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Principles of Geotechnical Enginee...

9th Edition
Braja M. Das + 1 other
ISBN: 9781305970939

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BuyFindarrow_forward

Principles of Geotechnical Enginee...

9th Edition
Braja M. Das + 1 other
ISBN: 9781305970939
Textbook Problem

Refer to Problem 8.4. Using the flow net drawn, calculate the hydraulic uplift force at the base of the hydraulic structure per meter length (measured along the axis of the structure).

8.24 For the hydraulic structure shown in Figure 8.24, draw a flow net for flow through the permeable layer and calculate the seepage loss in m3/day/m.

images

To determine

Find the hydraulic uplift force at the base of the hydraulic structure per meter length.

Explanation

Given information:

The hydraulic conductivity of the permeable soil layer k is 0.002cm/sec.

The head difference between the upstream and downstream H is 10 m.

The height of the water level H2 is 3.34 m.

The depth of permeable layer up to the tip of the hydraulic structure D is 1.67 m.

The depth of permeable layer D1 is 20 m.

Calculation:

Draw the free body diagram of the flow net for the given values as in Figure 1.

Determine the head loss for each drop using the relation.

ΔH=HNd

Here, Nd is the number of potential drop.

Refer Figure 1.

The number of potential drop Nd is 12.

Substitute 10 m for H and 12 for Nd.

ΔH=1012=0.83m

Determine the pressure head at D using the relation.

(ph)D=(H+H1)flowdis×ΔH

Here, flow dis is the flow net distance.

Substitute 10 m for H, 3.34 m for H1, 2 m for flow dis, and 0.833 for ΔH.

(ph)D=(10+3.34)2×0.833=11.67m

Determine the pressure head at E using the relation.

(ph)E=(H+H1)flowdis×ΔH

Substitute 10 m for H, 3.34 m for H1, 3 m for flow dis, and 0.833 for ΔH.

(ρh)E=(10+3.34)3×0.833=10.84m

Determine the pressure head at F using the relation.

(ph)F=(H+D)flowdis×ΔH

Substitute 10 m for H, 1.67 m for D, 3.5 m for flow dis, and 0.833 for ΔH.

(ph)F=(10+1.67)3.5×0.833=8.75m

Determine the pressure head at G using the relation.

(ph)G=(H+D)flowdis×ΔH

Substitute 10 m for H, 1.67 m for D, 8.5 m for flow dis, and 0.833 for ΔH.

(ph)G=(10+1.67)8.5×0.833=4.586m

Determine the pressure head at H using the relation.

(ph)H=(H+H1)flowdis×ΔH

Substitute 10 m for H, 3.34 m for H1, 9 m for flow dis, and 0.833 for ΔH.

(ph)H=(10+3.34)9×0.833=5.84m

Determine the pressure head at I using the relation.

(ph)I=(H+H1)flowdis×ΔH

Substitute 10 m for H, 3.34 m for H1, 10 m for flow dis, and 0.833 for ΔH.

(ph)I=(10+3.34)10×0.833=5.0m

Determine the hydraulic uplift force at the base of the hydraulic structure per meter length using the relation

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