Computational Science Module

Landslides and Slope Stability Analysis

Using an Infinite Slope Model to Delineate Areas Susceptible to Translational Sliding in the Cincinnati,

OH Area

developed by

John B. Ritter Department of Geology Wittenberg University

January, 2004

Overview or Description of the Module Landslides are a persistent cause of economic loss in every region of the United States, amounting to billions of dollars in property losses annually according to the U.S. Geological Survey (e.g., U.S. Geological Survey, 1982; Spiker, E.C. and Gori, P.L., 2000; Spiker, E.C. and Gori, P.L., 2003). One strategy for reducing losses from landslide hazards is to delineate susceptible areas for planning and decision-making purposes, the ultimate goal of this module. The objectives of this module will build toward that goal; they are to (1) explore different types of mass wasting processes using on-line resources and recent mass wasting events; (2) evaluate the sensitivity of slope stability to topographic and earth material variables according to the infinite slope method; and (3) assess the spatial variation in slope stability using a Geographic Information System (GIS). The final objective will focus on the urbanized area of Cincinnati and Hamilton County in southwestern Ohio. The highest documented per capita losses due to landslides, amounting to $5.80 per person per year, occur in Hamilton County, in the metropolitan area of Cincinnati (Fleming and Taylor, 1980). The module uses an infinite slope stability model to calculate a factor of safety. The infinite slope model is based on algebraic manipulation of various raster data layers to produce a map of factor of safety values and as such is a deterministic analysis of slope stability. It is particularly appropriate for slope failures with planar slip surfaces, such as translational slides, which are common in this area (Baum and Johnson, 1996). Introduction to the Problem

Mass wasting is a generic term referring to the downslope movement of soil or rock material under the influence of gravity. Landslides is nearly a synonymous term, implying a surface of failure along which slippage, flow, or fall occurs. Varnes (1958, 1975) classification system for landslides is the most widely-used and is reproduced in Table 1.

Table 1. Classification of landslide types (adapted from Varnes (1975).

Type of Material

Unconsolidated Sediment or Soil

Type of Movement

Bedrock Coarse Fine

Falls Rockfall Debris Fall Earth Fall

Rotational Rock Slump Debris Slump Earth Slump Slides

Translational Rock Block Glide

Rock Slide

Debris Block Glide

Debris Slide

Earth Block Glide

Earth Slide

Flows Rock Flow Debris Flow Earth Flow

Complex Combination of two or more types

The three primary types of landslides, falls, slides, and flows, are distinguished on the basis of the relationship between the unstable mass and the failure surface and the internal structure and deformation of the mass. In falls, the material may be in freefall, losing contact with the failure surface intermittently or entirely. In this type of landslide the mass moves as individual particles, with no coherent structure developing between particles. Slides move as coherent blocks or masses along the failure plane. Slides exhibit little internal shear or deformation such that patches of turf, trees, and structures on the surface may stay relatively intact and are not incorporated into the slide. Soil or sediment stratigraphy within the sliding mass also may be preserved. Flows move as a coherent but constantly changing mass, involving internal shear or mixing of the mass, even sorting based on particle size and position in the flow. Surface features such as turf, shrubs, trees, and structures are incorporated into the flow. Downslope materials

and surface features may be buried by the flow mass, but they may also be incorporated into the flow as this type of slide tends to be erosive as it travels along its path.

Of the different types of landslides classified in Table 1, slumps, slides, earthflows, and rockfalls all occur in Ohio (Figure 1) (Hansen, 1995), but are restricted to areas of high relief in the unglaciated portion of southeastern Ohio, along the Ohio River and other major rivers in the state, and along the shoreline.

Figure 1. Landslides occur in both weathered bedrock and unconsolidated

glacial deposits in Ohio (from Hansen, 1995). In Hamilton County and the metropolitan Cincinnati area, landslides are particularly common in high relief areas along the Ohio River and the Mill Creek and Little Miami River tributaries immediately in the areas where they join the Ohio River (Figure 2). Landslides in Hamilton County occur in unconsolidated deposits, including colluvium, till, glacial lake clays, and man-made till derived from colluvium and glacial deposits (Baum and Johnson, 1996). Both rotational and translational debris slides occur in colluvium underlain by the Kope and Fairview Formations (Baum and Johnson, 1996). The characteristics of this and other types of landslides in Hamilton County are summarized in Table 2.

Figure 2. Landslide damage on U.S. Route 52, along the Ohio River, in March, 1997 following eight inches of rainfall over two days. (Photographs by

Aaron Mitten, Ohio Department of Transportation.) (from The Atlantic Monthly, January 1999).

Damages resulting from landslides include both property damage and loss of life. Although landslides are among the most widespread and ubiquitous of geologic hazards, they occur over fairly restricted spatial and temporal scales, the extent of which is governed by the scale and duration of the triggering event such as an earthquake or extreme rainfall. Annually in the United States, landslides result in an estimated 25-50 deaths and damages exceeding $ 2 billion (Spiker and Gori, 2003). The highest documented per capita losses due to landslides, amounting to $5.80 per person per year, occur in Hamilton County, in the metropolitan area of Cincinnati (Fleming and Taylor, 1980). These losses are expanding as development pressures increase as a result of population growth.

