24.1 Lateral Earth/Water Pressure and Drainage

A retaining wall responds to soil, surcharge, and water, but those loads do not all use the same coefficient or pressure diagram. For July 2026, use the April 2024 PE Civil: Structural specification, current PE Civil Reference Handbook, AASHTO LRFD Bridge Design Specifications 8th edition with the listed May 2018 errata, and IBC 2018. Do not import April 2027 editions.

Select the Pressure State From Movement

Active pressure develops only after the wall moves sufficiently away from retained soil. Passive pressure develops when the wall moves into soil and usually requires much larger movement. At-rest pressure applies where lateral strain is restrained, such as a basement wall tied into stiff floors, or where movement is insufficient to mobilize active conditions.

For level, cohesionless backfill under the ideal Rankine assumptions,

K_a = (1 - sin φ)/(1 + sin φ)

K_p = (1 + sin φ)/(1 - sin φ)

For φ = 30°, K_a = 1/3 and K_p = 3. These reciprocal values do not mean passive resistance is automatically available. Soil in front of a toe can be excavated, disturbed, frozen, scoured, or too shallow to mobilize the assumed resistance. At-rest K_0 follows the applicable geotechnical model or problem data; do not replace it with K_a because the smaller number is convenient.

Cohesion, wall friction, sloping backfill, seismic effects, compaction, and non-Rankine geometry require the controlling method rather than these simple expressions. Long-term permanent-wall design often neglects apparent cohesion unless specifically justified.

Build the Pressure Diagram

For drained cohesionless soil, horizontal effective pressure can be written

σ'_h = Kσ'_v

where σ'_v includes the effective weight of all soil above the point. In layered soil, calculate vertical stress continuously through each layer, then apply the coefficient appropriate to the layer and interface assumptions. Do not draw an independent triangle beginning at zero at every layer boundary; the overburden from upper layers remains. Abrupt changes in K can create pressure jumps, while changes in unit weight alter the slope. Integrate each segment for force and moment.

A uniform surface surcharge q commonly contributes constant lateral pressure Kq over wall height, producing a rectangular diagram. A strip, line, footing, or traffic surcharge has a different distribution and must use the method stated by the problem or AASHTO. Compaction equipment can create temporary pressure exceeding the final static case.

Water Is a Separate Load

Hydrostatic pressure varies as

u = γ_w z

For water depth H_w, resultant per foot of wall is

P_w = (1/2)γ_wH_w^2

acting H_w/3 above the bottom. Below groundwater, soil effective stress uses submerged or buoyant unit weight as appropriate, while pore-water pressure is added separately. Using saturated total unit weight in an effective-stress soil diagram and then adding full water can double count. Conversely, using drained soil properties and omitting water without a reliable drain can be unconservative.

Water can also act beneath a footing as uplift, behind a wall during a storm, or at different elevations on two sides. Rapid drawdown can remove stabilizing water faster than pore pressure dissipates. Use the actual hydraulic boundary and stage.

Worked Soil, Surcharge, and Clogged-Drain Case

A 10 ft wall retains level granular soil. The problem specifies γ = 120 pcf, φ = 30°, active Rankine conditions, and uniform surcharge q = 200 psf. First calculate the drained forces. Then, solely for comparison, the problem instructs that the soil components remain as calculated while a clogged drain creates a full-height hydrostatic load using γ_w = 62.4 pcf.

K_a = 1/3

Soil force:

P_a = (1/2)K_aγH^2 = (1/2)(1/3)(120)(10^2) = 2,000 lb/ft = 2.00 kip/ft

It acts at H/3 = 3.333 ft above the base.

Surcharge force:

P_q = K_aqH = (1/3)(200)(10) = 667 lb/ft = 0.667 kip/ft

It acts at H/2 = 5.0 ft.

Clogged-drain water force:

P_w = (1/2)(62.4)(10^2) = 3,120 lb/ft = 3.12 kip/ft

It acts 3.333 ft above the base. Total lateral force becomes 2.00 + 0.667 + 3.12 = 5.787 kip/ft. Base moment is

M = 2.00(3.333) + 0.667(5.0) + 3.12(3.333) = 20.4 kip-ft/ft

Without water, moment is only 10.0 kip-ft/ft. The simplified comparison shows why a drainage assumption is structurally significant; a real saturated-soil calculation must also update effective unit weights consistently.

Drainage Is a Designed System

A drainage blanket or free-draining backfill needs a filter compatible with retained soil so fines do not clog it. Perforated drains need slope, outlets, cleanouts, and protection from crushing or freezing. Weep holes need a functioning path and safe discharge. Surface grading and caps limit infiltration; waterproofing protects occupied space but does not by itself relieve pressure. Redundant or maintainable outlets matter where blockage is credible.

Exam Workflow

1. Establish wall movement and select active, at-rest, or passive conditions.
2. Draw soil layers, groundwater, drainage, surcharge, and stages.
3. Calculate continuous effective vertical stress and lateral soil pressure.
4. Add water separately with a consistent stress basis.
5. Integrate force and moment segment by segment.
6. Carry the load into wall and stability checks.

A pressure answer is incomplete until its state, drainage assumption, resultant, and lever arm are labeled.

Lateral pressure also acts near wall returns and corners; three-dimensional restraint can change local demand, so a per-foot two-dimensional result applies only where the actual geometry supports that idealization.