Retaining Walls

Learning Objectives

  • Identify common retaining wall systems and the load paths that provide stability.
  • Distinguish active, passive, and at-rest earth-pressure states and the wall movement needed to mobilize them.
  • Apply Rankine and Coulomb earth-pressure models only within clearly stated assumptions.
  • Separate static earth pressure from seismic, surcharge, and water-pressure effects.
  • Evaluate overturning, sliding, resultant location, eccentricity, and bearing pressure using a consistent design basis.
  • Relate external stability to the structural design and reinforcement of the stem, heel, and toe.
  • Recognize drainage, geotechnical data, and model limitations that can govern retaining-wall safety.

Retaining Wall Function and Types

Retaining walls restrain soil or other retained material where a stable natural slope cannot be accommodated. Common systems include gravity walls, reinforced-concrete cantilever walls, counterfort walls, and buttressed walls. A cantilever wall uses its reinforced stem and base slab together with the self-weight of concrete and, commonly, the weight of soil over the heel to resist lateral actions.

Common Retaining Wall Systems

  • Gravity wall: relies primarily on its mass for stability and is typically suited to relatively low walls.
  • Cantilever wall: uses a reinforced-concrete stem, toe, and heel; soil over the heel contributes stabilizing vertical load when that load is reliable in the selected design combination.
  • Counterfort wall: uses webs on the backfill side to tie the stem and base and reduce bending demands in taller walls.
  • Buttressed wall: uses braces on the exposed side; the structural concept is similar to a counterfort wall but the braces occupy space in front of the wall.

Active Earth Pressure

Active earth pressure is the reduced lateral pressure state approached when a wall moves sufficiently away from the backfill for the soil to mobilize an active limit condition.

Passive Earth Pressure

Passive earth pressure is the high-resistance limit state approached when a wall or embedded element moves into the soil sufficiently to mobilize passive shear resistance.

At-Rest Earth Pressure

At-rest earth pressure is the lateral pressure state for soil that is not permitted to undergo the lateral strain needed to reach the active or passive limit state.

Retaining wall load determination

Choose compatible soil state, add distinct surface and water actions, and keep a consistent service free body.

Retaining wall load determinationChoose compatible soil state, add distinct surface and water actions, and keep a consistent service free body.. Define geometry, stages and soil data → Can wall move enough for active state?; Can wall move enough for active state? — Yes → Choose active Rankine or Coulomb basis; Can wall move enough for active state? — No → Use at-rest or restraint-specific pressure; Choose active Rankine or Coulomb basis → Resolve soil, surcharge and water actions; Use at-rest or restraint-specific pressure → Resolve soil, surcharge and water actions; Resolve soil, surcharge and water actions → Record forces, directions and lever arms

Define geometry, stages and soil data → Can wall move enough for active state?; Can wall move enough for active state? — Yes → Choose active Rankine or Coulomb basis; Can wall move enough for active state? — No → Use at-rest or restraint-specific pressure; Choose active Rankine or Coulomb basis → Resolve soil, surcharge and water actions; Use at-rest or restraint-specific pressure → Resolve soil, surcharge and water actions; Resolve soil, surcharge and water actions → Record forces, directions and lever arms

  • Define geometry, stages and soil data: terminator. Define geometry, stages and soil data
  • Can wall move enough for active state?: decision. Can wall move enough for active state?
  • Choose active Rankine or Coulomb basis: process. Only if outward movement and model assumptions are justified
  • Use at-rest or restraint-specific pressure: process. Account for restraint and compaction effects
  • Resolve soil, surcharge and water actions: process. Resolve soil, surcharge and water actions
  • Record forces, directions and lever arms: document. Record forces, directions and lever arms

Earth-Pressure State Depends on Wall Movement

The pressure coefficient is not selected only from soil type. A flexible cantilever wall that can yield away from the backfill may develop active conditions, while a rigidly braced basement wall may remain near at-rest conditions. Passive resistance usually requires substantially more movement than active pressure, so its dependable contribution to sliding resistance must be justified by soil conditions, geometry, embedment, displacement compatibility, and the selected design framework.

