PE-15-Lateral-Stresses

# PE-15-Lateral-Stresses - 15 Lateral Stresses 01 A simple...

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15 - Lateral Stresses 01: A simple wall subject to an active earth pressure. 02: Compare the Rankine and Coulomb coefficients. 03: Passive pressures using the Rankine theory. 04: At rest pressures upon an unyielding wall. 05: Cohesive effects upon a Rankine analysis. 06: Effects of a rising WT upon the stability of a wall. 07: The effects of a wall with friction. 08: What happens when the lower stratum is stronger? 09: Strata with different parameters. 10: The effect of a surface clay stratum. 11: Anchoring to help support a wall. 12: The effect of five strata upon a wall. 13: Stability of a reinforced concrete wall. 14: Derivation of a formula for σ H as a function of σ V . 300

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375 *Answers for Lateral-Quiz-01: What are four possible rigid wall failures? (Revision: March-2009) Solution: (a) The wall fails by sliding towards the left a distance x (sliding failure). (b) The wall rotates either about its toe, or about the footing centroid (rotational failure). (c) A deep slip plane fails and carries the entire wall and backfill (deep-seated failure). (d) An under-reinforced stem wall cracks and corrosion accelerates the failure.
375 *Answers for Lateral-Quiz-02: What are five possible flexible wall failures? (Revision: March-2009) Solution: (a) A deep slip surface fails and carries the entire wall and backfill (deep-seated failure). (b) The foot of the wall is insufficiently embedded into the soil, and it fails by rotating around the anchor rod (at the level of the waler). (c) The wall is cantilevered (not anchored) and insufficiently embedded, and thus fails by rotating about the foot at the ground level. (d) The tie-rod fails (either because it was improperly designed, corrosion, etc), which leads to a failure of the top of the anchored wall. (e) The sheet-pile wall buckles (due to a low section modulus, low material strength, etc).

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*Answers for Lateral-Quiz-03: What are the three differences between the Rankine and Coulomb analyses? (Revision: March-2009) Solution: William Rankine took Charles Coulomb’s analysis, and simplified it through three assumptions, which can be summarized through the three angles that he set to zero: (1) The backfill was assumed horizontal. That is, the angle α = 0; (2) There is no friction between the wall and the backfill soil. That means that the angle δ = 0; (3) The backfill side of the retaining wall is vertical. That is, the angle θ = 0.
*Lateral-01: A simple wall subjected to an active pressure condition. (Revision: Feb-2009) Consider a small 10-foot tall and 3 feet thick concrete retaining wall. The backfill behind the wall will be from local sandy gravel with a dry unit weight of 115 pcf and an angle of internal friction of 30 degrees. The wall will not have to retain water. Estimate, (a) the lateral force on the wall from the backfill in an active pressure condition, (b) its stability against overturning, and (c) its stability against sliding (use a Factor of Safety 2).

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PE-15-Lateral-Stresses - 15 Lateral Stresses 01 A simple...

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