PE Geotechnical Retaining Wall Design Problems: Cantilever, Anchored, MSE
Cantilever stability checks, anchored-bulkhead free-earth-support, and MSE wall external + internal stability for the PE Geotechnical exam — with three worked NCEES-style problems and the FoS reference table.
Three retaining-wall types appear on the PE Civil Geotechnical exam, and they fail differently. Cantilever walls fail by sliding, overturning, or bearing-capacity exceedance — you check three force/moment equations in sequence. Anchored bulkheads (sheet-pile walls with a tieback) fail by under-penetration: too little embedment depth and the wall rotates about the anchor. Mechanically Stabilized Earth (MSE) walls fail in two distinct modes: external (the entire reinforced block slides or tips) and internal (the reinforcement strips break in tension or pull out). Three wall types, three different design checklists. Pick the wrong checks for the wall in front of you and the answer is wrong before any arithmetic.
The good news: every check is a closed-form formula, every formula is reproduced in the NCEES PE Civil Reference Handbook (§3.1, Lateral Earth Pressures), and the factor-of-safety thresholds (sliding 1.5, overturning 2.0, bearing 3.0) are standard across NAVFAC DM-7.02 and FHWA NHI-06-088 / NHI-06-089. The skill the exam tests is recognizing which wall type the problem describes, then running the right sequence of checks in the right order.
This post walks through the three wall types with one fully solved worked example each — a cantilever wall stability check, an anchored bulkhead free-earth-support calculation, and an MSE wall combining external and internal checks. For the underlying earth-pressure theory (which feeds every calculation in this post), see our lateral earth pressure: Coulomb vs Rankine vs at-rest post.
Why retaining-wall design dominates the exam
Per the April 2024 NCEES PE Civil Geotechnical specification, Topic 8 (Retaining Structures, ASD or LRFD) carries 10–15 questions out of 80 — the highest-weight topic on the exam. Lateral earth pressure is the upstream input; design checks (this post) are downstream where most of the calculation happens. Combined, Topic 8 is roughly an eighth of a passing score, and design problems are the calc-heavy fraction inside it.
Core concepts you must master
The four cantilever-wall stability checks
For a cantilever (gravity or reinforced-concrete) wall, four checks are required (handbook §3.1, Lateral Earth Pressures; FHWA NHI-06-089):
- Sliding: FoS = (resisting friction + passive toe) / driving horizontal force ≥ 1.5
- Overturning: FoS = resisting moment about toe / overturning moment about toe ≥ 2.0
- Bearing capacity: FoS = qult / qmax ≥ 3.0 (Terzaghi/Meyerhof)
- Foundation settlement: elastic + consolidation settlement within tolerance (typically ≤ 1–2 in for residential structures, ≤ 25 mm for highway walls per FHWA)
The eccentricity check goes with bearing capacity: |e| ≤ B/6 keeps the resultant inside the middle third of the footing and avoids tension on the heel.
Anchored bulkhead: free-earth-support method
For a sheet-pile wall with a single tieback near the top, the free-earth-support method assumes the toe is free to rotate (no fixity) and finds the embedment depth D by setting the moment about the tie rod equal to zero:
where Pa is the active force on the back of the wall over the full length (H + D) and Pp is the passive force on the front over the embedded depth D. The "moment arms" are the distances from the tie rod to the force resultants. Solve for Dtheoretical, then design with Ddesign = 1.2 to 1.4 × Dtheoretical (a typical FoS of 1.3 covers uncertainty in Kp). The tie-rod force T follows from horizontal equilibrium: T = Pa − Pp.
MSE wall: external + internal stability
An MSE wall is a reinforced soil mass (galvanized steel strips, geogrids, or geosynthetic straps in a granular fill) faced with concrete panels or modular blocks. Two stability families:
- External: treat the entire reinforced block as a rigid gravity wall. Run sliding, overturning, and bearing checks against the retained earth pressure pushing on the back of the block.
- Internal: at each reinforcement layer, check (a) tensile capacity — the strip strength must exceed the applied tension with FoS ≥ 1.5; and (b) pullout resistance — the embedded length beyond the active wedge must develop enough friction to resist pullout, typically Pr = F* · α · σv · Le · C · Rc (the standard FHWA MSE pullout formulation).