Rankine Active Pressure Model Used in This Lesson

The simplified Rankine active model used here assumes a vertical smooth wall, level homogeneous cohesionless backfill, drained conditions, no wall friction, and sufficient wall movement to mobilize the active state.

Rankine Active Earth Pressure Coefficient

Simplified coefficient for the level, cohesionless, smooth-wall active case used in this lesson.

Ka=1−sin⁡ϕ1+sin⁡ϕK_a=\frac{1-\sin\phi}{1+\sin\phi}

Variables

SymbolDescriptionUnit
KaK_aRankine active earth-pressure coefficient for the stated assumptions-
ϕ\phiEffective angle of internal friction of the backfill∘^\circ

Static Active Thrust from Soil Self-Weight

Resultant of the triangular active-pressure distribution for dry or drained cohesionless backfill under the stated Rankine assumptions.

Pa,γ=12KaγH2P_{a,\gamma}=\frac{1}{2}K_a\gamma H^2

Variables

SymbolDescriptionUnit
Pa,γP_{a,\gamma}Static active thrust due to backfill self-weightkN/m\text{kN}/\text{m}
γ\gammaAppropriate soil unit weight for the stated drainage conditionkN/m3\text{kN}/\text{m}^3
HHRetained height represented by the pressure diagramm\text{m}

Rankine and Coulomb Are Different Models, Not Interchangeable Coefficients

The simplified Rankine expression above does not include wall friction and is tied to its wall and backfill geometry assumptions. Coulomb theory instead uses limit equilibrium of a potential soil wedge and can include wall friction, wall batter, and backfill slope through a consistent angle convention. Both are limit-state idealizations and both require compatible soil parameters, drainage assumptions, and sufficient wall movement.

For a common active case with positive wall friction on a wall that moves away from the backfill, Coulomb thrust on the wall can have a downward component. Under the vertical-wall angle convention used in the worked example, PH=Pacos⁡δP_H=P_a\cos\delta and the downward component is PV=Pasin⁡δP_V=P_a\sin\delta. That effect must not be borrowed into a Rankine calculation unless the chosen model explicitly includes it. Likewise, Coulomb is not automatically “less conservative” for every geometry, and passive resistance is especially sensitive to assumed wall friction and movement.

Coulomb Active Coefficient for the Vertical-Wall Convention Used Here

Worked-example form for a vertical wall retaining homogeneous cohesionless drained backfill with surface slope beta and wall friction delta; use only with the stated angle convention.

Ka=cos⁡2ϕcos⁡δ[1+sin⁡(ϕ+δ)sin⁡(ϕ−β)cos⁡δcos⁡β]2K_a=\frac{\cos^2\phi}{\cos\delta\left[1+\sqrt{\frac{\sin(\phi+\delta)\sin(\phi-\beta)}{\cos\delta\cos\beta}}\right]^2}

Variables

SymbolDescriptionUnit
KaK_aCoulomb active coefficient for this vertical-wall convention-
ϕ\phiEffective backfill friction angle∘^\circ
δ\deltaWall-soil interface friction angle using the stated active sign convention∘^\circ
β\betaBackfill surface slope above horizontal in this convention∘^\circ

Cohesion and Layered Backfill Require Additional Judgment

The simple equations in this lesson are for homogeneous cohesionless material. Cohesive soils, layered backfills, compaction-induced pressures, expansive soils, sloping groundwater surfaces, stratified unit weights, and nonuniform surcharges require a model appropriate to those conditions. Do not insert an apparent cohesion into a simple sand formula without considering tension cracks, drainage, long-term effective stress, and the governing geotechnical design basis.

Uniform Surcharge

A uniform surcharge qq is an additional surface pressure behind the wall that produces a lateral pressure increment when transferred through the selected earth-pressure model.

Lateral Thrust from a Uniform Surcharge

Rectangular lateral-pressure increment under the simplified active model used in this lesson.

