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Railway Ground Hazard Risk Management · Part VI · Geotechnical Analysis
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Chapter 13 — Slope Stability Analysis

Slope stability governs the design of railroad embankments, cut slopes, and side-hill fills across all nine railroad client systems.
Authors: Daniel P. Colwell and Mario Ruel

Railroad Geotechnical Services Manual | Primary Source: USACE EM 1110-1-1804 All equations and parameters expressed in English (Imperial) units throughout.

Apps for this Chapter4

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Analytical Tools for this Chapter4

Calculators and workbook tools from the Benesch Geotechnical Analysis Suite that support this chapter: 1 interactive calculator and 3 workbook guides. Each one is also placed inside the section it supports, in an orange tools strip.

SSResidual & Fully Softened Strength CorrelationsUsed in 13.6 Residual Strength and Progressive FailureCalculator ▸Guide
SSSlope Stability — Effective StressUsed in 13.3 Limit Equilibrium Methodsguide onlyGuide
SSSlope Stability — Total StressUsed in 13.3 Limit Equilibrium Methodsguide onlyGuide
SSStaged Slope Stability — Pore PressureUsed in 13.3 Limit Equilibrium Methodsguide onlyGuide

Tools open on dirtbert.com and need the Benesch sign-in. Drafts pending Benesch final review, not for use in design.

Reference Graphics
Executive Summary

Slope stability governs the design of railroad embankments, cut slopes, and side-hill fills across all nine railroad client systems. An embankment failure — whether a rotational slide in soft foundation clay, a translational wedge along a shale bedding plane, or a surficial slump after heavy rainfall — can result in track loss, derailment, emergency speed restriction, and weeks of service disruption. This chapter develops the complete slope stability analysis framework: the Bishop Simplified method for circular failure surfaces, the Janbu Generalized method for non-circular surfaces, pseudo-static seismic analysis, tension crack depth, progressive failure in strain-softening clays, and cut slope design in rock. Minimum factors of safety follow USACE EM 1110-2-1902 as the primary criterion, supplemented by client-specific requirements from CSXT ES, NSR ESM, BNSF EI, UPRR EIM, CPKC TS, Amtrak ES, G&W EB, CN ES, and AREMA MRE Chapter 8. Three worked examples address an NSR Appalachian embankment over residual clay, a BNSF staged construction embankment over soft foundation soil, and a CPKC prairie cut slope in glacial till. A full slope stability analysis checklist, representative design tables, and five practice questions with complete answers are provided.

Empirical Equations — Use and Limitations

The correlations below are used or referenced in this chapter. Each is a statistical fit to a particular data set, so a value from one is an estimate: it applies only within the materials and ranges stated, carries the scatter of the original data, and must be confirmed by site-specific testing or calibration before it is relied on for design.

When an equation is used, note it with the result: give the equation ID and source, state that the soil or rock is within its range of applicability, mark the value as correlated (not tested), and record the limitation that governs. The Empirical Equations & Correlations reference has every entry with its full references.

Referenced in this chapter

IS-25Field vane strength correctionSᵤ (field)
Su,field = μ · Su,FV
μ = 1.7 − 0.54 · log(PI)

Variables. PI = plasticity index (%)

Use. Soft clays, embankment stability on soft ground; based on back-analyzed failures. Typical PI 5–100%.

Limitations. Not applicable to fissured, varved, or organic clays without local calibration. Scatter about ±25%.

Source. Azzouz et al. 1983 (fit to Bjerrum 1972) · In this chapter: 13.1 · Full entry and references

Also applicable to this chapter

IX-06Normalized undrained strength from plasticitySᵤ/σ'
Su / σ'v0 = 0.11 + 0.0037 · PI

Variables. PI (%)

Use. Normally consolidated clays (field vane basis).

Limitations. Field vane values; apply Bjerrum correction (IS-25) for stability. Not for OC clays.

Source. Skempton 1957 · Full entry and references

IX-07SHANSEP undrained strength ratioSᵤ
Su / σ'v0 = S · OCRm
S ≈ 0.22 (DSS, NC); m ≈ 0.8

Variables. OCR = σ'p/σ'v0

Use. Mechanically overconsolidated, homogeneous clays; DSS loading (averaged mode).

Limitations. S and m vary with mode of shear, plasticity, and aging; determine from lab CK0U tests on project soils where possible.