Table 2. Characteristics of landslides in Hamilton County, Ohio (from Baum and Johnson, 1996).

Type

Style of Movement

Rate

Thickness

(m)

Materials

Rapid Earth Flow

Translation and flow

As much as several meters per second (?)

Geological Survey will provide an introduction to landslides. By studying recent events and well-documented historical events, you should understand the variation in landslide type according to types of movement and material involved (Table 1), their general distribution in the U.S. regarding physiographic position and general geology, and the conditions under which they occur, including any extreme triggering conditions.

Step 2. Sensitivity Analysis of the Infinite Slope Model. The infinite slope model is an

analysis of the ratio between driving and resisting forces of slope movement. The ratio value is called the Factor of Safety or Safety Factor. The infinite slope model is appropriate for evaluating translational landslides and is the basis for the GIS model in the next step. By evaluating a sensitivity analysis of the Factor of Safety to variables in the infinite slope model, you will better understand the importance of accurate parameter estimation as well as the significance of or confidence you might have in the GIS model.

Step 3. GIS Model of Slope Stability in Hamilton County, Ohio. A GIS model of slope

stability has been developed for portions of Hamilton County. Parameter values have been generalized from the literature, based on the geology and topography of the area. The resultant output is an overlay of values for the Factor of Safety, essentially a landslide susceptibility map. You will compare the landslide susceptibility map with two landslide inventories, one developed by the U.S. Geological Survey in cooperation with the City of Cincinnati and Hamilton County for occurrences of damaging landslides during the time period 1970-1979 (Bernknopf and others, 1990), the other more recently made available by the Hamilton County Soil and Water Conservation District (M.M. Islam, 2003, personal communication), the governmental agency responsible for permitting of earth excavation, construction, or grading on potentially unstable slopes in the unincorporated area of Hamilton County. Other simplified variants of the model, using single variables or combinations of variables (e.g., using combinations of the most sensitive parameters, slope, or geology) as predictors of slope instability, can also be evaluated. For those familiar with GIS and raster or map algebra functions, sufficient data is provided for completing a landslide susceptibility map for an adjacent area.

Statement of the Problem

Applying restrictive zoning codes for development or codes for excavation, construction, or grading, designed to reduce damages due to landslides, in areas not prone to landslides is itself costly. Delineating landslide-prone areas in which to apply loss reduction strategies requires a sound scientific basis. The summary problem being addressed here is whether the infinite slope model is an appropriate model on which to base a landslide susceptibility map for landslides in the Cincinnati area. The utility of the model and map will be evaluated by comparison with the the landslide inventories. Background Information The forces acting on a point along the potential failure plane are illustrated in Figure 3. All variables in the figures, equations, and tables are defined in Table 3.

Figure 3. Force diagram for thin to thick translational slides. Letters are

defined in Table 3. The resisting force of earth materials, whether consolidated bedrock or unconsolidated sediments, is the shear strength (S ) of the materials (Figures 3 and 4). Shear strength is a combination of forces, including the slope normal component of gravity (Figures 3 and 4) or normal stress (), pore pressure () within the material, which counteracts the normal stress, cohesion of the material (C), and the angle of internal friction (). Shear strength is given by the Coulomb Equation:

)tan - ( C S += (Eq 1)

Normal stress is the vertical component of gravity, resisting downslope movement (Eq 2).

coszcos = (Eq 2) The role of water is especially critical in slope stability, but it is incorrect to think of its role as that of lubrication. Water plays a dual role. In increasing the unit weight of material, it increases both the resisting (normal stress) and driving (shear stress) forces (Figure 4). It also creates pore pressure, which opposes the normal stress and therefore reduces the resisting force or shear strength of the material (it is subtracted from normal stress in Eq 1). It is represented by the following equation:

cosmzcos w= (Eq 3)

Figure 4. Geometry of the vector components of gravity. Unit width of the block is assumed; block length is infinite in the infinite slope model and is dropped from the equation.

The driving force is shear stress (), the slope parallel component of gravity (Figure 3). Shear strength is given by the following equation:

sincosz= (Eq 4) Slope stability is typically evaluated in terms of a safety factor, also referred to as a factor of safety and denoted as SF. As it applies to the infinite slope model, the SF is a ratio between resisting and driving forces as shown in Equations 5 and 6 and Figure 5.

S

===StressShear

StrengthShear Force DrivingForce ResistingSF (Eq 5) and

cossintancoscos)m-( CSF

zzw+= (Eq 6)

Figure 5. Definition diagram of variables in the infinite slope stability model. Variables are identified in Table 3.