Pa,q=KaqHP_{a,q}=K_a qH

Variables

SymbolDescriptionUnit
Pa,qP_{a,q}Resultant lateral thrust caused by a uniform surchargekN/m\text{kN}/\text{m}
qqUniform surface surchargekPa\text{kPa}
HHRetained heightm\text{m}

Hydrostatic Pressure

Hydrostatic pressure is lateral water pressure caused by a water head and acts independently of the effective-stress earth-pressure component of the soil skeleton.

Hydrostatic Resultant

Resultant water thrust for a triangular hydrostatic pressure distribution over water depth Hw.

Pw=12γwHw2P_w=\frac{1}{2}\gamma_w H_w^2

Variables

SymbolDescriptionUnit
PwP_wHydrostatic resultant per meter length of wallkN/m\text{kN}/\text{m}
γw\gamma_wUnit weight of waterkN/m3\text{kN}/\text{m}^3
HwH_wWater depth behind the wallm\text{m}

Drainage Assumption Must Match the Built Wall

A wall analyzed as drained must have a dependable drainage path, filter compatibility, and maintenance strategy. If water can accumulate, hydrostatic pressure and the appropriate submerged or saturated soil weights must be included rather than assuming that dry active pressure alone governs.

Static Earth Pressure Does Not Cover Seismic Demand

Ordinary static Rankine or Coulomb active-pressure equations do not by themselves represent earthquake-induced earth pressure. A pseudo-static method such as Mononobe-Okabe extends a Coulomb-type wedge model by introducing horizontal and, where applicable, vertical seismic coefficients, but it has its own assumptions and limitations. Seismic wall design must follow the governing seismic and geotechnical provisions for the site, including the required pressure distribution, resultant location, drainage condition, and deformation compatibility.

Traditional Service-Load Stability Format

The stability calculations in this lesson use a traditional service-load factor-of-safety format in which service actions and service resisting forces are compared directly without mixing them with strength-design load factors.

Do Not Mix Stability Design Frameworks

Many teaching examples use service loads with factors of safety such as overturning or sliding ratios, while modern project standards may instead use load-and-resistance-factor or strength-design frameworks with factored actions and geotechnical resistance factors. Use one internally consistent basis. The numerical targets shown in this lesson are illustrative traditional service-load criteria, not universal values for every jurisdiction or load case.

Factor of Safety against Overturning

Traditional service-load ratio of stabilizing to overturning moments about the selected rotation point.

FSOT=∑MR∑MOFS_{OT}=\frac{\sum M_R}{\sum M_O}

Variables

SymbolDescriptionUnit
FSOTFS_{OT}Traditional service-load overturning factor of safety-
∑MR\sum M_RSum of service-load resisting moments about the selected pointkN⋅m/m\text{kN}\cdot\text{m}/\text{m}
∑MO\sum M_OSum of service-load overturning moments about the selected pointkN⋅m/m\text{kN}\cdot\text{m}/\text{m}

Factor of Safety against Sliding

Traditional service-load ratio of dependable horizontal resistance to horizontal driving force.

FSS=FR+Pp,designPHFS_S=\frac{F_R+P_{p,\text{design}}}{P_H}

Variables

SymbolDescriptionUnit
FSSFS_STraditional service-load sliding factor of safety-
FRF_RDependable base-interface resistance, commonly related to the effective vertical force and interface frictionkN/m\text{kN}/\text{m}
Pp,designP_{p,\text{design}}Passive resistance credited on the selected design basiskN/m\text{kN}/\text{m}
PHP_HTotal horizontal driving forcekN/m\text{kN}/\text{m}
External stability

Check service equilibrium, contact and geotechnical acceptance using one un-factored basis.