Source. Ladd 1991; Mesri 1975 · Full entry and references

IX-08Friction angle of NC clay from plasticityφ'
sin φ' = 0.80 − 0.094 · ln(PI)

Variables. PI (%)

Use. Normally consolidated, inorganic clays; peak effective-stress φ'.

Limitations. Standard deviation about ±3°. Not residual or fully softened strength; for slope reactivation use residual/fully-softened correlations (e.g., Stark & Eid charts).

Source. Kulhawy & Mayne 1990 (data of Bjerrum & Simons 1960) · Full entry and references

IS-07Undrained shear strength of clay from SPTSᵤ
Su = f1 · N60
f1 ≈ 4.4 kPa (range ~4–6 kPa; higher for low PI)

Variables. f1 varies with plasticity index

Use. Insensitive, overconsolidated clays and weak rocks (U.K. data); PI ≈ 15–65%.

Limitations. Very large scatter; not reliable in soft or sensitive clays where N is very low. Use CPT, vane, or lab tests for design Su.

Source. Stroud 1974 · Full entry and references

IS-14Undrained shear strength from CPTSᵤ
Su = (qt − σv0) / Nkt

Variables. Nkt = empirical cone factor, typically 10–20 (average ≈ 14); decreases with increasing Bq

Use. Fine-grained soils penetrated undrained (Ic > ~2.6).

Limitations. Nkt depends on reference test (vane, CIUC, DSS) and plasticity; calibrate locally. Use Nkt toward upper end for conservative Su.

Source. Lunne et al. 1997 · Full entry and references

RK-06Slope Mass RatingSMR
SMR = RMRb + (F1 · F2 · F3) + F4

Variables. RMRb = basic RMR (no orientation adjustment); F1 parallelism of joint/slope strike; F2 joint dip (planar); F3 joint-to-slope dip relation; F4 excavation method (+15 natural to −8 deficient blasting)

Use. Rock slopes; planar and toppling modes (wedge by pairwise check).

Limitations. Continuous-function forms (Tomás et al. 2007) reduce step artifacts. Does not replace kinematic and limit-equilibrium analysis.

Source. Romana 1985 · Full entry and references

RK-07Generalized Hoek–Brown criterionm_b, s, a
σ'1 = σ'3 + σci (mb σ'3/σci + s)a
mb = mi · exp[(GSI − 100)/(28 − 14D)]
s = exp[(GSI − 100)/(9 − 3D)]
a = 1/2 + 1/6 (e−GSI/15 − e−20/3)

Variables. σci = intact UCS; mi = intact rock constant; D = disturbance factor (0 undisturbed – 1 heavily blasted)

Use. Isotropic, heavily jointed rock masses (4+ joint sets) or intact rock.

Limitations. Not for rock masses where failure is controlled by one or two discrete discontinuity sets; use structural (kinematic) analysis there. D strongly affects results in slopes.

Source. Hoek et al. 2002 · Full entry and references

RK-09Joint shear strength (Barton–Bandis)τ
τ = σ'n · tan [ JRC · log10(JCS/σ'n) + φr ]
φr = (φb − 20°) + 20° (r/R)

Variables. JRC = joint roughness coefficient (0–20); JCS = joint wall compressive strength; φb = basic friction angle; r, R = Schmidt rebound on weathered and fresh surfaces

Use. Unfilled rock joints at low to moderate normal stress.

Limitations. Limit arctan term to ≤ 70°. Scale effects reduce JRC and JCS at field scale (Bandis et al. 1981). Not for infilled joints.

Source. Barton & Choubey 1977 · Full entry and references

13.1 Background and Railroad Context

Slope failures impose direct costs on railroad operations through emergency repair, traffic rerouting, crane mobilization, and environmental spill response. They impose indirect costs through locomotive speed restrictions, customer delivery failures, and regulatory scrutiny. The Federal Railroad Administration does not prescribe slope stability factors of safety directly, but 49 CFR Part 213 mandates that track geometry be maintained within class tolerances — a failed or deforming slope that moves the track out of tolerance triggers an immediate slow order or line closure under FRA authority.

