In this exercise, a simple slope stability model (the infinite slope model) is used to calculate safety factor maps for different conditions. The effect of groundwater depth and seismic acceleration is evaluated using input maps of these factors for different return periods of rainfall (related to the groundwater level) and earthquakes (related to the seismic acceleration).
Introduction and data preparation
Two of the input maps are a slope map and a map of ash thickness:
The degree of slope hazard can be expressed by the Safety Factor (F) which is the ratio of the forces that make a slope fail and those that prevent a slope from failing.
To simplify matters, the infinite slope model is used. This is a 2-dimensional model describing the stability of slopes with an infinitively large failure plane.
The depth of the possible failure plane is taken at the contact of the volcanic ashes and the underlying material. The consequence of that is that safety factors will not be calculated for the entire area, but only for the areas where there is volcanic ash at the surface.
The formula to calculate the Safety Factor (Brunsden and Prior, 1979) reads:
With some Mapcalc calculations in which you will use the inbuilt ILWIS functions DEGRAD( ), SIN( ), COS( ), and SQ( ), first some maps are prepared that will be frequently used in this application:
Creating a user-defined function for the infinite slope model, and calculating Safety Factors for various groundwater scenarios
The Safety Factor formula as presented above will be transformed into a user-defined function FS. This function already contains the known parameters (maps ASHT, SI, CO, CO2 and the known constants) but it also contains the variables Gamma and m.
The function can then be easily applied for various heights of the watertable (zw), by filling out the variables Gamma and m. This will result in a number of Safety Factor maps for specific watertable heights.
Function FS reads:
The maps are (re)classified according to:
Subsequently, function FS is applied repeatedly on the command line and Safety Factor maps are calculated for a number of watertable height scenarios. For each scenario, a value for Gamma is provided and the values for m are found in a number of existing groundwater maps (M016, M1, M20, M50).
Safety Factors are calculated for groundwater peaks that occur:
Evaluating the effect of seismic acceleration
Besides groundwater fluctuations, also earthquake acceleration will be taken into account.
Compared to the original formula (see above), the new parameters are:
zw can be replaced with m*z, as m=zw/z.
Another user-defined function has to be created (FSNEW), which may read:
(10000+(ASHT*Gamma*CO2-ASHT*Rho*Alpha*CO*SI-10000*m*ASHT*CO2)*0.58) / (ASHT*Gamma*SI*CO+ASHT*Rho*Alpha*CO2)
With user-defined function FSNEW and some additional information, Safety Factors are then calculated for the following scenarios:
In order to compare the output maps, all maps are (re)classified according to:
Results of scenarios 5 and 6 are displayed below:
For more information on this case study, contact:
C.J. van Westen