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A concrete pile of 50 cm diameter is installed in a predominantly sand deposit. The total length of the pile is 20 m, out of which 17 m is embedded into the ground. The average density of the soil is 19 kN/m\(^3\) and the coefficient of horizontal subgrade modulus variation, \(h\), is 1.5 \times 10^4 \) kN/m\(^3\). Young's modulus of concrete is 20 MPa.

A. Find the lateral deflection in the beam using the IS:2911 approach. What happens if the top 3 m of the pile is not constructed and is fixed by a pile cap, as shown in the adjacent figure?

B. Solve this problem again using Brom's Chart Method.

C. Find the ultimate lateral resistance using Brom's Chart Method for both cases. If the allowable deflection at ground level is 25 mm, find the factor of safety against ultimate strength.

Answer :

Explore lateral deflection and resistance of a concrete pile using different methods and evaluate safety factor considerations.

Part A: Lateral Deflection using IS:2911: IS:2911 is a standard for pile design and construction in India. It offers approaches to determine lateral deflection using empirical formulas and tables, focusing on key factors like:

Subgrade Modulus: Represents soil stiffness, given as 15,000 kN/m³. Pile Properties: Includes diameter (50 cm), length (17 m in-ground), and Young's modulus (20 MPa). The detailed calculations involve factors like soil type, depth, and pile stiffness. Since the pile is embedded for 17 meters, it's designed to resist lateral forces. If the top 3 meters aren't constructed, reducing pile length, it would likely impact lateral stability due to decreased stiffness, making it more prone to deflection without a pile cap to stabilize it.

Part B: Lateral Deflection by Brom's Chart Method :Brom's method is a more straightforward approach to estimate lateral deflection. It uses a combination of pile dimensions, subgrade modulus, and other factors to determine deflection under lateral load.

Given:

Pile diameter: 50 cm

Embedded length: 17 m

Subgrade modulus: 15,000 kN/m³

Average soil density: 19 kN/m³

In Brom's method, you'd typically consult a chart or graph that considers these factors to determine lateral deflection. This method uses simplified assumptions to estimate deflection. Due to the variance in pile and soil conditions, precision often requires engineering software or detailed tables.

Part C: Ultimate Lateral Resistance by Brom's Chart Method : Ultimate lateral resistance is the maximum lateral force the pile can withstand before failure, taking into account pile and soil characteristics. Brom's method provides a way to estimate this resistance. You'd need details like the pile diameter, soil density, and subgrade modulus.

Given:

Pile diameter: 50 cm

Subgrade modulus: 15,000 kN/m³

Average soil density: 19 kN/m³

Ultimate lateral resistance can be calculated using these values, but it involves complex calculations or specialized software.

To find the factor of safety against ultimate strength, you'd calculate the ratio between the ultimate resistance and the load that causes a specific deflection, such as 25 mm at ground level. This ratio indicates the safety margin before the pile fails.

Since the exact solution requires engineering charts or software, consider consulting a geotechnical engineer for precise answers and further analysis.

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