Each railroad client's approach to slope stability risk reflects its operational philosophy and geographic exposure:

  • CSXT ES: Requires FS ≥ 1.5 for long-term static stability of mainline embankments; FS ≥ 1.3 during staged construction with pore pressure monitoring. Coastal and Piedmont territory includes frequent soft clay and organic soils.
  • NSR ESM: Mandates slope stability analysis for all embankments > 15 ft high and all cut slopes in the Appalachian coal territory (WV, VA, KY). NSR requires peer review by its Geotechnical Engineering group for FS < 1.7. Shale rock cuts are a specific concern in the Pocahontas and Clinch districts.
  • G&W EB: Low-speed branch line operations reduce the consequence of slow-rate creep failures; G&W accepts FS = 1.3 for non-critical sidings with annual monitoring. Active slide areas require FS ≥ 1.5.
  • UPRR EIM: Requires FS ≥ 1.5 static for all mainline embankments and fills supporting intermodal facilities. Loess embankments in Nebraska and Iowa are subject to rapid drawdown from river flooding — FS must be checked for drawdown condition.
  • BNSF EI: Transcon and northern mainlines require FS ≥ 1.5 static and FS ≥ 1.1 pseudo-static (seismic). Montana and Idaho mountain territory has documented rockfall and debris flow hazard — slope hazard rating required per BNSF EI Appendix D.
  • CPKC TS: Prairie cut slopes in glacially overconsolidated clays are subject to delayed failure — progressive failure along residual strength surfaces is the design concern, not peak strength. CPKC requires residual φ'_r analysis per Skempton (1985) for all cut slopes in Cretaceous clay shale.
  • Amtrak ES: NEC embankments and retaining walls require FS ≥ 1.75 static due to high-speed operations and minimal access for emergency response. Amtrak requires SLOPE/W or SLIDE analysis submitted electronically with every slope stability deliverable.
  • CN ES: Muskeg and quick clay in northern Ontario and Quebec require undrained stability analysis with Bjerrum-corrected VST strengths (Chapter 7); FS ≥ 1.4 for staged construction fills.
  • FRA/AREMA: AREMA MRE Chapter 8 recommends FS ≥ 1.5 for new construction embankments; emergency repair slopes may be temporarily accepted at FS = 1.1–1.2 pending permanent stabilization.

Reference graphics

Slope Stability
Slope Stability
Slope Instability and Landslides
Slope Instability and Landslides

Commonly used railway cut and fill slopes

Table 13-4. Commonly used slopes in railway earthworks (H : V)
EarthworkMaterialSlope
CutSilt2.5–3 : 1
CutMuddy (silty) sand2–3 : 1
CutGravel1.5–2 : 1
CutStable clay1–1.5 : 1
EmbankmentUsual soils1.5–2 : 1
EmbankmentGravel, sand2 : 1
EmbankmentErosion-prone soils2 : 1

Values quoted by Profillidis from Bowles. Starting points only; the factors of safety in this chapter govern.

Profillidis emphasizes studying the geological formation along a cut, especially its joint pattern, so as to disturb the existing equilibrium as little as possible; protecting slopes with vegetation; providing slope drainage to prevent softening; and checking the foundation beneath an embankment as well as the fill. Where the ground slope exceeds 1:10, he recommends benching the embankment base (Chapter 3, §3.2).

After Profillidis (2014), §9.12; values after Bowles (2001). Full reference under Supplemental Sources.

Empirical equation note · this section

Values from these correlations are estimates, not test results. State the equation ID and source when one is used, confirm the soil or rock is within its range, and calibrate against site testing before design.

  • IS-25 Field vane strength correction Sᵤ (field)Use: Soft clays, embankment stability on soft ground; based on back-analyzed failures. Typical PI 5–100%. Limits: Not applicable to fissured, varved, or organic clays without local calibration. Scatter about ±25%.
13.2 Failure Modes for Railroad Slopes

Railroad slopes exhibit four primary failure modes that drive the selection of analytical method:

  1. Rotational Circular Slide: The failure surface approximates a circular arc through a homogeneous or layered cohesive material. Typical in embankments over soft clay foundations, or in cut slopes through uniform residual soils. Analyzed by Bishop Simplified or Spencer methods.
  2. Translational (Planar) Slide: The failure surface is planar, controlled by a weak layer — bedding plane, shale parting, geosynthetic interface, or loose fill lift. Common in NSR and CPKC rock cut territory and in BNSF prairie fills over weak bentonitic shales. Analyzed by the infinite slope method or Janbu with a specified non-circular surface.
  3. Compound/Non-Circular Slide: Failure surface transitions from rotational through a weak layer to translational. Common in overconsolidated clays with a thin weak stratum. Requires Janbu Generalized or Morgenstern-Price analysis.
  4. Progressive Failure: In strain-softening clays and clay shales, the mobilized strength progressively reduces from peak to residual along the failure surface. A slope that was stable at FS = 1.5 (peak) may eventually fail at FS = 1.0 (residual) without any change in loading. Critical for CPKC prairie clay shale cuts and NSR Appalachian weathered shales.

