For the steady-state uniform seepage condition shown in the adjacent Figure, the cross-sectional area of the sample in the direction of flow is 40 cm?. Soil permeability k is 0.1 cm/s. The water levels are maintained at the levels shown with h1 = 50 cm, h2= 25 cm, h3 = 20 cm and h4 = 15 cm. (a) what is the total head loss across the system (from point A to point B)?

For the steady-state uniform seepage condition shown in the adjacent Figure, the cross-sectional area of the sample in the direction of flow is 40 cm?. Soil permeability k is 0.1 cm/s. The water levels are maintained at the levels shown with h1 = 50 cm, h2= 25 cm, h3 = 20 cm and h4 = 15 cm. (a) what is the total head loss across the system (from point A to point B)?

Fundamentals of Geotechnical Engineering (MindTap Course List)

5th Edition

ISBN:9781305635180

Author:Braja M. Das, Nagaratnam Sivakugan

Publisher:Braja M. Das, Nagaratnam Sivakugan

Chapter6: Hydraulic Conductivity

Section: Chapter Questions

Problem 6.17CTP

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Measuring site work, Excavation and Piling

Bid drawings typically include very little material about the precise requirements of site work operations, measuring site work and excavation work differs from measuring most other works on a construction project. The actual site work conditions are not provided and also the dimensions of the excavations are not known during the pre-construction phase. The precise measurement of the excavation and backfill of the earth material and topsoil is important for a contractor to decide upon the total cost required for the process. All the works should be carried out under OSHA (Occupational Safety and Health Administration) standards to ensure the safety of the workers.

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### Understanding Steady-State Uniform Seepage in Soil

#### Problem Statement:
2. For the steady-state uniform seepage condition shown in the adjacent figure, the cross-sectional area of the sample in the direction of flow is 40 cm². Soil permeability \( k \) is 0.1 cm/s. The water levels are maintained at the levels shown with \( h_1 \) = 50 cm, \( h_2 \) = 25 cm, \( h_3 \) = 20 cm, and \( h_4 \) = 15 cm.

(a) What is the total head loss across the system (from point A to point B)?

(b) What is the hydraulic gradient \( i \) through the soil sample?

(c) Determine the volume of water which discharges in 10 minutes.

#### Diagram Explanation:
The diagram illustrates a U-shaped tube filled with soil between two points, A and B. It shows different water levels at four different points:
- \( h_1 \) represents the initial water level (50 cm).
- \( h_2 \) represents the water level after discharge (25 cm).
- \( h_3 \) and \( h_4 \) are in-between levels (20 cm and 15 cm, respectively).

The soil sample is located between point A and B, through which the water flows from the higher water level at point A to the lower water level at point B.

#### Solution:

##### (a) Total Head Loss Across the System:
To calculate the total head loss, we use the difference in head between point A and point B.

\[ \text{Total head loss} = h_1 - h_2 \]
\[ \text{Total head loss} = 50 \ \text{cm} - 25 \ \text{cm} = 25 \ \text{cm} \]

##### (b) Hydraulic Gradient \( i \) through the Soil Sample:
The hydraulic gradient \( i \) is defined as the head loss per unit length of flow. Given that the length between point A and point B (assumed to be horizontal) is \( L \):

\[ i = \frac{\text{Head Loss}}{L} \]

Assuming the length \( L \) is equal to \( h_3 + h_4 \):

\[ L = h_3 + h_4 = 20 \ \text{cm} + 15 \

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