Answered: A soil profile is shown in Figure 8.21.…

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Question

Q 8.7 If the coefficient of consolidation for the clay layer in problem 8.3 is 0.0018 cm^2/Sec, how long will it take for 60% primary consolidation to take place? What will be the total compression due to consolidation at that time?

$### Soil Consolidation Problem #### Problem Statement: A soil profile is illustrated in Figure 8.21. If a uniformly distributed load $ \Delta \sigma $ is applied at the ground surface, what will be the settlement of the clay layer due to primary consolidation? Assume the sand above the groundwater table to be dry. The details are as follows: - **Given Data:** - $ \Delta \sigma = 1000 \, \text{lb/ft}^2 $ - $ H_1 = 23 \, \text{ft} $ - $ H_2 = 17 \, \text{ft} $ - $ H_3 = 8 \, \text{ft} $ - **Material Properties:** - **Sand:** - $ \gamma_{\text{dry}} = 110 \, \text{lb/ft}^3 $ - $ \gamma_{\text{sat}} = 115 \, \text{lb/ft}^3 $ - **Clay:** - $ \gamma_{\text{sat}} = 120 \, \text{lb/ft}^3 $ - Liquid Limit (LL) = 50 - Void Ratio ($ e $) = 0.9 *(Assume the clay to be normally consolidated.)* #### Diagram Explanation: The diagram accompanying this problem displays a cross-section of the soil layers under consideration: - **Layers:** - The layers consist of sand and clay. - Sand is present above and below the clay layer. - **Load Application ($ \Delta \sigma $):** - Arrows pointing downward at the surface indicate the applied load distributed uniformly across the ground surface. - **Dimensions:** - The diagram shows three main height dimensions: $ H_1, H_2, $ and $ H_3 $. - **Groundwater Table:** - A dashed line labelled "Groundwater table" separates two sections of the sand layer, suggesting the presence of water below this line. - **Notes:** - Assume conditions for the clay layer being normally consolidated in solving the problem. The void ratio and liquid limit are essential properties for understanding consolidation behavior. This setup forms the basis for calculating settlement in response to the specified load under the given environmental conditions.$

Transcribed Image Text:### Soil Consolidation Problem #### Problem Statement: A soil profile is illustrated in Figure 8.21. If a uniformly distributed load $ \Delta \sigma $ is applied at the ground surface, what will be the settlement of the clay layer due to primary consolidation? Assume the sand above the groundwater table to be dry. The details are as follows: - **Given Data:** - $ \Delta \sigma = 1000 \, \text{lb/ft}^2 $ - $ H_1 = 23 \, \text{ft} $ - $ H_2 = 17 \, \text{ft} $ - $ H_3 = 8 \, \text{ft} $ - **Material Properties:** - **Sand:** - $ \gamma_{\text{dry}} = 110 \, \text{lb/ft}^3 $ - $ \gamma_{\text{sat}} = 115 \, \text{lb/ft}^3 $ - **Clay:** - $ \gamma_{\text{sat}} = 120 \, \text{lb/ft}^3 $ - Liquid Limit (LL) = 50 - Void Ratio ($ e $) = 0.9 *(Assume the clay to be normally consolidated.)* #### Diagram Explanation: The diagram accompanying this problem displays a cross-section of the soil layers under consideration: - **Layers:** - The layers consist of sand and clay. - Sand is present above and below the clay layer. - **Load Application ($ \Delta \sigma $):** - Arrows pointing downward at the surface indicate the applied load distributed uniformly across the ground surface. - **Dimensions:** - The diagram shows three main height dimensions: $ H_1, H_2, $ and $ H_3 $. - **Groundwater Table:** - A dashed line labelled "Groundwater table" separates two sections of the sand layer, suggesting the presence of water below this line. - **Notes:** - Assume conditions for the clay layer being normally consolidated in solving the problem. The void ratio and liquid limit are essential properties for understanding consolidation behavior. This setup forms the basis for calculating settlement in response to the specified load under the given environmental conditions.

**Title: Soil Layer Consolidation**

The image depicts a cross-section of soil layers showing the process of consolidation. It is divided into three distinct layers of soil, each with different materials and properties:

1. **Top Layer: Sand**
- Thickness: 2 meters.
- Description: This layer is labeled "Sand" and represented with a uniform pattern. It is situated directly below ground level (GL).

2. **Middle Layer: Clay**
- Thickness: 1 meter.
- Description: This layer is labeled "Clay" and found beneath the sand. It shows symbols indicating the process of consolidation, such as arrows pointing downward, denoting compression, and the equation $ \sigma'_{0}, \, \sigma'_{f}, \, \Delta \sigma $, which likely relate to initial stress, final stress, and change in stress, respectively.

3. **Bottom Layer: Dense Gravel**
- Thickness: 2 meters.
- Description: This layer is labeled "Dense gravel" and shown with a more densely dotted pattern, indicating a coarser material.

Throughout the diagram, the layers are clearly marked with horizontal lines separating them, and vertical arrows indicating pressing forces or consolidation processes active within the clay layer.

**Figure Reference:**

- Figure 8.22

This diagram provides a visual understanding of how different soil materials are stacked and the stress conditions affecting them, essential for geotechnical analysis and civil engineering applications.

Expert Solution

Step 1 Given

$∆ δ = 1000 l b / f t^{2} H_{1} = 23 f t H_{2} = 17 f t H_{3} = 8 f t F o r s a n d, γ_{d r y} = 110 l b / f t^{3} γ_{s a t} = 115 l b / f t^{3} F o r c l a y, γ_{s a t} = 120 l b / f t^{3} L L = 50 e = 0.9$