Reference graphics

Slope Failure Mechanisms
Slope Failure Mechanisms
Foundation Slope Failure
Foundation Slope Failure
Debris Flow Landslide
Debris Flow Landslide
Supplemental reference · LEVI Library

Which failure modes does train loading actually drive?

Network Rail’s review of embankment failures (August 2003 – December 2009), carried out for RSSB, separates mechanisms by how much railway traffic contributes (Figure 13-S1):

Table 13-S1. Common embankment failure mechanisms and the role of traffic (RSSB 1386, Table 2.1, condensed)

MechanismImpact on trackTraffic influenceLikely triggers
Deep-seated failure through/below toe, daylighting next to trackCatastrophicSmallLoss of shear strength, high pore pressure
Deep-seated failure daylighting on the slopeSmall lateral/vertical deformationSmallLoss of shear strength, high pore pressure
Shallow slips daylighting near the crestSmall to medium; loss of lateral supportSmall to mediumTension cracks, seasonal deformation, high pore pressure
Unravelling of ballast/ash shoulderExcessive deformationLargeVibration, dry summer
Shear failure through fill below ballastSmall to catastrophicLargeHeavy traffic, high pore pressure
Plastic deformation of fill; subgrade failure (e.g., ballast pumping)Local subsidence, loss of supportLargeHeavy or more frequent traffic, high pore pressure
Seasonal shrink–swell (high-water-demand trees)Small to mediumSmallDry summer
Wash-outSmall to catastrophicSmallSurface flow, erosion channels

Key findings: ultimate-limit-state slips peaked in winter (wet ground), serviceability failures in late summer (desiccation), and failures were concentrated in medium- to high-plasticity fills. No correlation was found between large catastrophic failures and changes in traffic loading. Instead, traffic produces a fatigue-type mechanism that shows up as rising maintenance and poor trackbed performance rather than as a reported slip, so track maintenance records are the best indicator. The report also flags embankment–structure transitions and “hard spots” (culverts, walls) as stress concentrators that deserve more attention than they have received. Its preliminary models used only the static axle load, citing literature that the dynamic component is negligible at moderate speeds.

Source: Mott MacDonald (2011). The Effects of Railway Traffic on Embankment Stability. RSSB Research Project 1386 (Revised), Rail Safety and Standards Board

Supplemental figures · LEVI Library
Common railway embankment failure mechanisms: ultimate limit state (through crest, slope and shoulder; track bed) and serviceability limit state (seasonal shrink&ndash;swell). Numbers correspond to Table 13-S1.
Supplemental Figure 13-S1. Common railway embankment failure mechanisms: ultimate limit state (through crest, slope and shoulder; track bed) and serviceability limit state (seasonal shrink–swell). Numbers correspond to Table 13-S1. Source: Mott MacDonald (2011). The Effects of Railway Traffic on Embankment Stability. RSSB Research Project 1386 (Revised), Rail Safety and Standards Board, p. 12.

Slides from downhill and from uphill: field categories

Table 13-5. Slide categories used in the field course
CategoryField signatureTypical response
1.1 Scarp far below trackTension crack on lower slope; shallow creep shown by leaning poles, fences, treesWalk the slope; monitor and plan mitigation
1.2 Scarp at shoulderCrack in or at the toe of ballast; surfacing and cross-level defectsInstability retrogressing toward the track; investigate and act
1.3 Scarp directly below trackMain slide body at ballast level; slow or rapidDrainage/subdrainage, geometry (flatten, berm, divert) or structure (walls, nails)
1.4 Scarp uphill of track (very deep)Cross-level drops toward the high sideLarge toe berm about 1/3 of slide height; walls do not work
2.1 Uphill toe falling on or pushing trackCrack far above; toe bulge in ditchGravity or anchored wall; dewatering
2.2 Uphill toe heaving trackTrack lifted and shifted sidewaysGravity or anchored wall; dewatering
2.4 Slide taking track down“Whole hill moving”; up to about 60 ft deep; reactivated old slidesVery difficult; major engineering

