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Natalija [7]
4 years ago
11

Soil is to be excavated from a borrow pit to construct a 100-m-long trapezoidal levee that is 3 meters high, 5 meters wide at th

e top, and 15 meters wide at the base. The in situ total unit weight of the soil in the borrow pit is 21.7 kN/m3 with a water content of 11.4%. If levee construction requires the soil to be placed at a void ratio of 0.47, determine the volume that should be excavated from the borrow pit.
Engineering
1 answer:
shepuryov [24]4 years ago
4 0

Answer:

The answer is 2217.32m³

Explanation:

Given that:

V₂  = (15 + 5/2) * 3 * 100 = 3000 m³

r₁ = 21.7kN/m3

w (water) = 11.4%.

e₂ (void ratio) = 0.47

V₁ = ?

Now,

rd₁ =  r₁/1 + w₁ = 21.7/1 +(11.4/100)

= 19.47 kN/m3

Thus,

rd₂ = r₁/1 + e₂ = 21.7/1+ 0.47 = 14.76 kN/m3

Then,

V₁/V₂ = rd₁/ rd₂

V₁ = 3000 * 14.76/19.97

V₁ = 2217.32m³

Therefore, volume that should be excavated from the borrow pit is 2217.32m³

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Explanation:

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P_0= 14.696\ ps\\\\\ p _{0}= 0.00238 \frac{slue}{ft^{3}}\\\\\ A= 0.05 ft^2\\\\\ T_0= 59^{\circ}f = 518.67R\\\\\ air \ k= 1\\\\ \ cirtical \  pressure ( P^*)=P_0\times \frac{2}{k+1}^{\frac{k}{k-1}}\\

                                     = 14.696\times (\frac{2}{1.4+1})^{\frac{1.4}{1.4-1}}\\\\=7.763 Psia\\\\

if P flow is chocked

if P>P^{*} \to flow is not chocked

When  P= 10 psia < P^{*} \to not chocked

match number:

\ for \ P= \ 10\ G= \sqrt{\frac{2}{k-1}[(\frac{\ p_{0}}{p})^{\frac{k-1}{k}}-1]}

                       = \sqrt{\frac{2}{1.4-1}[(\frac{14.696}{10})^{\frac{1.4-1}{1.4}}-1]}

M_0=7.625

p=p_0(1+\frac{k-1}{2} M_0 r)^\frac{1}{1-k}

  =0.00238(1+\frac{1.4-1}{2}0.7625`)^{\frac{1}{1-1.4}}\\\\\ p=0.001808 \frac{slug}{ft^3}

\ T= T_0(1+\frac{k-1}{2} Ma^r)^{-1}\\\\\ T=518.67(1+\frac{1.4-1}{2} 0.7625^2)^{-1}\\\\\ T=464.6R\\\\

\ velocity \ of \ sound \ (C)=\sqrt{KRT}\\\\

                                    =\sqrt{1.4\times1716\times464.6}\\\\=1057 ft^3\\\\

R= gas constant=1716

m=PAV\\\\

    =0.001808\times0.05\times(Ma.C)\\\\=0.001808\times0.05\times0.7625\times 1057\\\\=0.0728\frac{slug}{s}

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3 years ago
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