Point A is located 3 meters under the ground surface of a saturated site where the silty soil has unit weights = 20 and 21 kN/m³, friction angle = 37 degrees, lateral stress ratio = 0.5, and cohesion intercept : 3 kPa. Determine the highest vertical effective stress that point A can support while the horizontal %3D %3D effective stress remains constant. Answer 81.5 kPa.
Point A is located 3 meters under the ground surface of a saturated site where the silty soil has unit weights = 20 and 21 kN/m³, friction angle = 37 degrees, lateral stress ratio = 0.5, and cohesion intercept : 3 kPa. Determine the highest vertical effective stress that point A can support while the horizontal %3D %3D effective stress remains constant. Answer 81.5 kPa.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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![### Vertical and Horizontal Effective Stress in Saturated Silty Soil
**Problem Statement:**
Given the silty soil characteristics and conditions at Point A (located 3 meters below the ground surface), determine the highest vertical effective stress while keeping the horizontal effective stress constant.
- **Depth of Point A:** 3 meters
- **Unit weights of silty soil:** 20 and 21 kN/m³
- **Friction angle (φ):** 37 degrees
- **Lateral stress ratio (K):** 0.5
- **Cohesion intercept (c):** 3 kPa
The goal is to calculate the highest vertical effective stress at Point A. According to the problem conditions, the answer is approximately 81.5 kPa.
### Explanation of Key Terms:
- **Unit Weight:** The weight of the soil per unit volume, which in this problem are 20 and 21 kN/m³ for different soil zones or layers.
- **Friction Angle (φ):** The angle indicating the shear resistance of soil due to friction, given here as 37 degrees.
- **Lateral Stress Ratio (K):** The ratio of horizontal effective stress to vertical effective stress, stated as 0.5.
- **Cohesion Intercept (c):** The portion of shear strength of the soil that is independent of the normal stress, provided as 3 kPa.
### Calculation Steps:
1. **Determine the Vertical Stress (σv):**
Vertical stress is determined by the weight of the soil column above Point A.
\[
\sigma_v = \text{Unit Weight} \times \text{Depth}
\]
2. **Calculate the Horizontal Stress (σh):**
Using the lateral stress ratio:
\[
\sigma_h = K \times \sigma_v
\]
3. **Effective Vertical Stress (σ'v):**
The effective vertical stress considers both the total vertical stress and the pore water pressure. However, for this problem, assume conditions that keep horizontal stress constant.
### Conclusion:
The highest vertical effective stress that Point A can support while maintaining a constant horizontal effective stress is approximately 81.5 kPa. This solution considers the given unit weights, friction angle, lateral stress ratio, and cohesion intercept.
Understanding these principles helps in the design and analysis of soil stability in geotechnical engineering applications.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F05bb32f4-a25c-4c4f-835f-8dd97a453348%2F4257f29c-deeb-4f99-a469-f81a8adbb3df%2Fv1my5l_processed.png&w=3840&q=75)
Transcribed Image Text:### Vertical and Horizontal Effective Stress in Saturated Silty Soil
**Problem Statement:**
Given the silty soil characteristics and conditions at Point A (located 3 meters below the ground surface), determine the highest vertical effective stress while keeping the horizontal effective stress constant.
- **Depth of Point A:** 3 meters
- **Unit weights of silty soil:** 20 and 21 kN/m³
- **Friction angle (φ):** 37 degrees
- **Lateral stress ratio (K):** 0.5
- **Cohesion intercept (c):** 3 kPa
The goal is to calculate the highest vertical effective stress at Point A. According to the problem conditions, the answer is approximately 81.5 kPa.
### Explanation of Key Terms:
- **Unit Weight:** The weight of the soil per unit volume, which in this problem are 20 and 21 kN/m³ for different soil zones or layers.
- **Friction Angle (φ):** The angle indicating the shear resistance of soil due to friction, given here as 37 degrees.
- **Lateral Stress Ratio (K):** The ratio of horizontal effective stress to vertical effective stress, stated as 0.5.
- **Cohesion Intercept (c):** The portion of shear strength of the soil that is independent of the normal stress, provided as 3 kPa.
### Calculation Steps:
1. **Determine the Vertical Stress (σv):**
Vertical stress is determined by the weight of the soil column above Point A.
\[
\sigma_v = \text{Unit Weight} \times \text{Depth}
\]
2. **Calculate the Horizontal Stress (σh):**
Using the lateral stress ratio:
\[
\sigma_h = K \times \sigma_v
\]
3. **Effective Vertical Stress (σ'v):**
The effective vertical stress considers both the total vertical stress and the pore water pressure. However, for this problem, assume conditions that keep horizontal stress constant.
### Conclusion:
The highest vertical effective stress that Point A can support while maintaining a constant horizontal effective stress is approximately 81.5 kPa. This solution considers the given unit weights, friction angle, lateral stress ratio, and cohesion intercept.
Understanding these principles helps in the design and analysis of soil stability in geotechnical engineering applications.
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