Fundamentals of Geotechnical Engineering (MindTap Course List)
Fundamentals of Geotechnical Engineering (MindTap Course List)
5th Edition
ISBN: 9781305635180
Author: Braja M. Das, Nagaratnam Sivakugan
Publisher: Cengage Learning
Question
Chapter 8, Problem 8.27CTP
To determine

Find the vertical stress increase at 4 m below A, B, and C.

Expert Solution & Answer
Check Mark

Answer to Problem 8.27CTP

The increase in the vertical stress (Δσ) at point A located at depth of 4 m is 38.964kN/m2_.

The increase in the vertical stress (Δσ) at point B located at depth of 4 m is 14.586kN/m2_.

The increase in the vertical stress (Δσ) at point C located at depth of 4 m is 14.322kN/m2_.

Explanation of Solution

Given information:

The depth of the point from the ground level, z=4m.

The intensity of the uniform pressure, q=60kN/m2.

Calculation:

Vertical stress increase at point A:

Show the free-body diagram of the L-shaped raft as in Figure 1.

Fundamentals of Geotechnical Engineering (MindTap Course List), Chapter 8, Problem 8.27CTP , additional homework tip  1

Rectangle 1:

Find the value of m1 using the relation:

m1=B1z

Substitute 4 m for B1 and 4 m for z.

m1=44=1

Find the value of n1 using the relation:

n1=L1z

Substitute 6 m for L1 and 4 m for z.

n1=64=1.5

Refer Figure 8.16 “Variation of I3 with m and n” in the textbook.

For m1=1 and n1=1.5;

The value of variation (I3)1 is 0.1935.

Find the increase in vertical stress (Δσ1) using the relation:

Δσ1=q(I3)1

Substitute 60kN/m2 for q and 0.1935 for (I3)1.

Δσ1=60×0.1935=11.61kN/m2

Rectangle 2:

Find the value of m2 using the relation:

m2=B2z

Substitute 8 m for B2 and 4 m for z.

m2=84=2

Find the value of n2 using the relation:

n2=L2z

Substitute 6 m for L2 and 4 m for z.

n2=64=1.5

Refer Figure 8.16 “Variation of I3 with m and n” in the textbook.

For m2=2 and n2=1.5;

The value of variation (I3)2 is 0.2234.

Find the increase in vertical stress (Δσ2) using the relation:

Δσ2=q(I3)2

Substitute 60kN/m2 for q and 0.2234 for (I3)2.

Δσ2=60×0.2234=13.404kN/m2

Rectangle 3:

Find the value of m3 using the relation:

m3=B3z

Substitute 8 m for B3 and 4 m for z.

m3=84=2

Find the value of n3 using the relation:

n3=L3z

Substitute 8 m for L3 and 4 m for z.

n3=84=2

Refer Figure 8.16 “Variation of I3 with m and n” in the textbook.

For m3=2 and n3=2;

The value of variation (I3)3 is 0.2325.

Find the increase in vertical stress (Δσ3) using the relation:

Δσ3=q(I3)3

Substitute 60kN/m2 for q and 0.2325 for (I3)3.

Δσ3=60×0.2325=13.95kN/m2

Find the increase in vertical stress (Δσ) at point A using the relation:

Δσ=Δσ1+Δσ2+Δσ3

Substitute 11.61kN/m2 for Δσ1, 13.404kN/m2 for Δσ2, and 13.95kN/m2 for Δσ3.

Δσ=11.61+13.404+13.95=38.964kN/m2

Therefore, the increase in the vertical stress (Δσ) at point A located at depth of 4 m is 38.964kN/m2_.

The vertical stress increase at point B:

Show the free-body diagram of the L-shaped raft as in Figure 2.

Fundamentals of Geotechnical Engineering (MindTap Course List), Chapter 8, Problem 8.27CTP , additional homework tip  2

Rectangle 1:

Find the value of m1 using the relation:

m1=B1z

Substitute 12 m for B1 and 4 m for z.

m1=124=3

Find the value of n1 using the relation:

n1=L1z

Substitute 6 m for L1 and 4 m for z.

n1=64=1.5

Refer Figure 8.16 “Variation of I3 with m and n” in the textbook.

For m1=3 and n1=1.5;

The value of variation (I3)1 is 0.2280.

Find the increase in vertical stress (Δσ1) using the relation:

Δσ1=q(I3)1

Substitute 60kN/m2 for q and 0.2280 for (I3)1.

Δσ1=60×0.2280=13.68kN/m2

Rectangle 2:

Find the value of m2 using the relation:

m2=B2z

Substitute 8 m for B2 and 4 m for z.

m2=84=2

Find the value of n2 using the relation:

n2=L2z

Substitute 14 m for L2 and 4 m for z.

n2=144=3.5

Refer Figure 8.16 “Variation of I3 with m and n” in the textbook.

For m2=2 and n2=3.5;

The value of variation (I3)2 is 0.2385.

Find the increase in vertical stress (Δσ2) using the relation:

Δσ2=q(I3)2

Substitute 60kN/m2 for q and 0.2385 for (I3)2.

Δσ2=60×0.2385=14.31kN/m2

Rectangle 3:

Find the value of m3 using the relation:

m3=B3z

Substitute 8 m for B3 and 4 m for z.

m3=84=2

Find the value of n3 using the relation:

n3=L3z

Substitute 6 m for L3 and 4 m for z.

n3=64=1.5

Refer Figure 8.16 “Variation of I3 with m and n” in the textbook.