It follows that if shear strength is greater than shear stress, then SF > 1 and the slope may be considered stable; if shear strength is less than shear stress, SF < 1 and the slope may be considered unstable. For SF = 1, the slope would be considered in a balanced state, but inherently unstable. In cases where SF 1, whether the slope actually fails is another matter as will be discussed later, but the potential for failure is high and mitigation would be warranted.

The infinite slope model generally relies on several simplifying assumptions which may cause some limitation to its application. It assumes that

failure is the result of translational sliding; the failure plane and water table parallel the ground surface; the failure plane is of infinite length; and failure occurs as a single layer.

It also does not account for the impact of adjacent factors like upslope development or downslope modifications of the hillslope or accentuating factors such as ground vibrations or acceleration due to earthquakes.

Table 3. Variable definitions, units, and probable value ranges.

Symbol

Definition

Units

Value Range

C

cohesion

kN/m2

0-250

unit weight of slope material

kN/m3 12-22

w unit weight of water

kN/m3 9.8

z thickness of slope material above the slide plane

m 1-20

zw thickness of saturated slope material above the slide plane

m 0-20

m vertical height of water table above the slide plane, expressed as a fraction of total thickness

dimensionless 0-1

slope of the ground surface which is assumed parallel to the slope of the failure plane

degrees 1-40

internal angle of friction

degrees 22-46

S shear strength

shear stress

normal stress

pore water pressure

Model Details Three models are included in this module. The first and second models are spreadsheet solutions of the infinite slope model as expressed by the Safety Factor (Eq 6) : Sensitivity Analysis of the Infinite Slope Model.xls This spreadsheet is intended to be used as an introduction to the infinite slope model and the Safety Factor equation. The first worksheet, Safety Factor Calculations, presents solutions for four general conditions (thin and dry, thin and wet, thick and dry, and thick and wet). These solutions are provided to discuss the role of water and slide thickness on slope stability. This section can be modified so that students or the instructor can input variable estimations to determine a site-specific SF value for a local situation. On the same worksheet, a variable by variable sensitivity analysis of SF is presented. The x-axis for each variable is the natural range for the variable and the y-axis is the same for each variable so that the relative differences in the variable-SF relationships illustrate model sensitivity. The relationships are shown for the four general conditions. The two right-most columns on this worksheet also pertain to a sensitivity analysis of SF and the graph comprising the second worksheet, Sensitivity Analysis. The methodology

for conducting the Sensitivity Analysis is included in the section on Suggestions to Instructors in the event the instructor wishes to delete these columns and the second worksheet in order to have the student do this. Rasterization of the Infinite Slope Model.xls This spreadsheet illustrates the principles of a raster model, the basis of the GIS model of slope stability for the Cincinnnati Area. Worksheets in the spreadsheet represent different data layers involved in the infinite slope model and calculation of the factor of safety. Each of these is a different raster dataset or layer in the GIS model. The final worksheet is the calculation itself and represents the map algebra (or algebra involving different data layers) that results in the calculation of the factor of safety. Data at the same x, y coordinate or cell position (or row and column in the case of the spreadsheet) from multiple layers are manipulated algebraically. The spreadsheet can be used for demonstration purposes. Slope Stability Model of the Cincinnati Area.mxd This is a Map Document file created in ArcGIS 8.2 that retains links to all files involved in producing the slope stability model for the Cincinnati, Ohio, area. The file structure (e.g., the location of the map document and the other layers and folders in the folder SlopeStabilityModule) must not be changed in any way except by users familiar with ArcGIS and using ArcCatalog. Solution Methodology/Implementation The solution methodology and implementation of the model are generally not applicable except in the case where advanced users create a slope stability map for the quadrangle adjacent the current slope stability map. General instructionsfor doing this, essentially written in enough detail for advanced users, are included in Problem 3, Part 2. Assessment of the Model Model assessment is part of Problem 2 (i.e., sensitivity analysis of the infinite slope model) and Problem 3, Part 1 (validating the slope stability GIS with a landslide inventory), and is addressed there. Empirical Data Data from the U.S. Geological Survey (Bernknopf, R.L., Campbell, R.H., Brookshire, D.S., and Shapiro, C.D., 1990) on the presence or absence of damages due to landslides is used in Problem 3. Data is also available from the Hamilton Soil and Water Conservation District (HSWCD) (M.M. Islam, pers. comm.). Both are included in the GIS model. The HSWCD data includes attribute data that can be accessed by right-clicking on the data layer title and accessing the attribute table through the context menu. Conceptual Questions In this module, an infinite slope stability model is used to calculate the factor of safety for translational slides. Why is the model used specific to landslide type or process? What is the significance or importance of conducting a sensitivity analysis? An unstable slope, as indicated by a low factor of safety, does not necessarily mean that the slope has failed or that failure is imminent. Why not? Why then does slope failure occur? What are the implications of this relative to using a landslide susceptibilty map or to other mitigation strategies?

