In this example, a cohesion of 0.5 Ib/in^ (3.4 kPa) and a friction 

 angle of 35' are assumed. When the piezometric surface dou- 

 bles in height, the factor of safety drops below one. This 

 relationship is shown by the dashed lines in figures 28 and 29, 

 respectively. 



Yet another type of sensitivity analysis (Simons and others 

 1 978)^ can be employed that not only reveals the sensitivity, but 

 also the direction of change in slope safety factor corresponding 

 to a change in any input variable in the infinite slope equation. 

 This approach is useful for examining the influence of vege- 

 tation removal on slope stability and the influence of changes in 

 such variables as surcharge, the effects of which are more 

 obscure or counter-intuitive. 



This approach is conducted in four steps. First, a realistic 

 range of values (AX,) is selected for each input variable (X,). 

 Second, a base safety factor is computed by using the median 

 values for all variables. Third, each input parameter is changed 

 across its range of values and a new factor of safety is com- 

 puted for each altered input. Fourth, the results are plotted as a 

 relative percentage. 



This sensitivity analysis was conducted for the range of input 

 variables and their median values shown in table 7. These 

 medians are believed typical of conditions for natural slopes in 

 forested watersheds in the Idaho batholith. The ranges include 

 conditions believed typical of conditions in both forested and 

 cutover watersheds. In order to conduct the sensitivity analysis, 

 the factor of safety equation was rewritten in a slightly different 

 form as follows: 



(9) 



2(Cs + Cr) ^ f go . ( 7SAT .... . 7 ..Itan i>' 



7vvH sin 2p 



7wH 



7w 



1) M 



M) 



tan 3 



I 7wH 



(2§^]_)M + 1- (1-M) 

 7w 7w 



where M = relative ground water height (= 



H 



Table 7. — Range of input variables and their estimated medians 

 for soil and slope conditions in watersheds of the 

 Idaho batholith 



Input variable 



Range 



Median 



Variables not particularly influenced by vegetation: 



H 



7SAT 

 Cs 



20-40° 

 27-42° 

 12-48 in 

 90-120 Ib ft^ 

 110-140 Ib/ft^ 

 0-2 Ib. in^ 



30° 



35° 

 30 in 

 100 Ib/ft^ 

 1 20 Ib/ft^ 

 0.75 Ib'in^ 



Variables strongly influenced by vegetation: 



qo 



Cr 



M 



0-200 lb ft^ 

 0-1.5 lb in^ 

 0-1 



20 Ib/ft^ 

 0.5 Ib'in^ 

 0.25 



^Simons, D. B., R. M. Li, and T, J. Ward, 1978. Mapping of potential landslide 

 areas in terms of slope stability. Report prepared by Eng Res Cent.. Colo. State 

 Univ, for USDA For. Serv.. Rocky Mt. For. and Range Exp. Stn., Fort Collins, Colo. 

 74 p 



The results of the sensitivity analysis shown in figure 30 

 revealed that some inputs have a linear effect on F while others, 

 notably H and (3, have strongly nonlinear effects. Factor of 

 safety is quite sensitive to both root (Cr) and soil cohesion (Cs). 

 In contrast, the slope safety factor is relatively insensitive to 

 changes in density (y) and surcharge (loss) qo. Changes in soil 

 friction (6) do not have nearly as much influence on safety factor 

 as changes in cohesion (Cs and Cr). This finding corrobrates 

 the results shown in figures 28 and 29. The influence of relative 

 ground water height (M) or piezometric elevation is intermediate 



in effect, except at very high ground water elevations (M ►I ) 



where safety factors decrease sharply. 



PERCENT aF 



-r60 Basis: 



Central Values 



PERCENTaX- 



Figure 30. — Percent change in slope safety factor versus percent 

 change in input variables. Base safety factor (F) was computed 

 using the median or central value for all variables (table 7). 



CONSEQUENCES OF VEGETATION 

 REMOVAL 



The preceding sensitivity analyses can be used to help evalu- 

 ate the consequences of vegetation removal on the stability of 

 slopes in the Idaho batholith. The input variables most strongly 

 influenced by vegetation are M, qo, and Cr. Removal of slope 

 vegetation tends to decreased root cohesion (Cr), increased 

 piezometric levels (M), and decreased slope surcharge (qo). 

 The net effect of these changes is to adversely affect stability: 

 their extent and significance will be explored further. An excep- 

 tion appears to be surcharge that decreases following clearcut- 

 ting, which should improve stability based on the sensitivity 

 analysis previously discussed. On' the other hand, this im- 

 provement is marginal: moreover, it can be shown that at low 

 values of cohesion and high ground water elevations surcharge 

 has a beneficial influence (Ward 1976). 



19 



