SW $-$ Well graded SAND, $\backslash (\backslash$mathrm$\{$N$\}=10\backslash )$

An increasing awareness of the dangers of flooding has changed Vermont's public perception of the state's bridges, and their resilience to erosion. Placement of piles $($both driven and drilled$)$ underneath abutments has been adopted as a "best management practice" for keeping abutments from suffering erosion damage. In this case the abutment is designed to be supported entirely on piles; assuming all soils can be washed away at the base of the abutment.

As a preliminary assessment find the capacity for a precast concrete driven pile, driven using vibratory and impact driving $($full displacement$)$ techniques:

$1.$ Side friction $-$ Analyze the pile system side friction for

Sand $\backslash (\backslash$mathrm$\{$N$\}=10\backslash )$ in the top $100$ feet $($we have this soil correlated already$)$

a$)$ Pile lengths from $\backslash (20-50\backslash$mathrm$\{$ft$\}\backslash )$ using $5$ ft increment $($for $\backslash (1-\backslash$mathrm$\{$ft$\}\backslash )$ diameter pile$)$

$2.$ Side friction $-$ Analyze the pile system side friction for

Sand $\backslash (\backslash$mathrm$\{$N$\}=25\backslash )$ in the top $100$ feet $($we have this soil correlated already$)$

b$)$ Pile lengths from $\backslash (20-50\backslash$mathrm$\{$ft$\}\backslash )$ using $5$ ft increment $($for $\backslash (1-\backslash$mathrm$\{$ft$\}\backslash )$ diameter pile$)$

$3.$ End Bearing $-$ Analyze the pile system end bearing for these three site conditions

c$)$ Sand $\backslash (\backslash$mathrm$\{$N$\}=10\backslash )$ in the top $100$ feet

d$)$ Shale at $25$ ft depth $($assuming drilled in $5-$ ft mobilizing the shale$)$ "low durability shale" similar to Paine Mtn: $(\backslash (\backslash$gamma$=140\backslash$mathrm$\{$pcf$\},\backslash$phi $\backslash )\text{'}=26$ degrees; c$=10,500$ psi$)$

$4.$ Prepare an annotated summary table of these results, clearly stating which portions of the capacities are likely to be mobilized.

$5.$ Summarize your engineering observations of this analysis in a brief note.