External stabilityCheck service equilibrium, contact and geotechnical acceptance using one un-factored basis.. Assemble service free body → Sum toe moments and check overturning; Sum toe moments and check overturning → Check sliding with dependable resistance; Check sliding with dependable resistance → Resultant within base?; Resultant within base? — No → Revise wall and ground model; Resultant within base? — Yes → Use full or partial no-tension contact; Use full or partial no-tension contact → Check bearing and settlement

Assemble service free body → Sum toe moments and check overturning; Sum toe moments and check overturning → Check sliding with dependable resistance; Check sliding with dependable resistance → Resultant within base?; Resultant within base? — No → Revise wall and ground model; Resultant within base? — Yes → Use full or partial no-tension contact; Use full or partial no-tension contact → Check bearing and settlement

  • Assemble service free body: terminator. Assemble service free body
  • Sum toe moments and check overturning: process. Sum toe moments and check overturning
  • Check sliding with dependable resistance: process. Check sliding with dependable resistance
  • Resultant within base?: decision. Resultant within base?
  • Use full or partial no-tension contact: process. Use full or partial no-tension contact
  • Revise wall and ground model: process. Revise wall and ground model
  • Check bearing and settlement: terminator. Check bearing and settlement

External Stability Checks

  1. Define one physical geometry. State the retained height, footing thickness, stem thickness, base width, toe, and heel dimensions and use those same dimensions for pressure resultants, weights, lever arms, and the drawing.
  2. Assemble service actions on a consistent basis. Include soil pressure, surcharge, water, self-weight, reliable soil weight over the heel, and any other applicable loads. Separate horizontal and vertical components when the earth-pressure model produces an inclined resultant.
  3. Check overturning about the selected toe or rotation point. The triangular soil thrust acts at one-third of its pressure-diagram height above the base of that triangle; a uniform surcharge component acts at midheight. Add the footing elevation when moments are taken about the bottom of a footing rather than the top.
  4. Check sliding. Use a justified base-interface resistance and only the passive resistance that can be dependably mobilized under the project soil and displacement conditions. A shear key may improve sliding resistance but does not automatically make the wall satisfactory.
  5. Locate the base resultant. For a service vertical resultant ∑V\sum V, the distance from the toe is x=(∑MR−∑MO)/∑Vx=(\sum M_R-\sum M_O)/\sum V when moments use consistent signs and the same reference point.
  6. Check eccentricity and contact. With base width BB, e=B/2−xe=B/2-x. If ∣e∣≤B/6|e|\le B/6, a full-contact linear bearing-pressure distribution is compatible with the middle-third assumption. If the resultant leaves the middle third but remains above the base, replace the full-contact formula with a no-tension triangular contact model. If it leaves the base, the assumed rigid-base equilibrium has no compressive contact solution.
  7. Compare bearing pressure with geotechnical resistance. A no-tension check does not establish adequate bearing capacity; the maximum applicable contact pressure must also satisfy the geotechnical design criterion, and settlement may govern.

Full-Contact Bearing Pressure

Linear service contact pressure for a rectangular base when the resultant remains within the middle third.

qtoe,heel=∑VB(1±6eB),∣e∣≤B6q_{\text{toe,heel}}=\frac{\sum V}{B}\left(1\pm\frac{6e}{B}\right),\qquad |e|\le\frac{B}{6}

Variables

SymbolDescriptionUnit
qtoe,heelq_{\text{toe,heel}}Toe and heel service contact pressures for full contactkPa\text{kPa}
∑V\sum VTotal service vertical force per meter lengthkN/m\text{kN}/\text{m}
BBBase widthm\text{m}
eeResultant eccentricity from the base centerlinem\text{m}

No-Tension Partial-Contact Pressure

Rigid-base triangular compression when the service resultant remains over the base but outside the middle third.

c=3min⁡(x,B−x),qmax⁡=2∑Vcc=3\min(x,B-x),\qquad q_{\max}=\frac{2\sum V}{c}

Variables

SymbolDescriptionUnit
cccompressed contact length measured from the loaded base edgem\text{m}
xxservice resultant distance from toem\text{m}
BBbase widthm\text{m}
qmax⁡q_{\max}maximum triangular service contact pressurekPa\text{kPa}

Partial Contact Is a State, Not an Acceptance

When B/6<∣e∣<B/2B/6<|e|<B/2, a simple rigid no-tension triangle can estimate compressive pressure but rotation, settlement, foundation stiffness, and project-specific acceptance still require geotechnical evaluation. A resultant outside the base is not rescued by this formula.