Problems and Projects The following set of problems and projects is cumulative or additive in nature, with latter steps building on knowledge, information, or results from earlier earlier steps. Problem 1. Introduction to Landslide Processes. Appropriate mitigation strategies depend on recognition of the landslide type or process. On-line sites developed by the U.S. Geological Survey will provide an introduction to landslides. By studying recent events and well-documented historical events, you should understand the variation in landslide type according to types of movement and material involved (Table 1), their general distribution in the U.S. regarding physiographic position and general geology, and the conditions under which they occur, including any extreme triggering conditions. Objective: To understand different types of landsliding and mass wasting, their distribution in the U.S., slope or material conditions contributing slope instability, and their potential triggering events. Exercise: 1. Access the Landslides page of the U.S. Geological Surveys Geologic Hazards website at http://landslides.usgs.gov/. The general information presented here will provide an additional background to landslides to supplement the information from the module and from class lectures. Select Recent Landslide Events (http://landslides.usgs.gov/html_files/landslides/newsinfo.html) from the links found at the bottom of the page to access newspaper reports or U.S. Geological Survey briefs on recent landslide events in the United States and elsewhere. At the bottom of the page, you can access archival information.

a. For five events occurring in the U.S., summarize the following information for each:

Location and Year: Where did the failure generally occur (e.g., northern

California) and in what year did it occur? Landslide type: Given the basic definitions of the different types of

landslides (i.e., falls, slides, and flows), their classification in Table 1, and the description provided in the brief, what type(s) of landslide occurred?

Equation 6 Factors: From the article or briefing, list any variables or factors

included in Equation 6 (e.g., high slope) that might have contributed to the event.

Other Factors: Are other factors cited that do are not represented in

Equation 6? If you are unsure as to whether the factor is represented in Equation 6, list it here as well for later discussion.

b. Compare your information with your peers.

c. For a class discussion, compare your information with the map

(http://pubs.usgs.gov/pp/p1183/plate1.html) accompanying Radbruch-Hall, D.H., Colton, R.B., Davies, W.E., Skipp, B.A., Lucchitta, I., and Varnes, D.J., 2001, Landslide Overview Map of the Conterminous United States: U.S. Geological Survey Professional Paper 1183 Version 1.0 (http://pubs.usgs.gov/pp/p1183/ )

2. Access the U.S. Geological Survey website associated with real-time monitoring of landslides along Highway 50 in northern California REPORT: Real-time Monitoring of Active Landslides Along Highway 50, El Dorado County, California (http://vulcan.wr.usgs.gov/Projects/CalifLandslide/Publications/ReidLaHusen/framework.html). Select the Report link with TABLE format and in-line graphics to answer the following questions.

a. Given the basic definitions of the different types of landslides (i.e., falls, slides, and flows), their classification in Table 1, and the descriptions of the Highway 50 landslides in the report, what type(s) of landslide occurred along Highway 50?

b. From the description and associated figures, provide a relative estimate of the

parameters included in Equation 6 (e.g., high or low slope) that might have contributed to the landslide event.

c. What event or series of events actually triggered the landslides? In which

variable(s) of Equation 6 is(are) the events represented? 3. From the website, select the link Monitoring California Highway 50 Landslides - Project Menu (http://vulcan.wr.usgs.gov/Projects/CalifLandslide/framework.html), then select "Real-Time" Data (http://vulcan.wr.usgs.gov/Projects/CalifLandslide/Maps/landslide_monitor.html) to access an interactive graphic of one of the monitored sites along Highway 50.

a. Which of the monitored variables relate to the evaluating the conditions causing landsliding? Of these variables, which are represented in Equation 6? Which are not?

b. Of those that are not represented in Equation 6, what role does it or do they play

in driving or resisting landslides?

c. Which monitored variables relate to the detection of landsliding? d. Examine the graphs of downslope movement. Has there been significant

movement in the recent past? If there has been, examine data from the other instruments and summarize the conditions associated with movement.

e. Examine the rainfall data in particular. If it has rained in the previous 4 days or 4

weeks and movement has not occurred, what is the greatest magnitude of rainfall that occurred for which landslides did not occur?

f. If movement did occur, what magnitude of rainfall was sufficient to cause

movement? How did shallow and deep pore pressure respond? g. Between your answers to e and f may be a threshold of rainfall and pore

pressure beyond which failure occurs. The threshold itself though may depend on other variables or factors. Describe or discuss other factors that might be important to establishing a threshold set of conditions beyond which you might expect failure.

4. Go back to the previous page Monitoring California Highway 50 Landslides - Project Menu (http://vulcan.wr.usgs.gov/Projects/CalifLandslide/framework.html). Access the archived data from the instrument from the three wet seasons available. The following link is to the 1999-2000 wet season: Graphic [16K,GIF]: Summary of data collected during the 1999-2000 wet season (http://daffy.wr.usgs.gov/public/text/RCC99_00.gif).

a. Under what conditions has movement occurred in the past? Can you refine your threshold set of conditions under which failure occurs?

b. Does movement immediately follow a significant or triggering rainfall event?

