BuyFindarrow_forward

Principles of Geotechnical Enginee...

9th Edition
Braja M. Das + 1 other
ISBN: 9781305970939

Solutions

Chapter
Section
BuyFindarrow_forward

Principles of Geotechnical Enginee...

9th Edition
Braja M. Das + 1 other
ISBN: 9781305970939
Textbook Problem

A slope with steady-state seepage has the following characteristics: H = 30 m, β = 18.43° (3:1 slope), γ' = 18 kN/m3, ϕ' = 23°, c' = 27 kN/m2, and ru = 0.5. Use Bishop and Morgenstern’s method to determine the minimum factor of safety.

To determine

Find the minimum factor of safety Fs using the Bishop and Morgenstern’s method.

Explanation

Given information:

The height (H) of the slope is 30 m.

The inclination β of a slope (3:1slope) is 18.43°.

The unit weight γ is 18kN/m3.

The angle of friction ϕ is 23°.

The cohesion c is 27kN/m2.

The value non-dimensional quantity ru is 0.5.

Calculation:

Determine the minimum factor of safety Fs from Table (15.5), using the procedure as follows:

  • Step 1. Obtain the values of angle of friction, inclination of a slope, and the value of cγH
  • Step 2. Obtain the value of nondimensional quantity.
  • Step 3. Refer Table (15.5) “Values of m and n for cγH=0” in the text book. Obtain the values of m and n for D=1,1.25,and1.5.
  • Step 4. calculate the factor of safety value, using the values of m and n for each value of D.
  • Finally, the required value of factor of safety is the smallest one obtained in step 4.

Trial 1:

Determine the value of cγH.

Substitute 27kN/m2 for c, 18kN/m3 for γ, and 30 m for H.

cγH=2718(30)=0.05

Refer Table (15.5d) “Stability coefficients m and n for cγH=0.05 and D=1.00” in the text book.

Take the stability coefficient m as 2.014 when the angle of friction ϕ is 22.5°.

Take the stability coefficient m as 2.193 when the angle of friction ϕ is 25°.

Determine the stability coefficient m when the angle of friction ϕ is 23° using the interpolation.

m=(2322.5)(2.1932.014)(2522.5)+2.014=2.049

Take the stability coefficient n as 1.568 when the angle of friction ϕ is 22.5°.

Take the stability coefficient n as 1.757 when the angle of friction ϕ is 25°.

Calculate the stability coefficient n when the angle of friction ϕ is 23° using the interpolation.

n=(2322.5)(1.7571.568)(2522.5)+1.568=1.606

Calculate the factor of safety using the formula.

Fs=mnru

Substitute 2.049 for m, 1.606 for n, and 0.5 for ru.

Fs=2.0491.606(0.5)=1.25

Trial 2:

Refer Table (15.5e) “Stability coefficients m and n for cγH=0.05 and D=1.25” in the text book

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Additional Engineering Solutions

Find more solutions based on key concepts

Show solutions add

How many 5 in. diameter, 1/4-in. thick disks can be fitted into a 4 ft long, 5 1/4 in. diameter cylindrical con...

Engineering Fundamentals: An Introduction to Engineering (MindTap Course List)

What two functions can the lathe tailstock perform?

Precision Machining Technology (MindTap Course List)

What is network fingerprinting?

Principles of Information Security (MindTap Course List)

Provide suggestions for reducing input volume.

Systems Analysis and Design (Shelly Cashman Series) (MindTap Course List)

Who is to furnish the range hood? _____

EBK ELECTRICAL WIRING RESIDENTIAL

What are some examples of popular operating systems?

Enhanced Discovering Computers 2017 (Shelly Cashman Series) (MindTap Course List)

Voltage can be described as ____________ .

Welding: Principles and Applications (MindTap Course List)