   Chapter 8, Problem 8.1CTP Principles of Geotechnical Enginee...

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

Solutions

Chapter
Section Principles of Geotechnical Enginee...

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

Refer to Problem 8.12. Given k x = 4 × 10 − 5 m / min and k z = 1 × 10 − 5   m / min , calculate the rate of seepage through the dam (m3/min/m) using Schaffernak’s solution.8.12 An earth dam section is shown in Figure 8.28. Determine the rate of seepage through the earth dam using Pavlovsky’s solution. Use k = 4 × 10–5 mm/s. To determine

Find the seepage rate through the earth dam using Schaffernak’s solution.

Explanation

Given information:

The height of the water level H is 32 m.

The height of the earth dam Hd is 35 m.

The length of earth dam top B is 7 m.

The hydraulic conductivity of the permeable soil layer along x axis kx is 4×105m/min.

The hydraulic conductivity of the permeable soil layer along y axis kz is 1×105m/min.

Calculation:

The value of kxkz, the soil is anisotropic with respect to hydraulic conductivity.

Determine the horizontal distance L1 using the relation.

L1=H2+(verthori)2

Here, vert is the vertical distance in the given slope and hori is the horizontal distance in the given slope.

Substitute 32 m for H, 1 for vert, and 2 for hori.

L1=322+(12)2=32m

Determine the horizontal distance L2 using the relation.

L2=H22+(verthori)2

Here, H2 is the height of the dam above the water table.

Substitute 3 m for H2, 1 for vert, and 2 for hori.

L2=32+(12)2=3.0m

Determine the value of kzkx.

Substitute 1×105m/min for kz and 4×105m/min for kx.

kzkx=1×1054×105=0.5

Determine the horizontal distance L3 using the relation.

L3=kzkx×B

Substitute 0.5 for kzkx and 7 m for B.

L3=0.5×7=3.5m

Determine the horizontal distance L4 using the relation.

L4=H12+(verthori)2

Substitute 32 m for H, 1 for vert, and 2 for hori.

L4=352+(12)2=35m

Draw the transformed section of the earth dam as in Figure 1

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