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You are a staff engineer for a local geotechnical engineering firm. As part of the

geotechnical exploration for a project, several subsurface tests have been conducted. You

are given the results of one traditional soil boring with Standard Penetration Testing

$($SPT$).$ The results of this boring, labeled as B$-2,$ are presented on page $4$ of this

assignment. Based on testing of collected soil samples, the encountered soils have the

unit weights listed in Table $1.$ The figure below presents the general cross$-$section of two

planned footings at your project site.

The project structural engineer has given you design loads of $90$ kips for the columns and

$7$ kips per linear foot for the wall loads. Refer to Boring B$-2$ on page $4$ for the soil profile at both

footing locations.

Table $1.$ Summary of Soil Unit Weights from Boring B$-2.$

NOTE: Assume the asphalt and base course layers are removed and replaced with material

identical to that underneath them.

Consolidation testing was conducted on a soil sample that was taken from the first ML layer $($its

depth ranging from $8$ to $12$ ft $).$ The table below summarizes the applied pressure and recorded

sample thickness after the deformation under each of the applied pressures has reached their

steady levels. The initial height of the consolidation testing specimen was $20\mathrm{.}0$ mm and its initial

water content was $59\mathrm{.}7\%($G$\_($s$)=2\mathrm{.}73).$

Table $2.$ Summary of consolidation testing data of the ML sample

$1$a$)$ Plot the void ratio vs applied pressure curve $($e$-$sigma$^(\text{'}))$ and determine the pre$-$consolidation

pressure $($ sigma$\_($c$)^(\text{'})),$ compression index and recompression indices $($ C$\_($r$)$&C$\_($c$)),$ by using the

Casagrande's graphic procedure; $($Hint: you need to derive the initial void ratio, from which the

void ratio after the application of each of pressure increments can be derived from the change in

sample's thickness$/$height$)$

$1$b$)$ Based on the consolidation testing results derived from $1$a$),$ calculate the primary

consolidation settlement of the ML layer due to the Column footing and the Wall footing,

respectively;

$1$c$)$ What would be the water elevation of the mid$-$point of the first ML layer measured by a

piezometer at the instant when the column footing and the wall footing have been completely

constructed, respectively $($assuming the construction processes were rapid$)($Using the sea level

as the datum to calculate the elevation head of the mid$-$point of the first ML layer; also the

elevation of the soil strata is provided in the attached boring log$)$;

$1$d$)$ The time rate of consolidation settlement data shown in Table below $($Table $3)$ is for the

increment from $225$ to $450$ psf from the consolidation testing. The initial sample height is $20$

mm $,$ and there are porous stones on the top and at the bottom of the consolidation sample.

Determine the coefficient of consolidation $($c$\_($v$))$ by the log time$-$method $($hint: you can calculate

H$\_($dr$)$ by using H$=19\mathrm{.}5$mm as the sample's thickness during this loading increment of the

consolidation testing$)$;

$1$e$)$ Based on the coefficient of consolidation derived from $1$d$),$ determine the time required to reach $80\%$ of primary consolidation settlement for the first ML layer;

$1$f$)$ Based on the coefficient of consolidation derived from $1$d$),$ what would be the water elevation of the mid$-$point of the first ML layer measured by a piezometer at a time $3$ months after the construction of the column footing and the wall footing, respectively.

Table $3.$ Summary of elapsed time and dial gauge reading of the ML consolidation sample for the pressure increment from $225$ to $450$ psf

Elapsed time $($min$)$ Dial reading $($mm$)03\mathrm{.}9510\mathrm{.}13\mathrm{.}8270\mathrm{.}253\mathrm{.}7890\mathrm{.}53\mathrm{.}7413\mathrm{.}66723\mathrm{.}5643\mathrm{.}40583\mathrm{.}192152\mathrm{.}945302\mathrm{.}676602\mathrm{.}461202\mathrm{.}3332402\mathrm{.}1865052\mathrm{.}09414851\mathrm{.}95$

SHOW ALL STEPS, DO NOT USE CHAT GPT