pts) A written report no more than 3 pages long (12 pt font, 1.5 line spacing, 1 margins), which should include the following A brief introduction (no more than 1 paragraph) A description of the methods/approach used for mapping landslide scars (1 paragraph) A description of the results including results of your mapping and the provided maps of bedrock and older landslides, and a description of the results for each of the 3 factor of safety models. (~2 paragraphs focused on observations and measurements) A discussion focused on addressing the following questions: 1) What is your estimate of landscape-averaged erosion (in mm) due to landslides associated with Hurricane Irene? If you assume that the long-term erosion rate of this region is approximately 0.1 mm/yr, estimate the recurrence interval of events the size of Hurricane Irene. 2) Are these landslides randomly distributed throughout the landscape, or is there a pattern to where the failures occur? Is there a difference in landscape position* between the pre-2009 landslides and the landslides associated with Hurricane Irene? *Hint: use the slope-area plots as a guide (continued on next page) 13

14 3) How does the dry factor of safety compare to the distribution of persistent bedrock exposure? How does the addition of a uniform pore pressure influence the pattern of slope stability relative to the dry case? How does the addition of the spatially variable pore pressure model influence the pattern of slope stability? 4) How well do the models predict the distribution of failures associated with Hurricane Irene? Do all landslides occur in regions mapped as unstable? Do all regions mapped as unstable show evidence of slope failure? 14