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11.7 A retaining wall is shown in Figure 11.22. Determine the Rankine active force, P, per unit length of the wall and the location of the resultant for each of the following cases: a. H = 12 ft, H = 4 ft, y1 = 105 lb/ft', y2 = b. H = 20 ft, H, = 6 ft, y, = 110 lb/ft', 122 Ib/ft', oi = 30°, bi = 30°, q = 0 126 Ib/ft', of = 34°, $ = 34°, q = 300 lb/ft %3= Y2 = %3D

11.7 A retaining wall is shown in Figure 11.22. Determine the Rankine active force, P, per unit length of the wall and the location of the resultant for each of the following cases: a. H = 12 ft, H = 4 ft, y1 = 105 lb/ft', y2 = b. H = 20 ft, H, = 6 ft, y, = 110 lb/ft', 122 Ib/ft', oi = 30°, bi = 30°, q = 0 126 Ib/ft', of = 34°, $ = 34°, q = 300 lb/ft %3= Y2 = %3D

Structural Analysis
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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Q 11.7
**Figure 11.22 Explanation:** This diagram illustrates a vertical cross-section of a retaining wall system interacting with sand under the influence of a surcharge and groundwater. - **Retaining Wall:** Shown on the left, it's labeled as having a "frictionless wall." - **Dimensions:** - The total height of the wall is labeled as \( H \). - The height from the top to the groundwater table is \( H_1 \). - **Surcharge:** Represented by vertical arrows at the top of the soil, labeled as "Surcharge = q." This indicates an additional load applied on the surface. - **Sand Layers:** - Above the groundwater table, the sand is characterized by \(\gamma_1\), \(\phi'_1\), and \(c'_1 = 0\). - Below the groundwater table, the properties change to \(\gamma_2\) (saturated unit weight), \(\phi'_2\), and \(c'_2 = 0\). - **Groundwater Table:** Illustrated with a horizontal line dividing the two sand layers, indicating the transition from unsaturated to saturated conditions. This diagram is used to understand the forces and pressures acting on the retaining wall due to soil and water interactions.
Transcribed Image Text:**Figure 11.22 Explanation:** This diagram illustrates a vertical cross-section of a retaining wall system interacting with sand under the influence of a surcharge and groundwater. - **Retaining Wall:** Shown on the left, it's labeled as having a "frictionless wall." - **Dimensions:** - The total height of the wall is labeled as \( H \). - The height from the top to the groundwater table is \( H_1 \). - **Surcharge:** Represented by vertical arrows at the top of the soil, labeled as "Surcharge = q." This indicates an additional load applied on the surface. - **Sand Layers:** - Above the groundwater table, the sand is characterized by \(\gamma_1\), \(\phi'_1\), and \(c'_1 = 0\). - Below the groundwater table, the properties change to \(\gamma_2\) (saturated unit weight), \(\phi'_2\), and \(c'_2 = 0\). - **Groundwater Table:** Illustrated with a horizontal line dividing the two sand layers, indicating the transition from unsaturated to saturated conditions. This diagram is used to understand the forces and pressures acting on the retaining wall due to soil and water interactions.
## Topic: Earth Pressure and Retaining Walls ### Problem 11.6 A 4-meter-high smooth vertical wall retains a granular backfill with a unit weight (γ) of 18.0 kN/m³ and an angle of internal friction (φ') of 33°. Using Rankine's earth pressure coefficients, determine the active force per unit length \( P_a \) for the following cases: a. **Horizontal Backfill** b. **Inclined Backfill with α = 10°** c. **Inclined Backfill with α = 20°** ### Problem 11.7 A retaining wall is shown in Figure 11.22. Determine the Rankine active force, \( P_a \), per unit length of the wall and the location of the resultant force for each of the following cases: a. **Given Conditions:** - Height of wall (H) = 12 ft - Height above wall (H₁) = 4 ft - Unit weight of soil for section 1 (γ₁) = 105 lb/ft³ - Unit weight of soil for section 2 (γ₂) = 122 lb/ft³ - Angle of internal friction for section 1 (φ'₁) = 30° - Angle of internal friction for section 2 (φ'₂) = 30° - Surcharge (q) = 0 b. **Given Conditions:** - Height of wall (H) = 20 ft - Height above wall (H₁) = 6 ft - Unit weight of soil for section 1 (γ₁) = 110 lb/ft³ - Unit weight of soil for section 2 (γ₂) = 126 lb/ft³ - Angle of internal friction for section 1 (φ'₁) = 34° - Angle of internal friction for section 2 (φ'₂) = 34° - Surcharge (q) = 300 lb/ft² Note: Detailed calculations and graphical representations are needed to solve the above problems but are not included in the current text. **Disclaimer:** The material provided is intended for educational purposes and should not be used in practice without further validation. Proper interpretation of the formulas and coefficients is crucial in engineering applications.
Transcribed Image Text:## Topic: Earth Pressure and Retaining Walls ### Problem 11.6 A 4-meter-high smooth vertical wall retains a granular backfill with a unit weight (γ) of 18.0 kN/m³ and an angle of internal friction (φ') of 33°. Using Rankine's earth pressure coefficients, determine the active force per unit length \( P_a \) for the following cases: a. **Horizontal Backfill** b. **Inclined Backfill with α = 10°** c. **Inclined Backfill with α = 20°** ### Problem 11.7 A retaining wall is shown in Figure 11.22. Determine the Rankine active force, \( P_a \), per unit length of the wall and the location of the resultant force for each of the following cases: a. **Given Conditions:** - Height of wall (H) = 12 ft - Height above wall (H₁) = 4 ft - Unit weight of soil for section 1 (γ₁) = 105 lb/ft³ - Unit weight of soil for section 2 (γ₂) = 122 lb/ft³ - Angle of internal friction for section 1 (φ'₁) = 30° - Angle of internal friction for section 2 (φ'₂) = 30° - Surcharge (q) = 0 b. **Given Conditions:** - Height of wall (H) = 20 ft - Height above wall (H₁) = 6 ft - Unit weight of soil for section 1 (γ₁) = 110 lb/ft³ - Unit weight of soil for section 2 (γ₂) = 126 lb/ft³ - Angle of internal friction for section 1 (φ'₁) = 34° - Angle of internal friction for section 2 (φ'₂) = 34° - Surcharge (q) = 300 lb/ft² Note: Detailed calculations and graphical representations are needed to solve the above problems but are not included in the current text. **Disclaimer:** The material provided is intended for educational purposes and should not be used in practice without further validation. Proper interpretation of the formulas and coefficients is crucial in engineering applications.
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