Worked example: cantilever wall full stability check
Worked example 1 — cantilever wall. A reinforced-concrete cantilever wall has stem height 12 ft, stem thickness 1.5 ft, footing thickness 1.5 ft, heel projection 6 ft, toe projection 3 ft (total footing width B = 10.5 ft). Backfill is cohesionless: γ = 120 pcf, φ = 32°, c = 0, level surface, no surcharge. Foundation soil has the same parameters. Concrete unit weight = 150 pcf. Base interface friction angle δb = (2/3)·φ = 21.3°. Check sliding, overturning, eccentricity, and bearing capacity. Neglect passive toe resistance (conservative).
Step 1 — Active force. Rankine (vertical wall, level fill, no wall friction):
Total height for pressure (top of footing-base): H = 12 + 1.5 = 13.5 ft
Pa = ½·Ka·γ·H2 = 0.5 · 0.307 · 120 · 13.52 = 3,360 lb/ft
Acts horizontal at H/3 = 4.5 ft from base.
Step 2 — Vertical loads (per foot of wall).
Footing (10.5 × 1.5 × 150) = 2,363 lb/ft at x = 5.25 ft
Soil on heel (6 × 12 × 120) = 8,640 lb/ft at x = 7.50 ft
ΣV = 2,700 + 2,363 + 8,640 = 13,703 lb/ft
Step 3 — Moments about toe.
ΣMOT = 3,360 · 4.5 = 15,120 lb·ft/ft
Step 4 — Stability checks.
FoSsliding = (ΣV·tan δb) / Pa = (13,703 · 0.390) / 3,360 = 5,344 / 3,360 = 1.59 ≥ 1.5 ✓
Step 5 — Eccentricity and bearing.
e = B/2 − xR = 5.25 − 5.27 = −0.02 ft → |e| ≪ B/6 = 1.75 ft ✓
qavg = ΣV/B = 13,703/10.5 = 1,305 psf
With e ≈ 0, pressure essentially uniform. Meyerhof bearing capacity (φ=32°, Df=1.5 ft, Nq=23.18, Nγ=22.02):
qult = 180·23.18 + ½·120·10.5·22.02 = 4,172 + 13,873 = 18,045 psf
FoSbearing = 18,045 / 1,305 = 13.8 ≥ 3.0 ✓
Answer: All four checks pass. FoSOT = 5.78, FoSsliding = 1.59, FoSbearing = 13.8, eccentricity within middle third. Sliding is the governing check (closest to its FoS threshold) — typical for cantilever walls. If sliding had failed, you'd add a base key, increase the footing width, or include passive toe resistance in the resisting force.
Worked example: anchored bulkhead free-earth-support
Worked example 2 — anchored sheet-pile bulkhead. A sheet-pile wall retains 16 ft of sandy soil with a single tieback at depth a = 4 ft below the top. Soil: γ = 110 pcf, φ = 30°, c = 0, no water table. Find the theoretical embedment depth D by free-earth-support, the design embedment with FoS = 1.3 on Kp, and the tie-rod force.
Step 1 — Earth-pressure coefficients.
Kp = 1/Ka = 3.0
Step 2 — Set up moment equilibrium about the tie rod (active drives, passive resists).
arma from tie rod = (2/3)(H+D) − a = (2/3)(16+D) − 4
Pp = ½·Kp·γ·D2 = ½·3·110·D2 = 165·D2
armp from tie rod = H + (2/3)D − a = 16 + (2/3)D − 4 = 12 + (2/3)D
Step 3 — Solve Pa·arma = Pp·armp by trial. Try D = 6 ft:
Pa·arma = 8,872 · 10.67 = 94,665 lb·ft/ft
Pp = 165·36 = 5,940 lb/ft; armp = 12 + 4 = 16 ft
Pp·armp = 5,940 · 16 = 95,040 lb·ft/ft
Difference: 95,040 − 94,665 = 375 (≈ 0.4%) → Dtheoretical ≈ 6.0 ft
Step 4 — Design embedment and tie-rod force.
Tie-rod force (horizontal equilibrium at D=6): T = Pa − Pp = 8,872 − 5,940 = 2,930 lb/ft
Answer: Use D = 8 ft of embedment (theoretical 6.0 ft × 1.3 FoS), tie-rod force T ≈ 2,930 lb/ft of wall. Common errors: forgetting to apply the FoS on D (or applying it on Kp = 2.3 instead, which gives roughly the same answer); confusing the moment-arm sign convention; placing the tie rod too low so arma < 0.