Shared Service-Action Scenario Model

Both explorers use one deterministic per-metre wall model. Rankine is available only for level smooth backfill; the vertical-wall Coulomb case permits a slope smaller than the friction angle and a separately selected wall friction angle. The Rankine scenario can add uniform surcharge and a horizontal groundwater table with separate hydrostatic thrust. The Coulomb scenario is dry and unsurcharged so that it does not borrow an unsupported surcharge or effective-stress extension of the wedge coefficient. The groundwater case assumes an 18 kN/m³ total saturated soil unit weight and subtracts 9.81 kN/m³ from the effective-stress soil skeleton below the table. It omits uplift, seepage, pressure in front, compaction, seismic demand, and passive resistance. The service stem, heel, and toe root actions are instructional and must be factored separately for RC design.

Cantilever retaining wall scenario explorer

Concept and model scope

Service actions per metre. Rankine is level and smooth; the Coulomb mode models dry unsurcharged sloped backfill at a vertical wall with downward wall-friction component. Sufficient wall movement is needed for active pressure.

Groundwater uses total saturated weight 18 kN/m³ and submerged effective weight 18 − 9.81 kN/m³. Hydrostatic thrust is separate. Uplift, seepage, front water, compaction, passive resistance, global stability and seismic effects are outside this model.

Traditional service FS targets are illustrative. Stem, heel and toe values are signed service actions; factored RC strength, shear, anchorage and geotechnical capacity require separate checks.

Retained height H4.5 m
Base width B3.0 m
Backfill friction φ30 °
Base friction μ0.5
Uniform surcharge0 kPa
Water height0.0 m
Toe → B 3.0 m; resultant 1.29 m
Kₐ
0.333
Soil thrust
60.8 kN/m
Surcharge thrust
0.0 kN/m
Water thrust
0.0 kN/m
Horizontal thrust
60.8 kN/m
Downward wall friction
0.0 kN/m
FS overturning
3.22 (lesson target 2.0)
FS sliding
1.72 (lesson target 1.5)
Eccentricity
0.209 m
Contact
full
Toe / heel pressure
98.8 / 40.4 kPa

Maximum compressive contact 98.8 kPa. Partial contact uses a no-tension triangular distribution; outside contact has no valid base equilibrium. Bearing resistance and settlement remain separate geotechnical checks.

Signed service root actions (not factored RC design)
Stem M / V
91.1 kN·m/m / 60.8 kN/m
Heel M / V
54.0 kN·m/m / 59.2 kN/m
Toe M / V
40.1 kN·m/m / 77.0 kN/m

No seismic mode: site coefficients, pressure distribution and displacement compatibility require a separate project basis. Reinforcement and wall dimensions shown are conceptual.

3D Stability Studio: Soil–Structure Load Path and Base Contact

Shared 2D and 3D Service-Action Model

The 3D geometry, sloped soil prism, force arrows, resultant, contact distribution, and reinforcement face cues use the same scenario inputs and service resultants as the 2D model. The Rankine scenario handles surcharge and water; the Coulomb scenario remains dry and unsurcharged. The Rankine failure-plane cue is displayed only in the level smooth case. Coulomb wall friction adds a vertical component at the back of the stem; the water pressure remains horizontal. The member root moments are service actions, not factored reinforcement design. Bar lengths, diameters, cover, development, durability, and final bending/shear design are illustrative or excluded.

Cantilever Retaining Wall — 3D Stability & Soil–Structure Cutaway

Concept and model scope

Trace active earth pressure, wall and soil weights, sliding resistance, overturning about the toe, base resultant, contact pressure, and principal RC reinforcement zones using one shared geometry.