Never, sometimes, always? Explain.

c. How much movement occurs during an event? For the archived data, what is the range of movement during an event?

d. How long does an event last?

Problem 2 Sensitivity Analysis of the Infinite Slope Model. The infinite slope model is an analysis of the ratio between driving and resisting forces of slope movement. The ratio value is called the Factor of Safety or Safety Factor. The infinite slope model is appropriate for evaluating translational landslides and is the basis for the GIS model in the next step. By evaluating a sensitivity analysis of the Factor of Safety to variables in the infinite slope model, you will better understand the importance of accurate parameter estimation as well as the significance of or confidence you might have in the GIS model. Objective Understand the governing equation of the infinite slope model, variables involved, and the sensitivity of the Safety Factor to them. 1. Access the spreadsheet Sensitivity Analysis of the Infinite Slope Model.xls This spreadsheet is intended to be used as an introduction to the infinite slope model and the Safety Factor equation. The first worksheet, Safety Factor Calculations, presents solutions for four general conditions (thin and dry, thin and wet, thick and dry, and thick and wet).

a. Under what thickness conditions (thinner or thicker) and wetness conditions (wetter, dryer) are landslides more likely to occur?

b. What factors might control how thick a landslide is? These might be site specific

factors or more regional factors.

c. What factors might control how wet a landslide is? Again, these might be site specific factors or more regional factors.

d. According to the safety factor equation (Eq 6), slopes are considered unsafe

when the factor of safety value is less than 1. For the thin, dry slide, increase slope a degree at a time until the slope would be considered unsafe. At what slope would the hillslope be considered unsafe?

e. Do the same for the thick, dry slide. At what slope would the hillslope be

considered unsafe?

f. For the thick, wet slide, make the hillslope safe by adjusting a single variable of your choosing?

g. Is there a way to physically alter the variable you chose in f to make the hillslope

stable? If yes, this would be an example of a structural means of mitigating damages due to slope failure.

Close the spreadsheet without saving your changes.

2. On the same worksheet (Sensitivity Analysis of the Infinite Slope Model.xls), a variable by variable sensitivity analysis of SF is calculated and illustrated. The relationships are shown for the four general conditions. The x-axis for each variable is the natural range for the variable and the y-axis is the same for each variable so that the relative differences in the variable-SF relationships illustrate model sensitivity.

a. Which variables have a positive relationship with SF? Which have a negative relationship with SF?

b. Which variables have a linear relationship with SF? Which have a non-linear

relationship with SF?

c. What characteristics of the relationship between a variable and SF, as indicated in the graphs to the right of each variable, would indicate high sensitivity? Low sensitivity?

d. To which variables does SF appear to most sensitive? Least sensitive.

e. For those variables for which the relationship is nonlinear, in what general

variable range(s) is SF most sensitive?

f. Is the sensitivity of SF to each variable the same under wet and dry and thick and thin conditions? Describe this relationship for those variables for which sensitivity of SF does vary and suggest reasons why this is the case.

g. Of the variables presented, which might most easily be physically modified (e.g.,

re-grading slope) as a means of structural mitigation? 3. The two right-most columns on the Safety Factor Calculation worksheet pertain to a sensitivity analysis of SF and the graph comprising the second worksheet, Sensitivity Analysis. This graph presents the variables together, with both variables and SF presented as a percentage of change in SF over the percentage of change of the variable over its range under natural conditions (i.e., changes are essentially normalized so that they can be plotted together on one graph for comparison). Click on the Sensitivity Analysis worksheet to complete the following questions.

a. Is your answer in d of the previous section supported by information presented in this graph?

b. If you were in charge of evaluating the susceptibility of slopes in a given region of

the country and you had limited dollars available for studying material properties of the region, how could you use the sensitivity analysis to your advantage?

c. Prioritize your data collection variable by variable to get the most useful

information?

d. Would this prioritization be changed if you were also in charge of mitigating slopes that were susceptible to failure in a given area within the region, say an area under immediate development pressures? Consider that you actually have to be able to physically alter the variable when it comes to mitigation. Describe how and why your prioritization would change.

Close the spreadsheet without saving any changes.