For m3=2 and n3=1.5;

The value of variation (I3)3 is 0.2234.

Find the increase in vertical stress (Δσ3) using the relation:

Δσ3=q(I3)3

Substitute 60kN/m2 for q and 0.2234 for (I3)3.

Δσ3=60×0.2234=13.404kN/m2

Find the increase in vertical stress (Δσ) at point B using the relation:

Δσ=Δσ1+Δσ2Δσ3

Substitute 13.68kN/m2 for Δσ1, 14.31kN/m2 for Δσ2, and 13.404kN/m2 for Δσ3.

Δσ=13.68+14.3113.404=14.586kN/m2

Therefore, the increase in the vertical stress (Δσ) at point B located at depth of 4 m is 14.586kN/m2_.

The vertical stress increase at point C:

Show the free-body diagram of the L-shaped raft as in Figure 3.

Fundamentals of Geotechnical Engineering (MindTap Course List), Chapter 8, Problem 8.27CTP , additional homework tip  3

Rectangle 1:

Find the value of m1 using the relation:

m1=B1z

Substitute 12 m for B1 and 4 m for z.

m1=124=3

Find the value of n1 using the relation:

n1=L1z

Substitute 14 m for L1 and 4 m for z.

n1=144=3.5

Refer Figure 8.16 “Variation of I3 with m and n” in the textbook.

For m1=3 and n1=3.5;

The value of variation (I3)1 is 0.2447.

Find the increase in vertical stress (Δσ1) using the relation:

Δσ1=q(I3)1

Substitute 60kN/m2 for q and 0.2447 for (I3)1.

Δσ1=60×0.2447=14.682kN/m2

Rectangle 2:

Find the value of m2 using the relation:

m2=B2z

Substitute 12 m for B2 and 4 m for z.

m2=124=3

Find the value of n2 using the relation:

n2=L2z

Substitute 8 m for L2 and 4 m for z.

n2=84=2

Refer Figure 8.16 “Variation of I3 with m and n” in the textbook.

For m2=3 and n2=2;

The value of variation (I3)2 is 0.2385.

Find the increase in vertical stress (Δσ2) using the relation:

Δσ2=q(I3)2

Substitute 60kN/m2 for q and 0.2385 for (I3)2.

Δσ2=60×0.2385=14.31kN/m2

Rectangle 3:

Find the value of m3 using the relation:

m3=B3z

Substitute 8 m for B3 and 4 m for z.

m3=84=2

Find the value of n3 using the relation:

n3=L3z

Substitute 8 m for L3 and 4 m for z.

n3=84=2

Refer Figure 8.16 “Variation of I3 with m and n” in the textbook.

For m3=2 and n3=2;

The value of variation (I3)3 is 0.2325.

Find the increase in vertical stress (Δσ3) using the relation:

Δσ3=q(I3)3

Substitute 60kN/m2 for q and 0.2325 for (I3)3.

Δσ3=60×0.2325=13.95kN/m2

Find the increase in vertical stress (Δσ) at point B using the relation:

Δσ=Δσ1Δσ2+Δσ3

Substitute 14.682kN/m2 for Δσ1, 14.31kN/m2 for Δσ2, and 13.95kN/m2 for Δσ3.

Δσ=14.68214.31+13.95=14.322kN/m2

Therefore, the increase in the vertical stress (Δσ) at point C located at depth of 4 m is 14.322kN/m2_.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
Consider a circularly loaded flexible area on the ground surface. Given: radius of the circular area, R = 3 m; uniformly distributed load, q = 250 kN/m 2.Calculate the vertical stress increase Δσ at a point located 5 m (z) below the ground surface (immediately below the center of the circular area).
The loaded area shown in Fig. 23 applies a uniform pressure of 80kPa to the underlying soil. Find the normal vertical stress increase at 4 III below A, B, and C.
Fig 8 shows an embankment load for a silty clay soil layer. Determine the vertical stress increase at points A, B, and C.
Knowledge Booster
Similar questions
    • SEE MORE QUESTIONS
    Recommended textbooks for you
  • Fundamentals of Geotechnical Engineering (MindTap...
    Civil Engineering
    ISBN:9781305635180
    Author:Braja M. Das, Nagaratnam Sivakugan
    Publisher:Cengage Learning
    Principles of Foundation Engineering (MindTap Cou...
    Civil Engineering
    ISBN:9781337705028
    Author:Braja M. Das, Nagaratnam Sivakugan
    Publisher:Cengage Learning
    Principles of Geotechnical Engineering (MindTap C...
    Civil Engineering
    ISBN:9781305970939
    Author:Braja M. Das, Khaled Sobhan
    Publisher:Cengage Learning
  • Fundamentals of Geotechnical Engineering (MindTap...
    Civil Engineering
    ISBN:9781305635180
    Author:Braja M. Das, Nagaratnam Sivakugan
    Publisher:Cengage Learning
    Principles of Foundation Engineering (MindTap Cou...
    Civil Engineering
    ISBN:9781337705028
    Author:Braja M. Das, Nagaratnam Sivakugan
    Publisher:Cengage Learning
    Principles of Geotechnical Engineering (MindTap C...
    Civil Engineering
    ISBN:9781305970939
    Author:Braja M. Das, Khaled Sobhan
    Publisher:Cengage Learning