Rankine mode is limited to a level smooth wall-backfill interface and can add uniform surcharge plus a horizontal groundwater table with separate hydrostatic thrust. Coulomb mode uses a dry, unsurcharged vertical wall with controlled backfill slope and wall friction. Both use the same wall geometry, γs = 18 kN/m³, γc = 24 kN/m³, a 0.50 m footing, a 0.40 m stem, and toe = B/3.

The teaching model excludes seismic earth pressure, passive resistance, uplift, seepage, water in front of the wall, compaction-induced pressure, global stability, and final RC strength/detailing checks.

The 2.0 overturning and 1.5 sliding values are lesson targets rather than universal code criteria. Bearing arrows use full or partial no-tension contact, and the reinforcement graphics are detailing-location cues rather than a completed RC design.

Displayed traditional service-load lesson targets are satisfied.

Overturning FS ≥ 2.0, sliding FS ≥ 1.5, and the resultant remains within the middle third. These are lesson targets, not universal project acceptance criteria.

Preparing retaining-wall cutaway…

Use the guided sequence to trace the external-stability load path, resultant location, contact-pressure condition, and structural reinforcement zones.

0.0 kPa
0.0 m
4.5 m
3.0 m
30°
0.50

Service structural actions per metre (unfactored)

Stem: 91.1 kN·m/m; heel: 54.0 kN·m/m; toe: 40.1 kN·m/m. Signed heel and toe actions come from net bearing, soil, surcharge and base self-weight; factored combinations, shear and RC detailing are separate.

Soil thrust 60.8, surcharge 0.0, water 0.0 kN/m; horizontal total 60.8 kN/m.

Earth pressure / stability
Ka
0.333
Pa
60.8 kN/m
FS overturning
3.22
FS sliding
1.72
ΣMR
391.0 kN·m/m
ΣMO
121.5 kN·m/m
Resultant / contact
x from toe
1.291 m
e
0.209 m
Middle third
full
ΣV
208.8 kN/m
qtoe
98.8 kPa
qheel
40.4 kPa

Preliminary Proportioning Is Not Design Acceptance

Rules of thumb such as a base width on the order of 0.4H0.4H to 0.7H0.7H, a toe near one-third of the base width, or a footing thickness related to wall height can be useful for a first trial only. Final dimensions must come from stability, geotechnical, structural, drainage, seismic, durability, and constructability checks using the actual project geometry and design basis.

Stem, heel and toe RC design

Separate factored member actions from service foundation checks and detail the verified tension faces.

Stem, heel and toe RC designSeparate factored member actions from service foundation checks and detail the verified tension faces.. Choose structural load combinations → Factored stem lateral shear and bending; Factored stem lateral shear and bending → Net heel and toe factored loads; Net heel and toe factored loads → Check flexure and shear at critical sections; Check flexure and shear at critical sections → Detail bars, cover, development and joints; Detail bars, cover, development and joints → Recheck constructible geometry

Choose structural load combinations → Factored stem lateral shear and bending; Factored stem lateral shear and bending → Net heel and toe factored loads; Net heel and toe factored loads → Check flexure and shear at critical sections; Check flexure and shear at critical sections → Detail bars, cover, development and joints; Detail bars, cover, development and joints → Recheck constructible geometry

  • Choose structural load combinations: terminator. Choose structural load combinations
  • Factored stem lateral shear and bending: process. Factored stem lateral shear and bending
  • Net heel and toe factored loads: process. Net heel and toe factored loads
  • Check flexure and shear at critical sections: process. Check flexure and shear at critical sections
  • Detail bars, cover, development and joints: process. Detail bars, cover, development and joints
  • Recheck constructible geometry: terminator. Recheck constructible geometry

Structural Design of Stem, Heel, and Toe

After the external stability model is established, reinforced-concrete component design uses the factored load combinations required by the governing structural code. The stem behaves primarily as a vertical cantilever under lateral pressure, with principal vertical tension steel generally on the soil face for the usual active-pressure direction. The heel and toe are horizontal cantilevers subjected to net factored pressure distributions, not simply one isolated load component.

