NOTE: Mohr Circles must be drawn to scale with equal scales for $\backslash ($ x $\backslash )$ and $\backslash ($ y $\backslash )$ axes.

NOTE: for Problems $1$ and $2$ below it is common practice to compute the net stress applied to the soil after construction. For example, in Problem $1($Problem $10\mathrm{.}29$ in Holtz et al$.)$ the foundation will be constructed at a depth of $2$ meters below ground surface at which prior to construction the effective stress $\backslash (=(2\backslash$mathrm$\{$~m$\})\backslash$left$(16\backslash$mathrm$\{$kN$\}/\backslash$mathrm$\{$m$\}^\{3\}\backslash$right$)=32\backslash$mathrm$\{$kPa$\}\backslash ).$ After construction the foundation has an applied stress $\backslash (\backslash$mathrm$\{$q$\}=200\backslash$mathrm$\{$kPa$\}\backslash )$ and thus the net change in stress applied to the soil at the base of the foundation $\backslash (=200-32=168\backslash$mathrm$\{$kPa$\}\backslash ).$

$1.$ Problem $10\mathrm{.}29$ in Holtz et al$.$ For part $($a$)$ the question is asking for $\backslash (\backslash$sigma$^\{\backslash$prime$\}$ w $\backslash )$ prior to installation of the foundation. For part $($b$)$ use Table $10\mathrm{.}4$ to solve for increase in stress at Point $0$ in the middle of clay layer. For Part $($c$)$ treat the clay layer as a single unit and compute settlement due to increase in stress at middle of clay layer determined in Part $($b$)($i$.$e$.,$ we are not assuming $1-$D loading in this problem$).$

$2.$ Problem $10\mathrm{.}30$ in Holtz et al$.$ You can do this problem in English units $($TSF $=$ tons per square foot$).$ Give final answer in pounds per square foot $($psf$).$ Use Tables $10\mathrm{.}4$ and $10\mathrm{.}5$ to solve. Note the header in Table $10\mathrm{.}5$ that has $\backslash ($ r $/($B $/2)\backslash )$ should be $\backslash ($ x $/($B $/2)\backslash )$

$3.$ For a soil element under geostatic stress conditions with a vertical stress equal to $500$ kPa and a horizontal stress equal to $250$ kPa $.$ Draw Mohr circle and determine: a$)$ the maximum shear stress and the orientation of the plane upon which it acts $($i$.$e$.,$ angle of the plane relative to the horizontal$),$ and b$)$ the normal and shear stress on a plane oriented $+30$ degrees from the horizontal.

$4.$ Draw Mohr circle and determine the magnitude of the principal stresses and the orientation of the planes which they act upon $($i$.$e$.,$ angle of the plane relative to the horizontal$)$ for the following stress condition.

$10\mathrm{.}29$ Figure P$1029$ shoss the plan and profle viese of a rectangular foundation $(\backslash (3\backslash$mathrm$\{$~m$\}\backslash$times $5\backslash$mathrm$\{$~m$\}\backslash ))$ that is embedded The applied foundation stres $\backslash (4=200\backslash$mathrm$\{$kP$2\}\backslash ).$

$($b$)$ Use the Bousinesy method to fisd the serss inctese under pount $\backslash ($ O $\backslash )$ in the middle of the clay layet. Point $0$ Fies on the foundition centerline, $2$ mo outide the foundation.

$($c$)$ Detonsise how much setulencat vill ocyar in the day layet after the foundation is constructed in the point $0.$

B Chapter $10$ Shallow Foundations

ROURE PIO.

$10\mathrm{.}30$ Fipure Plo:$30$ shows the plan and clevation views of a museum that will consist of a circular building atiached to a rectangular huilding The foundatinn sits $14$ fi below ground surface and is uniformly loaded with an applied stress, $\backslash (4=4\backslash )$ TSF$.$ What vertical stress increase $\backslash (\backslash$left$(\backslash$Delta $\backslash$sigma$\_\{2\}\backslash$right$)\backslash )$ sill occur in the midlle of the clay layer under point O $($where the two buildings touch$)$ dae to this foundatios loaling?" Use the Boussinesy methods

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