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Given that the height of the specimen ring used for the one-dimensional consolidation test was 1 inch and one porous stone was used during the test, find the value of coefficient of consolidation, c, using the deformation versus logarithm of time graph in Figure 1 (Please show each step clearly on the graph). You may use TD 0.197D² C, =: 50

Given that the height of the specimen ring used for the one-dimensional consolidation test was 1 inch and one porous stone was used during the test, find the value of coefficient of consolidation, c, using the deformation versus logarithm of time graph in Figure 1 (Please show each step clearly on the graph). You may use TD 0.197D² C, =: 50

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
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### Problem Statement 1. Given that the height of the specimen ring used for the one-dimensional consolidation test was 1 inch and one porous stone was used during the test, find the value of the coefficient of consolidation, \(c_v\), using the deformation versus logarithm of time graph in Figure 1. (Please show each step clearly on the graph). You may use the formula: \[ c_v = \frac{T_{50}D^2}{t_{50}} = \frac{0.197D^2}{t_{50}} \] ### Graph Explanation #### Figure 1: Logarithm of Time - Deformation Plot - **Axes**: - **X-axis**: Represents the logarithm of time in minutes (min), ranging from approximately 0.1 to 100. - **Y-axis**: Represents deformation in inches (in), ranging from approximately 0.14 to 0.18. - **Curve Description**: - The curve starts at a higher deformation value close to 0.18 inches, decreases gradually as the logarithm of time increases, and ends close to 0.14 inches. - The slope of the curve indicates the rate at which deformation occurs over time under constant load. This graph is used to determine the coefficient of consolidation, \(c_v\), which is a measure of the rate at which a soil consolidates under load. The curve allows for the calculation of the time it takes for 50% of the primary consolidation to occur, denoted as \(t_{50}\), which is then used in the given formula to find \(c_v\).
Transcribed Image Text:### Problem Statement 1. Given that the height of the specimen ring used for the one-dimensional consolidation test was 1 inch and one porous stone was used during the test, find the value of the coefficient of consolidation, \(c_v\), using the deformation versus logarithm of time graph in Figure 1. (Please show each step clearly on the graph). You may use the formula: \[ c_v = \frac{T_{50}D^2}{t_{50}} = \frac{0.197D^2}{t_{50}} \] ### Graph Explanation #### Figure 1: Logarithm of Time - Deformation Plot - **Axes**: - **X-axis**: Represents the logarithm of time in minutes (min), ranging from approximately 0.1 to 100. - **Y-axis**: Represents deformation in inches (in), ranging from approximately 0.14 to 0.18. - **Curve Description**: - The curve starts at a higher deformation value close to 0.18 inches, decreases gradually as the logarithm of time increases, and ends close to 0.14 inches. - The slope of the curve indicates the rate at which deformation occurs over time under constant load. This graph is used to determine the coefficient of consolidation, \(c_v\), which is a measure of the rate at which a soil consolidates under load. The curve allows for the calculation of the time it takes for 50% of the primary consolidation to occur, denoted as \(t_{50}\), which is then used in the given formula to find \(c_v\).
**Educational Resource: Soil Consolidation Analysis** 2. **Problem Statement:** For the same consolidation test, if the height of solids (\(H_s\)) was 0.55 inches and the diameter of the specimen ring was 2.5 inches, calculate the initial void ratio of the specimen. 3. **Problem Statement:** From the e-log\(P\) graph in Figure 2, determine the pre-consolidation pressure using Casagrande’s Method. (Please show each step clearly on the graph). **Figure 2: e-log\(P\) Plot:** - **Graph Description:** - The graph is a plot of the void ratio (e) versus the logarithm of pressure (log\(P\), in psf). - The y-axis represents the void ratio, ranging from 0.4 to 0.8. - The x-axis represents the pressure in psf, ranging from 100 to 100,000. - **Graph Details:** - The data points in the graph form a curve that initially decreases at a decreasing rate and then exhibits a sharper decrease. - The curve shows the typical consolidation behavior of the soil, as the void ratio decreases with increasing pressure. - The shape of the curve is crucial for identifying the pre-consolidation pressure using Casagrande’s method, which involves analyzing the point of maximum curvature. This depiction provides insight into how soils behave under varying compressive stresses and is essential for geotechnical engineering and soil mechanics.
Transcribed Image Text:**Educational Resource: Soil Consolidation Analysis** 2. **Problem Statement:** For the same consolidation test, if the height of solids (\(H_s\)) was 0.55 inches and the diameter of the specimen ring was 2.5 inches, calculate the initial void ratio of the specimen. 3. **Problem Statement:** From the e-log\(P\) graph in Figure 2, determine the pre-consolidation pressure using Casagrande’s Method. (Please show each step clearly on the graph). **Figure 2: e-log\(P\) Plot:** - **Graph Description:** - The graph is a plot of the void ratio (e) versus the logarithm of pressure (log\(P\), in psf). - The y-axis represents the void ratio, ranging from 0.4 to 0.8. - The x-axis represents the pressure in psf, ranging from 100 to 100,000. - **Graph Details:** - The data points in the graph form a curve that initially decreases at a decreasing rate and then exhibits a sharper decrease. - The curve shows the typical consolidation behavior of the soil, as the void ratio decreases with increasing pressure. - The shape of the curve is crucial for identifying the pre-consolidation pressure using Casagrande’s method, which involves analyzing the point of maximum curvature. This depiction provides insight into how soils behave under varying compressive stresses and is essential for geotechnical engineering and soil mechanics.
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