For the usual cantilever-wall load pattern, the heel often requires top main reinforcement and the toe often requires bottom main reinforcement, but the sign of net bending must be verified from the actual upward bearing and downward dead/surcharge loads. Development length, anchorage into the stem/base joint, minimum distributed steel, shear, cover, durability, and construction joints must also be checked.

Integrated wall design iteration

Iterate geometry, external stability, RC design and drainage as a coupled wall design.

Integrated wall design iterationIterate geometry, external stability, RC design and drainage as a coupled wall design.. Trial wall and ground assumptions → Run external stability and contact checks; Run external stability and contact checks → Design stem, heel and toe; Design stem, heel and toe → All applicable checks and details pass?; All applicable checks and details pass? — Yes → Document verified design basis; All applicable checks and details pass? — No → Revise dimensions or drainage; Revise dimensions or drainage → Run external stability and contact checks

Trial wall and ground assumptions → Run external stability and contact checks; Run external stability and contact checks → Design stem, heel and toe; Design stem, heel and toe → All applicable checks and details pass?; All applicable checks and details pass? — Yes → Document verified design basis; All applicable checks and details pass? — No → Revise dimensions or drainage; Revise dimensions or drainage → Run external stability and contact checks

  • Trial wall and ground assumptions: terminator. Trial wall and ground assumptions
  • Run external stability and contact checks: process. Run external stability and contact checks
  • Design stem, heel and toe: process. Design stem, heel and toe
  • All applicable checks and details pass?: decision. All applicable checks and details pass?
  • Revise dimensions or drainage: process. Revise dimensions or drainage
  • Document verified design basis: terminator. Document verified design basis

Factored RC Component Design after Service Stability

  1. Select governing structural load combinations and retain separate dead, surcharge, soil, water, and other applicable action cases; do not multiply a service FS by a strength load factor.
  2. Analyze the stem as a vertical cantilever with factored lateral pressure; check root flexure and shear and verify the compression and tension faces for each combination.
  3. Analyze the heel and toe as horizontal cantilevers using their net factored bearing and downward loads, including self-weight and soil or surcharge above the heel; reverse reinforcement faces if the moment sign reverses.
  4. Size the stem and base for flexure and one-way shear with the governing material and code edition; check minimum and distributed reinforcement.
  5. Detail bar development through the stem-base joint, cover, spacing, cutoff, construction joints, drainage penetrations, durability, and a buildable sequence.
  6. Recompute all service and strength actions after changing dimensions, water assumptions, or reinforcement arrangement.

Drainage and Constructability

Typical drainage details include free-draining granular zones, geotextile filters selected to prevent soil migration, perforated collector drains with positive outlets, and weep holes where appropriate. Drainage details must remain maintainable and must not discharge where erosion or icing creates another hazard. A clogged drain can invalidate the drained design assumption even when the concrete reinforcement itself is adequate.

Key Takeaways
  • Active, passive, and at-rest pressures are different soil states governed by wall movement; they are not interchangeable coefficients.
  • The simple Rankine KaK_a equation in this lesson assumes a smooth vertical wall, level homogeneous cohesionless backfill, drained conditions, and sufficient movement to mobilize active pressure.
  • Coulomb is a different wedge-equilibrium model that can include wall friction, wall batter, and backfill slope; neither method should be treated as a universal black box.
  • Static earth-pressure equations do not automatically include seismic demand, surcharge, or hydrostatic pressure; each additional action must be modeled explicitly on a compatible basis.
  • Traditional service-load factors of safety and factored strength/LRFD approaches must not be mixed within the same stability calculation.
  • Base width changes the wall weights, lever arms, resultant, eccentricity, and bearing distribution, so geometry must be propagated through every downstream calculation.
  • Full or partial contact must be modeled without tensile soil pressure; adequate bearing resistance and settlement still require geotechnical verification.
  • Drainage assumptions are structural assumptions because trapped water can add a large lateral load that was absent from a drained-wall model.

References