Problem 3 GIS Model of Slope Stability in Hamilton County, Ohio. Part 1. A GIS model of slope stability has been developed for portions of Hamilton County. Parameter values have been generalized from the literature, based on the geology and topography of the area. The resultant output is an overlay of values for the Factor of Safety, essentially a landslide susceptibility map. You will compare the landslide susceptibility map with two landslide inventories, one developed by the U.S. Geological Survey in cooperation with the City of Cincinnati and Hamilton County for occurrences of damaging landslides during the time period 1970-1979 (Bernknopf and others, 1990), the other more recently made available by the Hamilton County Soil and Water Conservation District (M.M. Islam, 2003, personal communication), the governmental agency responsible for permitting of earth excavation, construction, or grading on potentially unstable slopes in the unincorporated area of Hamilton County. Other simplified variants of the model, using single variables or combinations of variables (e.g., using combinations of the most sensitive parameters, slope, or geology) as predictors of slope instability, can also be evaluated. Objective Evaluate the model by comparison with observational data; understand the usefulness of the model for planning/remedial purposes 1. You are involved in a creating a comprehensive plan for future development in Hamilton County. You are concerned about slope stability in a certain area of the county and have contracted the creation of a slope susceptibility map of the area to a geotechnical engineering firm. You have a copy of their preliminary GIS model of slope stability for the Cincinnati West Quadrangle. Open a copy of the ArcMap document entitled Slope Stability Model of the Cincinnati Area (with file extension .mxd). The GIS model opens to the area of the Cincinnati West Quadrangle, with data layers for the safety factor values and data from landslide inventories from the U.S. Geological Survey for landslide damages reported during the period 1970-1979 and from the Hamilton Soil and Water Conservation District of more recent damages overlain on black and white orthophotographs of the area. The area of interest is shown in the yellow rectangle on the map. Before you examine this area more closely, examine the other data layers presented with the model by clicking on the boxes in the Table of Contents along the left-hand side of the model. For the geology layer, lithologic descriptions for the formations are included in Appendix A as Table 1.

2. Zoom to the area of concern by selecting the View > Bookmarks > Area of Concern for the Comprehensive Plan. Using this area, you will evaluate the factors resulting in unsafe slopes, consider the quality of your model, and address the problem of planning for development in this area.

a. Using the Information Tool, click on any point on the map to get information on one or more of the layers.

b. In the Identify Results window, click on . Consider unstable slopes any which have an SF value less than or equal to 1.25. Click on an a series of unstable slopes and note the safety factor value, slope value, geology symbol, and other data included in the GIS model. Provide a range of SF and slope from 10 or so queries in the map area. What formations generally underlie unstable slopes?

c. In validating the model or considering its quality, you want to compare SF values respresenting instability (less than or equal to 1.25) to a landslide inventory of damages. According to the U.S. Geological Surveys landslide inventory, 46 100- x 100-m cells contained damages from landslides as reported for the period 1970-1979. For those cells with reported damages, how many occur within stable areas? How many occur within unstable areas? Note the cell resolution of the inventory raster is lower than the resolution of the SF raster as indicated by the size of the squares. (The SF raster has a 30- x 30-m resolution.)

d. For the cells within stable areas but indicating damage, use the information button

to click on an a series of damaged cells, noting the safety factor value, slope value, geology symbol, and other data included in the GIS model. Provide a range of SF and slope from 10 or so queries in the map area. What formations generally underlie these sites?

e. Four different situations may be possible relative to SF and landslide damage:

unstable areas in which damages are reported stable areas in which no damages are reported

unstable areas (red and yellow) in which no damages are reported stable areas in which damages are reported

The first two situations may be construed to mean the model is working appropriately as they would be an obvious expected outcome. The latter two might be evidence that the model does not accurately portray slope stability in the area. What are reasons why this might happen? For example, do not ignore data provided by the orthophotographs relative to land use.

f. Gather reasons from the entire class and discuss them relative to overarching

categories (e.g., variables the model does or does not include as indicated in Equation 6, static variables versus dynamic or time-variant variables).

g. Given your analysis to this point, create a recommendation for future development

in the area of interest. 3. As part of your analysis, you may want to prohibit development on all undeveloped but like-hillslopes for which damages were reported in the landslide inventory. To explore the areal extent this sort of criteria might prohibit development from occurring on, you need to manipulate the GIS model. You recall an earlier study by Bernknopf and others (1988) that used a simplified infinite slope model to estimate a hillside stability index for the Cincinnati area. You dig up the description from their original paper because you want to use it in your manipulation, but you also want to remember it to justify your actions:

Because most of the landslides in the study area have the general shape of planar slabs that were displaced along slip surfaces approximately parallel to the topographic slope, the failure mechanism can be represented by the static factor-of-safety equation (infinite slope model). For cohesionless, dry material, the equation reduces to the ratio of tan/tan, where tan is the tangent of the effective residual angle of internal friction of the geologic material and tan is the tangent of the topographic slope. Because the available shear strength and slope data are generalized regional observations, we have termed this ratio the hillside stability index (SI) and, for a given cell (i), designated the index SIi. (Bernknopf and others, 1988).

