Find the Rankine active force
Answer to Problem 13.19P
The Rankine active force
The location
Explanation of Solution
Given information:
The height (H) of the retaining wall is 12 m.
The depth
The unit weight
The sand friction angle
The cohesion
The surcharge pressure (q) is
The depth
The saturated unit weight
The saturated sand friction angle
The cohesion
Calculation:
For sand:
Determine the active earth pressure coefficient
Substitute
For saturated sand:
Determine the active earth pressure coefficient
Substitute
Determine the total stress
Substitute
Determine the pore water pressure at 0 m depth using the relation.
Here,
Take the unit weight of the water as
Substitute
Determine the effective active earth pressure
Substitute
Determine the total stress (sand)
Substitute
Determine the total stress (saturated sand)
Substitute
Determine the pore water pressure at 3.0 m depth using the relation.
Substitute
Determine the effective active earth pressure (sand)
Substitute
Determine the effective active earth pressure (saturated sand)
Substitute
Determine the total stress
Substitute
Determine the pore water pressure at 8 m depth using the relation.
Substitute
Determine the effective active earth pressure
Substitute
Show the variation of effective active earth pressure and pore water pressure for the respective depth as in Figure 1.
Refer Figure 1.
Determine the active earth pressure per unit length for area 1 using the relation.
Here, b is the width and h is the depth.
Substitute
Determine the active earth pressure per unit length for area 2 using the relation.
Substitute
Determine the active earth pressure per unit length for area 3 using the relation.
Substitute 8.0 m for b and
Determine the active earth pressure per unit length for area 4 using the relation.
Substitute 8.0 m for b and
Determine the active earth pressure per unit length for area 5 using the relation.
Substitute 8.0 m for b and
Determine the Rankine active force
Substitute
Thus, the Rankine active force
Determine the location
Substitute
Thus, the location of the resultant force is
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Chapter 13 Solutions
MindTap Engineering for Das/Sobhan's Principles of Geotechnical Engineering, SI Edition, 9th Edition, [Instant Access], 2 terms (12 months)
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