more, the data show that some 60 to 70 percent of this strength 

 is lost due to root deterioration or decay 5 to 10 years after 

 cutting. This elapsed time coincides with the period of greatest 

 landslide activity as observed by Megahan and others (1978), 

 figure 7. With slightly higher root area ratios (up to 0.1 5 percent), 

 which appear to be entirely possible based on data from Mega- 

 han and others (1978) and Wu (1976), the rooting contribution 

 to soil shear strength increase will be still higher (assuming 

 tensile strength of the roots remains the same). 



Table 4. — "Root cohesion" of soil at various elapsed times after 

 felling Douglas-fir for root size class to 1 centimeter 



Residual root cohesion' (Cr), lb/inch^ 



t = (fresh) 



t = 1 year t = 5 years t = 



1 years 





1.50 



0.70 0.50 



0.40 





'Calculated from equation (5a) and root tensile strength data in Burroughs and 

 Thomas (1977). 



SOIL ARCHING RESTRAINT MODEL 



Arching in slopes occurs when soil begins to move through 

 and around a row of piles (or trees) firmly embedded or 

 anchored in an unyielding layer. Under the right conditions, the 

 trees are in effect both cantilever piles and abutments of "soil 

 arches" that form in the ground upslope from the trees. The 

 requirement of firm anchoring or embedment of trees in an 

 unyielding layer of a slope can occur under the following condi- 

 tions: 



(1 ) Overlying an inclined bedrock contact in shallow residual 

 soils or glacial till. 



(2) In sandy slopes, where tree stem bases are deeply 

 buried as a result of sand accretion. 



Other conditions pertaining to spacing and diameter of the tree 

 trunks, thickness and inclination of the yielding portion of the soil 

 profile, and shear strength properties of the soil also determine 

 arching effectiveness. 



An arching theory developed for soil slopes by Wang and Yen 

 (1 974) is based on a semi-infinite slope model and rigid-plastic- 

 solid soil behavior. Their theory was developed for a single row 

 of embedded piles (of diameter d) spaced a distance (B) apart 

 across a slope as shown schematically in figure 21 . According 

 to this theory, the average arching pressure (p) in a slope and 

 the critical spacing (Bcru) for arching to occur are given by the 

 following equations: 



2C c 



(mcospsinp - KoCosptancj) -'^cosp - mcos^ptan6i — — m 



P =1 7H 7H 



yH I 2 Ko cos p tan <t) 



X [ {1 -exp(-2Koncosptan(t))} + 1/2Koexp( - 2Kon cosptand))] (6) 



LEGEND 



B = Spacing between piles 

 d = Pile diameter 

 H = Depth of yielding layer 

 P = Arching force or reoction 



transfered to soil element 

 /9 = Slope angle 



Figure 21 . — State of plastic deformation and soil arching action around 

 a row of piles (trees) embedded in a slope (from Wang and Yen 

 1974). 



where 8 = clear spacing or opening between piles 

 BcRiT = critical clear spacing between piles 

 Cs = cohesion in soil 



Ci = cohesion along basal sliding surface 

 H = depth of yielding or sliding plane 

 Ko = coefficient of lateral earth pressure at rest 

 m = B/H = relative width or dimensionless spacing 

 n = X/B = relative distance (in direction of slope) 



p = average lateral pressure or arching pressure 

 P = slope angle 

 7 = unit weight of soil 

 4) and 4)i = angle of internal friction in soil and along 

 basal sliding surface, respectively. 



The total force (P) developed against a pile of diameter (d) 

 embedded in a slope with a thickness or depth of yielding soil 

 (H) is given by: 



Ko 



yH^ d + (^yH - p)BH 



(8) 



The load on each pile embedded in a slope is thus the summa- 

 tion of two loads, one from the pressure at rest of the soil 

 immediately uphill from the pile, similar to the lateral pressure 

 on a retaining wall. The other is the soil arching pressure trans- 

 ferred to the adjacent piles as if each pile is an abutment of an 

 arch dam. When the average lateral pressure (p) approaches 

 zero, arching action is a maximum. 



and B 



CRIT - 



H Ko (Ko + 1)tan <i> + 2Cs 



cosp (tan (3 - tan ^) - 



^Hcosp 



(7) 



13 