To calculate the SI, follow these steps. a. Load the Spatial Analyst extension.

b. Add the Spatial Analyst toolbar.

c. You will use the Raster Calculator to calculate tan/tan. You will have to create calculate tan, but a variable TanPhi(times100) is already available in the GIS model with is tan x 100. To calculate tan, access the Raster Calculator.

d. In the raster calculator, enter the following equation using your mouse to click on the appropriate layers and functions. Values for slope () are in the layer Slope, in Degrees. You will need to enter it exactly as shown. Click on the Evaluate button.

e. The result will be labeled Calculation and will show up on the map as the top layer as well as be added to the layers list for the next raster calculation.

f. Access the Raster Calculator again, and complete the calculation for SI according to the formula below. Again, enter the formula using only the mouse to enter data layers, numbers, and functions. Ignore the warning and click on Yes to continue.

g. The resulting calculation will show up with default colors. You will adjust this map to meet your needs by right-clicking on the title Calculation2 and selecting properties.

h. Bernknopf and others (1988) original work include four classes of data. Select 4 from the Classes menu, then select Classify...

i. Adjust the break values so that the first three are 4, 6, and 9 and click OK.

j. Change the color scheme by clicking on the box for the 9-132.xxxx value and selecting No Color. These slopes are stable, so the No Color will de-emphasize their importance.

k. Click on the label column and change the labels as shown below. Click Apply.

l. Before you leave the Layer Properties box, select Display across the top and make the layer 50 % transparent.

m. Examine your result. You can adjust your class values until all the areas that exhibited damage during the period 1970-1979 to evaluate a threshold SI above which damages would not be expected based on historical data.

n. How would you use this information in your comprehensive plan? What does it mean relative to development in the area of concern? o. Finally, a quintessential aspect of American property rights is that a person has a right to do with their land as they wish. How do you manage this as developers and landowners approach you with concerns on the comprehensive plan? p. What you have been developing is along the lines of a non-structural or administrative approach to hazard mitigation. What structural approaches might increase the area of developable land in the area of concern? Finish your recommendation developed in the previous exercise to include this discussion. Part 2. For those familiar with GIS and raster or map algebra functions, sufficient data is provided for completing a landslide susceptibility map for the Cincinnati East Quadrangle, the subject of future developments of this module.

Solutions The models are in their solved state as presented. Suggestions to Instructors The methodology for conducting the sensitivity analysis is taken from Hammond and others (1992) following (Simons and others, 1978):

A sensitivity analysis of the infinite slope model is helpful to identify the most important variables and thus guide the user in expending time and money collecting information. One method for evaluating the sensitivity of the factor of safety (FS) to each variable has been outlined by Simons and others (1978):

1. Select a realistic range of values for each input variable. 2. Calculate a base FS value using some central value for each

variable, such as the mean, median, or mode value [median is used in the module].

3. Vary the value for one input variable at a time over the range of

realistic values and compute the FS values. 4. Plot the percentage of change in FS (% FS) relative to the base

value against the percentage of change in each input variable relative to the central value (% X), where the percentage of change is calculated as:

100% xcentral using FS

x central using FS - xusing FSFS % - i =

100% xcentral

x central - xX % - i =

(Hammond and others, 1992)

Glossary of Terms Terms are defined within the text and tables as needed. References Baum, R.L. and Johnson, A.M., 1996, Overview of landslide problems, research, and mitigation, Cincinnati, Ohio, area: U.S. Geological Survey Bulletin 2059-A, U.S. Geological Survey, Washington, DC, 33 p. Bernknopf, R.L., Campbell, R.H., Brookshire, D.S., and Shapiro, C.D., 1988, A probabilistic approach to landslide hazard mapping in Cincinnati, Ohio, with applications for economic evlauation: Bulletin of the Association of Engineering Geologists, v. 25, p. 39-56. Bernknopf, R.L., Campbell, R.H., Brookshire, D.S., and Shapiro, C.D., 1990, Cincinnati Landslide Database: U.S. Geological Survey Open-file Report 90-256 A and B: Disk and 3 p.

Fleming, R.W. and Taylor, F.A., 1980, Estimating the costs of landslide damage in the United States: U.S. Geological Survey Circular 832, U.S. Geological Survey, Washington, DC, 21 p. Ford, J.P., 1974, Bedrock geology of the Cincinnati West Quadrangle and part of the Covington Quadrangle, Hamilton County, Ohio: Ohio Department of Natural Resources, Division of Geological Survey, Report of Investigations No. 93, 1:24000 scale. Hammond, C., Hall, D., Miller, S., and Swetik, P., 1992, Level I stability analysis (LISA) Documentation for Version 2.0: U.S. Department of Agriculture, Forest Service Intermountain Research Station, General Technical Report INT-285, 190 p. Hansen, M.C., 1995, Landslides in Ohio: GeoFacts No. 8, Ohio Department of Natural Resources (available at http://www.ohiodnr.com/geosurvey/geo_fact/geo_f08.htm), 5 p. Osborne, R.H., 1974, Bedrock geology of the Cincinnati East Quadrangle, Hamilton County, Ohio: Ohio Department of Natural Resources, Division of Geological Survey, Report of Investigations No. 94, 1:24000 scale. Selby, M.J., 1982, Hillslope materials and processes: Oxford University Press, Oxford, 264 p. Spiker, E.C. and Gori, P.L., 2000, National landslide hazards mitigation strategy A framework for loss reduction: U.S. Geological Survey Open-File Report 00-450, U.S. Geological Survey, Washington, DC, 49 p. Spiker, E.C. and Gori, P.L., 2003, National landslide hazards mitigation strategy A framework for loss reduction: U.S. Geological Survey Circular 1244, U.S. Geological Survey, Washington, DC, 56 p. U.S. Geological Survey, 1982, Goals and tasks of the landslide part of a ground-failure hazards reduction program: U.S. Geological Survey Circular 880, U.S. Geological Survey, Washington, DC, 48 p. Varnes, D.J., 1958, Landslide types and processes: Highway Research Board Special Report, Washington DC, p. 20-47. Varnes, D.J., 1975, Slope movements in the western United States, in Mass Wasting: Geoabstracts, Norwich, p. 1-17.

