Principles Of Geotechnical Engineering, Si Edition
Principles Of Geotechnical Engineering, Si Edition
9th Edition
ISBN: 9781305970953
Author: Braja M. Das, Khaled Sobhan
Publisher: Cengage Learning
Question
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Chapter 13, Problem 13.1P
To determine

Find the magnitude of the lateral earth forces Po per unit length of the wall and find the location z¯ of the resultant measured from the bottom of the wall.

Expert Solution & Answer
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Answer to Problem 13.1P

The magnitude of the lateral force is 393.1kN/m_.

The location of the resultant measured from the bottom of the wall is 2.5m_.

Explanation of Solution

Given information:

The height (H) of the retaining wall is 7.5 m.

The soil friction angle ϕ is 31°.

The angle of wall friction δ is 0.

The unit weight γ of the sand is 19.2kN/m3.

The over-consolidation ratio (OCR) is 2.2.

Calculation:

Calculate the earth pressure coefficient (Ko) using the relation.

Ko=(1sinϕ)(OCR)sinϕ

Substitute 31° for ϕ and 2.2 for OCR.

Ko=(1sin31°)(2.2)sin31°=0.48496×1.5009=0.7279

Calculate the total force per unit length (Po) using the relation.

Po=12KoγH2

Substitute 0.7279 for Ko, 19.2kN/m3 for γ, and 7.5m for H.

Po=12×0.7279×19.2×(7.5)2=393.1kN/m

Thus, the magnitude of the lateral earth force per unit length (Po) is 393.1kN/m_.

Calculate the location of the resultant (z¯) using the relation.

z¯=H3

Substitute 7.5m for H.

z¯=7.53=2.5m

Thus, the location of the resultant (z¯) measured from the bottom of the wall is 2.5m_.

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Note: Provide a clear, step-by-step simplified handwritten solution (with no extra explanations) that is entirely produced by hand without any AI help. I require an expert-level answer, and I will assess it based on the quality and accuracy of the work, referring to the attached image for additional guidance. Make sure every detail is carefully verified for correctness before you submit. Thanks!.
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