Find the factor of safety against overturning, sliding, and bearing capacity.
Answer to Problem 17.1P
The factor of safety against overturning is
The factor of safety against sliding is
The factor of safety against bearing capacity failure is
Explanation of Solution
Given information:
The frictional angle of backfill
Unit weight of backfill
The backfill makes an angle of
Unit weight of concrete is
Calculation:
Calculate the weight and moment arms by dividing the retaining wall and soil regions interest into rectangles and triangles.
Show the rectangles and triangles divided in the structure as in Figure 1.
Refer Table 16.3, “Values of
The value of active earth pressure
From Figure 1.
The total height from base is
Find the total force per unit length of the wall
Substitute
Find the horizontal force
Substitute
Find the vertical force
Substitute
Find the weight and moment about C for the sections as in Table 1.
Section |
Weight |
Moment arm from C (m) |
Moment about C |
1 | 1 | 108 | |
2 | 1.75 | 126 | |
3 | 2.67 | 384.5 | |
4 | 3.33 | 369.6 | |
5 | 3.33 | 33.3 | |
4 | 121.6 | ||
Analyze the stability with respect to overturning:
Find the overturning moment
Substitute
From Table 1, the value of resisting moment is
Find the factor of safety against overturning using the relation:
Substitute
Therefore, the factor of safety against overturning is
Find the passive earth pressure coefficient
Substitute
Find the passive force
Here, D is the depth of retaining wall below the soil.
Substitute
Find the value of
Substitute
Find the factor of safety against sliding using the relation:
Substitute
Therefore, the factor of safety against sliding is
Analyze the stability with respect to bearing capacity failure:
Find the eccentricity (e) of the resulting force using the relation:
Here, B is the base width of the retaining wall.
Substitute 4 m for B,
The value of
The calculated eccentricity value is less than the value of
Find the maximum value of pressure at
Substitute
Find the ultimate bearing capacity
Find the value of
Substitute
Find the value of
Substitute 4 m for B and 0.116 m for e.
Refer Table 6.2, “Bearing capacity factors” in the textbook.
The value of
Find the depth factor
Substitute
For
Find the inclination of load on the foundation with respect to vertical
Substitute
Find the inclination factor
Substitute
Find the inclination factor
Substitute
Substitute
Find the factor of safety against bearing capacity failure using the relation:
Substitute
Therefore, the factor of safety against bearing capacity failure is
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Chapter 17 Solutions
Principles of Foundation Engineering (MindTap Course List)
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