SOIL ARCHING RESTRAINT 



Preliminary analyses of field data obtained from forested, 

 sandy slopes on the Idaho batholith indicate that these slopes 

 meet theoretical criteria for arching restraint between trees. 

 Tree spacings, or more importantly the width of openings be- 

 tween "vertical root cylinders" are of the right order of magni- 

 tude for soil arching to manifest itself according to the Wang- 

 Yen theory (Wang and Yen 1 974). Tree trunks and their associ- 

 ated "vertical root cylinders," which are firmly anchored to 

 bedrock (fig. 19), potentially can behave as arch abutments. 



Openings between vertical root cylinders appear to average 

 around 30 feet (9.1 m) based on stem counts in forested plots on 

 the nearby Silver Creek study area (table 3). These data were 

 obtained from large survey units which include some unforested 

 areas in streams, brush, and rock outcrop. On a smaller more 

 localized scale, spacings are considerably less, particularly in 

 groves of trees (fig. 26). Based on these last field observations, 

 the width of opening between vertical root cylinders in the 

 slopes averages about 6 to 7 ft. (1 .8 to 2.1 m). 



The maximum allowable opening or critical distance (Bcr) 

 between piles (or trees) embedded in a slope can be calculated 

 from soil arching theory. This critical distance is shown plotted in 

 figure 27 using the soil arching theory for slopes derived by 

 Wang and Yen (1974), The critical distance is plotted versus 

 cohesion for various assumed values of residual friction and 

 cohesion (61 , Ci ) along the basal sliding surface. Other soil and 

 slope parameters used in the analysis are typical of shallow 

 coarse-textured, granitic soils overlying a steep bedrock rock 

 contact (p = 40°, d) = 35", H = 3 ft [0.9 m] 7 = 100 lb ft^ 

 [1.6 g cm=]). 



The soil arching analyses show that the critical distance in a 

 shallow mantle is very sensitive to cohesion, particularly cohe- 

 sion along the basal sliding surtace (c,). If no cohesion is 

 assumed, and the residual friction (6,) along the basal sliding 

 surtace is one-half the peak friction (6), then the critical spacing 

 is 4 ft (1 .2 m). On the other hand, if a cohesion (Cj) of only 0.35 

 Ib/in^ (2.4 kPa) is assumed with the residual cohesion (c,) along 



40 





P 



= 40° 





'P 



= 35° 







H 



= 3 ft. 







y 



= 100lb/ft3 



30 



20 



C, = 

 C, =0.125Cs 



0.25 0.50 0.75 



COHESION^Cs). Ib/in2 



1.0 



Figure 26. — Row of ponderosa pine trees at spacings sufficiently 

 close to manifest soil arching restraint between trees. Silver Creek 

 study area, Boise National Forest. 



Figure 27. — Theoretical critical openings (Bcr) versus cohesion for 

 piles (trees) embedded in a steep, sandy slope ((3 = 40°, * = 35°, 

 H = 3 ft.). Influence of cohesion and friction along the base 

 ((bi, Ci) is also shown. 



the basal sliding surtace a mere 12 percent of this value, then 

 the critical spacing increases to 21 ft (6.3 m). This distance 

 usually approaches or exceeds the size openings between 

 "vertical root cylinders" observed in the field, particularly in 

 groves of trees (fig. 26). Based on his analysis of granitic slopes 

 in the batholith, Prellwitz (1975) suggested that 0.35 lb in^ (2.4 

 kPa) is a reasonable lower limit for cohesion of soils beneath the 

 phreatic surtace. With slightly higher values of cohesion, the 

 critical distance increases further thus insuring that soil arching 

 effects will be manifest. These values of cohesion in granitic 

 soils are well within reason. Possible sources of cohesion or 

 apparent cohesion include root reinforcement, cementation, 

 clay binder, and capillary stresses (above the phreatic surtace). 



SENSITIVITY ANALYSES 



The relative importance of various soil-slope-hydrologic pa- 

 rameters on slope stability and the direction of change in slope 

 safety factor that may be produced by altering these parameters 

 may be determined by conducting sensitivity analyses or para- 

 metric variation studies. These same studies also permit eva- 

 luation of effect of vegetation removal on slope stability through 

 the influence of removal on the parameters themselves. 



There are several types of slope sensitivity analyses that can 

 be conducted. All are based in the present case on the infinite 

 slope model and on the effect of altering input variables on the 

 general stability relationship expressed in equation 2. 



Table 6 includes a summary of stability relationships for each 

 of the stations or locations where borehole shear tests were 

 conducted. Shown in table 6 are calculated factors of safety for 

 each station based on existing or measured values of soil depth 



17 