Worked example: MSE wall external + internal stability
Worked example 3 — MSE wall (steel-strip reinforcement). A 20-ft MSE wall has reinforcement length L = 14 ft (= 0.7H), reinforced backfill γr = 130 pcf, φr = 34°. Retained backfill behind the reinforced zone: γb = 120 pcf, φb = 30°. Foundation soil φf = 32°, γf = 120 pcf. Reinforcement: galvanized steel strips, vertical spacing sv = 2.5 ft, allowable tensile Tallow = 5,000 lb/ft. Run external stability and check tensile capacity at the bottom layer.
Step 1 — External: active force from retained backfill.
Pa = ½·0.333·120·202 = 7,992 lb/ft at H/3 = 6.67 ft from base
Step 2 — Reinforced block weight + sliding.
Base friction (use min(φr, φf) = 32°): Ffric = 36,400·tan 32° = 36,400·0.625 = 22,747 lb/ft
FoSsliding = 22,747 / 7,992 = 2.85 ≥ 1.5 ✓
Step 3 — External: overturning about toe.
MOT = Pa·H/3 = 7,992 · 6.67 = 53,294 lb·ft/ft
FoSOT = 254,800 / 53,294 = 4.78 ≥ 2.0 ✓
Step 4 — External: bearing.
|e| = 1.46 < L/6 = 2.33 ✓; effective width B′ = L − 2|e| = 14 − 2.92 = 11.08 ft
q′ = W/B′ = 36,400/11.08 = 3,287 psf
Foundation bearing (Meyerhof, φf=32°, Df=0): qult = ½·120·11.08·22.02 = 14,635 psf
FoSbearing = 14,635/3,287 = 4.45 ≥ 3.0 ✓
Step 5 — Internal: tensile capacity at the bottom reinforcement layer (z = 20 ft).
σh(z = 20) = Ka,r·γr·z = 0.283·130·20 = 736 psf
Tmax per layer = σh·sv = 736 · 2.5 = 1,840 lb/ft
Allowable: Tallow / FoS = 5,000 / 1.5 = 3,333 lb/ft → Tmax < allowable ✓
Answer: External stability passes (FoSsliding=2.85, FoSOT=4.78, FoSbearing=4.45). Tensile capacity at the bottom layer passes with margin (Tmax=1,840 vs. allowable 3,333). Pullout is checked separately at each layer using Pr = F*·α·σv·Le·C·Rc (the standard FHWA MSE pullout formulation) — for steel strips with F* = 0.4 at depth, the bottom layer has Le ≈ 14 ft (entire reinforcement is in the resistance zone since the active wedge meets the wall at the base), giving very large pullout margin. Top-layer pullout is the tighter check because Le is shorter and σv is smaller.
Common errors that cost points
Confusing base interface friction with soil friction
The sliding check uses the interface friction angle δb between the base of the wall (concrete or steel) and the underlying soil — typically (1/2)·φ to (2/3)·φ, not the full φ. Using φ directly overestimates sliding resistance by 30–50% and the wall passes a check it should fail.
Forgetting passive resistance for anchored bulkheads
Free-earth-support is a moment balance between active and passive forces about the tie rod. If you forget the passive term entirely (treating the wall like a cantilever sheet pile), the calculated D goes to infinity. Conversely, if you include too much passive resistance — using full Coulomb Kp with high wall friction — you'll under-design the embedment because Coulomb passive overpredicts at large δ. Default to Rankine Kp for anchored bulkhead design unless the question specifies Coulomb.
Mis-applying reinforcement spacing in MSE
Tensile force per linear foot of wall on a single reinforcement layer is T = σh · sv. The horizontal strip-spacing factor enters only when converting to per-strip force for tensile-capacity comparison against the published Tallow of a single strip. Read the units in the spec table: per linear foot of wall vs. per individual strip.
Using the wrong factor of safety
Standard FoS thresholds for retaining-wall design (FHWA / NAVFAC, ASD): sliding 1.5, overturning 2.0, bearing 3.0, MSE pullout 1.5, MSE tensile 1.5, anchored-bulkhead embedment 1.3. Mixing them up is a unit-of-conservatism error that lands you on a wrong-but-plausible answer.