Supporting Information

Appendix A. Table 1. Description of lithologic descriptions of formations on the Cincinnati West and

Cincinnati East Quadrangles (taken from the Cincinnati West Quadrangle, Ford, 1974).

Formation1

Formation Symbol2

Description1

Undifferentiated

alluvium and outwash

Q

Recent alluvial silt, sand, and gravel, generally less than 10 feet thick. Pleistocene fluvial gravel, sand, silt, and clay, comprising dissected terraces and abandoned river channels; laminated silt and clay of probable fluviolacustrine origin along many valleys: one or more intercalated till unites in places.

Bellevue

Limestone and overlying Rocks

Ob

Limestone with minor interbedded mudstone. Limestone (75-85 percent), medium-light- to medium-gray, mottled with light-olive-gray patches and streaks, very fine- to very coarse-grained, very poorly sorted, argillaceous, biogenic; in lenticular or irregular beds from 1 to as much as 8 inches thick; locally fine- to coarse-grained, moderately sorted, in even beds. Mudstone, medium- to medium-dark-gray, calcareous; present as thin partings and as sets up to 4 inches thick between limestone beds. Formation fossiliferous throughout; Platystrophia ponderosa one of the most conspicuous faunal elements; formation weathering to produce a distinctive rubble or slabby float.

Miamitown

Shale

Om

Interbedded shale and limestone. Shale, medium- to dark-gray, calcareous, fissile; present as partings and sets up to 3 feet thick; calcareous light- to medium-gray mudstone and siltstone present as partings within some of the shale units. Limestone (10-20 percent), light- to medium-gray, very fine- to coarse-grained, moderately sorted to well-sorted, argillaceious, biogenic; some beds nodular; generally in even to slightly irregular beds from 1 to 4 inches thick. Miamitown Shale medium bedded and fossiliferous throughout; upper contact placed to separate it from the very poorly sorted irrgularly bedded argillaceous limestone of the Bellevue.

Fairview

Formation

Of

Interbedded shale and limestone. Shale, medium- to dark-gray, calcareous, fissile; present as thin partings and sets up to 1 foot thick; calcareous light- to medium-gray mudstone and siltstone present as partings in the shale units. Limestone (30-40 percent), light- to medium-gray, fine- to very coarse-grained, moderately sorted to well-sorted, argillaceous, biogenic; generally in even to slightly irregular beds from 1 to 4 inches thick; ripple marked in many places. Fairview Formation thin bedded and fossiliferous throughout; several argillaceous limestone beds composed largely of Rafinesquina valves present in upper third of unit; upper contact placed to separate the thin-bedded shale and limestone sequence of the Fairview from the medium-bedded shale and limestone sequence of the Miamitown Shale.

Kope Formation

Ok

Interbedded shale and limestone. Shale, medium- to dark-gray, calcareous, fissile; present between limestone beds as thin partings and sets up to 3 feet thick; mudstone and siltstone present as partings within some of the shale units. Limestone (20-30 percent), light- to medium-gray, very fine- to coarse-grained, moderately sorted to well-sorted, argillaceous, biogenic; generally in beds from 1 to 4 inches thick; ripple marked in many places. Formation fossiliferous throughout, although shales less fossiliferous than limestones; upper contact gradational and placed to separate the medium-bedded units of the Kope Formation from the thin-bedded sequence of limestone and shale of the Fairview Formation.

Notes 1 Names and formations are taken directly from the Bedrock Geology Map of the Cincinnati West

Quadrangle (Ford, 1974) 2 Symbol as it is used in the GIS relative to the information tool, attribute tables, and reclassifications in

Spatial Analyst.

Table 2. Values used in the reclassification of rasters used in the calculation of driving

and resisting forces in the GIS model for slope stability of the Cincinnati West Quadrangle. These same values can be a starting point for creating a similar model for the Cincinnati East Quadrangle.

Formation1

Formation Symbol2

Dry Unit Weight

Wet Unit Weight

Cohesion

Internal Angle of Friction

Undifferentiated alluvium and

outwash

Q

17

21

0

33

Bellevue

Limestone and overlying Rocks

Ob

16

20

0

38

Miamitown

Shale

Om

16

20

0

26

Fairview

Formation

Of

16

20

0

32

Kope Formation

Ok

16

20

0

16.5