Find the factors of safety with respect to overturning, sliding, and bearing capacity failure.
Answer to Problem 15.4P
The factor of safety with respect to overturning is
The factor of safety with respect to sliding is
The factor of safety with respect to bearing capacity failure is
Explanation of Solution
Given information:
The cohesion
The unit weight
The friction angle
The unit weight
The cohesion
The unit weight of soil
The friction angle
The backfill angle
Calculation:
Check stability with respect to overturning.
Consider point C as the left end of the toe base as named as C.
Divide the retaining wall into section as in Figure 1.
Sketch the section of the retaining wall as shown in Figure 1.
Here,
Refer Table 14.2, “Values of
Take the value of active earth pressure coefficient
Refer Figure 1.
Find the height of the inclined portion of backfill
Substitute 2 m for
Find the total height of the inclined backfill
Here, H is the height of retaining wall and D is the depth to the bottom of the base slab.
Substitute 5.0 m for H, 1.0 m for D, and 0.353 m
Find the active earth pressure
Substitute
Find the vertical component of the active earth pressure
Substitute
Find the horizontal component of the active earth pressure
Substitute
Find the weight of section 1
Here,
Substitute 1.5 m for
Find the moment arm or lever arm
Substitute 1.5 m for
Find the moment about point C
Substitute
Find the weight of section 2
Here,
Substitute 0.5 m for
Find the moment arm or lever arm
Substitute 1.5 m for
Find the moment about point C
Substitute
Find the weight of section 3
Here,
Substitute 2.0 m for
Find the moment arm or lever arm
Substitute 0.5 m for
Find the moment about point C
Substitute
Find the weight of section 4
Here,
Substitute 2.0 m for
Find the moment arm or lever arm
Substitute 2.0 m for
Find the moment about point C
Substitute 108 kN/m for
Find the weight of section 5
Substitute 2 m for
Find the moment arm or lever arm
Substitute 2.0 m for
Find the moment about point C
Substitute
Find the moment arm or lever arm
Substitute 0.5 m for
Find the moment about point C
Substitute
Find the total moment about the point C
Substitute
Find the total vertical load
Substitute
Summarize the values of weight, moment arm from C, and moment about C as shown in Table 1.
Section | weight | moment arm from C | moment about C |
1 | 108 | 1 | 108 |
2 | 72 | 1.75 | 126 |
3 | 144 | 2.67 | 384.5 |
4 | 108 | 3.33 | 359.6 |
5 | 6.35 | 3.33 | 21.15 |
4 | 75.56 | ||
Find the overturning moment
Substitute
Find the factor of safety
Substitute
Therefore, the factor of safety with respect to overturning is
Check the stability with respect to sliding.
Find the coefficient of passive earth pressure
Substitute
Find the passive earth pressure
Here,
Substitute 1 m for D,
Find the angle of friction
Substitute
Find the factor of safety against sliding
Substitute
Therefore, the factor of safety with respect to sliding is
Check the stability with bearing capacity failure.
Find the eccentricity (e) using the equation:
Substitute 4 m for B,
Check for eccentricity.
Substitute 0.22 m for e and 4 m for B.
The eccentricity is within the limit. Therefore, there is no tensile stress produced at the end of the steel section.
Find the maximum pressure
Substitute
Find the effective breadth
Substitute 4 m for B and 0.22 m for e.
Refer Table 16.2, “Bearing Capacity Factors” in the textbook.
Take the value of bearing capacity factor,
Take the value of bearing capacity factor,
Take the value of bearing capacity factor,
Find the depth factor
Substitute 1 m for D and 4 m for B.
Find the load (q) due the soil in front of heel using the equation:
Substitute
Find the inclination angle of vertical load
Substitute
Find the inclination factor
Substitute
Find the depth factor
Here,
Substitute
The depth factor
Find the inclination factor
Substitute
Find the ultimate bearing capacity of the shallow foundation
Substitute
Find the factor of safety against bearing capacity failure
Substitute
Therefore, the factor of safety with respect to bearing capacity failure is
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Chapter 15 Solutions
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