How to study retaining-wall design for the PE Geotechnical exam
Phase 1 — Wall-type identification (Week 1)
Read handbook §3.1 (Lateral Earth Pressures), §3.13 (Geosynthetics), and §3.18 (Earth Retention—Anchored Walls), plus FHWA NHI-06-088/089 sections on cantilever and MSE walls end-to-end. Practice classifying any wall description into cantilever / anchored bulkhead / MSE / braced excavation in under 30 seconds. Each type has its own checklist; the wrong checklist gives the wrong answer.
Phase 2 — Worked-problem drills (Weeks 2–3)
Work twelve problems: four cantilever (vary backfill slope, surcharge, water table), four anchored bulkhead (vary H, soil φ, water table), four MSE (vary L, reinforcement type, foundation soil). Time yourself: four to six minutes per problem. PEwise's Modules 12 and 13 (Advanced Retaining Wall Analysis and Earth Retention — Anchored Walls) cover cantilever, anchored, MSE, and braced wall design with worked NCEES-style stability checks.
Phase 3 — Integration with bearing capacity and lateral earth pressure (Week 4)
Solve five integration problems where you start from backfill conditions, compute lateral earth pressure (Topic 8), run wall stability checks, and verify bearing capacity (Topic 9) on the foundation soil — all in one problem. That cross-topic chain is the realistic exam pattern, and it brings together everything Topics 8 and 9 test.
Quick reference: FoS thresholds and key formulas
| Wall type | Check | FoS threshold |
|---|---|---|
| Cantilever / gravity | Sliding | 1.5 |
| Overturning (about toe) | 2.0 | |
| Bearing capacity | 3.0 | |
| Eccentricity (in middle third) | |e| ≤ B/6 | |
| Anchored bulkhead | Embedment depth (free-earth-support) | 1.2–1.4 on D |
| Tie-rod tensile | 1.5–2.0 | |
| MSE wall | External (sliding / OT / bearing) | 1.5 / 2.0 / 3.0 |
| Internal: reinforcement tensile | 1.5 | |
| Internal: pullout | 1.5 |
Sources: NCEES PE Civil Reference Handbook §3.1 (Lateral Earth Pressures), §3.13 (Geosynthetics), and §3.18 (Earth Retention—Anchored Walls); NAVFAC DM-7.02 §7 (Anchored Bulkhead — Free Earth Support); FHWA NHI-06-088 / NHI-06-089 (Soils and Foundations, Vol I & II).
See Wall Failure Modes Animated
PEwise's PE Geotechnical course walks through cantilever sliding, anchored-bulkhead rotation, and MSE pullout as animations — once you can SEE which mode the wall is failing in, the design check sequence becomes automatic.
Connecting this to your overall PE Geotechnical exam strategy
Retaining-wall design sits downstream of lateral earth pressure (which feeds every horizontal force on the wall) and upstream of bearing capacity (which checks whether the foundation soil can support the wall and its loads). Get the wall-type identification automatic, get the FoS thresholds right, and the design checks collapse to a sequence of clean steps. For the upstream earth-pressure theory that feeds every calculation in this post, see our lateral earth pressure: Coulomb vs Rankine vs at-rest post. For the broader Topic 1 / Topic 2 fundamentals plus the full 24-module curriculum, our geotechnical PE exam study guide walks the syllabus end-to-end.
Final thoughts
Retaining-wall problems reward engineers who treat the wall-type call as the first 30 seconds of every question. Cantilever or gravity? Run sliding / overturning / bearing / eccentricity. Anchored bulkhead? Run free-earth-support and check the embedment FoS. MSE? Run external first (sliding / OT / bearing), then internal (tensile and pullout at the critical layer). Once the wall type is fixed, the checklist is fixed, and the calculation is mechanical. Drill the wall-type check until it's automatic.
Master Retaining-Wall Design with PEwise
PEwise's Modules 12 and 13 of the PE Geotechnical course (Advanced Retaining Wall Analysis and Earth Retention — Anchored Walls) cover cantilever, anchored, MSE, and braced wall design with worked stability checks — including the four cantilever checks, the free-earth-support method for anchored bulkheads, and external + internal stability for MSE. Course author Mahdi Bahrampouri, Ph.D., Geotechnical Earthquake Engineer, built the curriculum directly against NAVFAC DM-7.02, FHWA NHI-06-088 / NHI-06-089, and the NCEES PE Civil Reference Handbook (§3.1 Lateral Earth Pressures, §3.13 Geosynthetics, §3.18 Earth Retention—Anchored Walls).
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