A permeable layer is underlain by an impervious layer, as shown in Figure 7.30. With k = 5.2 × 10¬ª cm/s for the permeable layer, calculate the rate of seepage through it in m'/hr/m if H = 3.8 m and a = 12°.

Structural Analysis
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Chapter2: Loads On Structures
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**7.8** A permeable layer is underlain by an impervious layer, as shown in Figure 7.30. With \( k = 5.2 \times 10^{-4} \) cm/s for the permeable layer, calculate the rate of seepage through it in m\(^3\)/hr/m if \( H = 3.8 \) m and \( \alpha = 12^\circ \).

**Diagram Explanation:**

The diagram illustrates the arrangement of a permeable layer above an impervious layer. The key features include:

- **Permeable Layer**: Represented in a light color, where water can seep through.
- **Impervious Layer**: Shown in a darker color, acting as a barrier to water flow.
- **Groundwater Table (Free Surface)**: A line indicating the upper level of saturation in the permeable layer.
- **Direction of Seepage**: Indicated by an arrow showing the path taken by water as it moves through the permeable layer.
- **Slope Angle (\(\alpha\))**: The angle of inclination of the layers, given as \( 12^\circ \).
- **Layer Thickness (\(H\))**: The vertical distance between the groundwater table and the impervious layer, given as 3.8 m.

The problem requires calculating the seepage rate through the permeable layer using the given hydraulic conductivity (\( k \)) and physical parameters (\( H \) and \( \alpha \)).
Transcribed Image Text:**7.8** A permeable layer is underlain by an impervious layer, as shown in Figure 7.30. With \( k = 5.2 \times 10^{-4} \) cm/s for the permeable layer, calculate the rate of seepage through it in m\(^3\)/hr/m if \( H = 3.8 \) m and \( \alpha = 12^\circ \). **Diagram Explanation:** The diagram illustrates the arrangement of a permeable layer above an impervious layer. The key features include: - **Permeable Layer**: Represented in a light color, where water can seep through. - **Impervious Layer**: Shown in a darker color, acting as a barrier to water flow. - **Groundwater Table (Free Surface)**: A line indicating the upper level of saturation in the permeable layer. - **Direction of Seepage**: Indicated by an arrow showing the path taken by water as it moves through the permeable layer. - **Slope Angle (\(\alpha\))**: The angle of inclination of the layers, given as \( 12^\circ \). - **Layer Thickness (\(H\))**: The vertical distance between the groundwater table and the impervious layer, given as 3.8 m. The problem requires calculating the seepage rate through the permeable layer using the given hydraulic conductivity (\( k \)) and physical parameters (\( H \) and \( \alpha \)).
Expert Solution
Step 1

Area of cross sectionA=Hcosα×BA=3.8cos12×1mHydraulic gradienti=ΔhLcosαΔh=headloss=Ltanαi=LtanαLcosα=sinαi=sin12

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