Figures · click to zoom

Figure 13-11. Landslide features: crown, head scarp, surface of rupture, transverse cracks and ridges, toe.
Figure 13-11. Landslide features: crown, head scarp, surface of rupture, transverse cracks and ridges, toe.
Figure 13-12. Tension scarps forming below the track.
Figure 13-12. Tension scarps forming below the track.
Figure 13-13. A river removing the toe bulge of a large slide and reactivating it.
Figure 13-13. A river removing the toe bulge of a large slide and reactivating it.
Figure 13-14. Reactivation of an old landslide beneath the fill.
Figure 13-14. Reactivation of an old landslide beneath the fill.
Figure 13-15. Track heave severe enough to need excavator repair.
Figure 13-15. Track heave severe enough to need excavator repair.

After Geotechnology for Railroaders Program, Module 5; §03–07. Full reference under Supplemental Sources.

Slips on existing lines: where they occur and what usually fixes them

Failures on operating lines fall into four locations, each with its own usual trigger and fix:

  • Cut slopes. Water pressure is the usual cause. Fixes: divert water away from the crest, install internal drains, flatten or bench the slope, or add tieback anchors or a retaining structure.
  • Embankment slopes. Infiltration from rain or flooding lowers strength and adds weight. Fixes: drain water off the top of the fill. In flood areas, flatten the slopes or add berms, or add a retaining structure.
  • Embankment foundations: handled with normal new-construction practice.
  • Track subgrade (Chapter 2, §2.5).

Sidehill fills are the most critical. They slide through the fill or the natural hillside soil, often long after construction, and the trigger is commonly a change in drainage. Correct the drainage before failure, not after.

Train load in stability analysis. A loaded 100-ton car is roughly 1,400 psf over the 8.5-ft tie length. Embankment geometry reduces the track’s bearing factor of safety by up to about 30% compared with flat ground (Chapter 11, Table 11-SW1).

After Selig & Waters (1994), chs. 10 and 11. Full reference under Supplemental Sources.

13.3 Limit Equilibrium Methods
13.3.1 General Limit Equilibrium Framework

All limit equilibrium methods divide the failure mass into vertical slices and apply static equilibrium to the slice forces. They differ in which inter-slice forces they include and which equilibrium equations they satisfy:

MethodSatisfies Moment Eq.Satisfies Force Eq.Inter-Slice ForcesBest Use
Ordinary (Fellenius)Yes (moment)NoNeglectedQuick check only; underestimates FS
Bishop SimplifiedYesVertical onlyHorizontal onlyCircular surfaces, most railroad practice
Janbu SimplifiedNoYesHorizontal onlyNon-circular; requires correction factor
Janbu GeneralizedYesYesFull (specified)Non-circular, compound
SpencerYesYesConstant inclinationRigorous; all surface types
Morgenstern-PriceYesYesVariable (f(x))Most rigorous; CSXT/Amtrak complex cases

Reference graphics

Stability of a Slope
Stability of a Slope
Slope
Slope
13.3.2 Bishop Simplified Method

The Bishop Simplified method (1955) satisfies overall moment equilibrium and vertical force equilibrium for each slice. It is the standard method for circular failure analysis in railroad embankment design.

For a failure mass divided into n vertical slices, each of width b and height h at its center:

Equation 13-1 — Bishop Simplified Factor of Safety:

FS = Σ [1/mα,i · (c'i·bi + (Wi − ui·bi) tan φ'i)] / Σ Wi·sin αi

Equation 13-2 — m_α Factor:

mα,i = cos αi · [1 + (tan αi · tan φ'i) / FS]

Where:

  • c' = effective cohesion at slice base (psf)
  • φ' = effective friction angle at slice base (°)
  • W_i = total weight of slice i (lb/ft of embankment width)
  • u_i = pore water pressure at slice base (psf); u = γ_w × h_w where h_w = piezometric head above slice base
  • b_i = slice width (ft)
  • α_i = inclination of slice base from horizontal (°; positive = dip in direction of sliding)

Because FS appears on both sides of Equation 13-1, the solution is iterative: assume FS, compute m_α, compute new FS, repeat until convergence (typically 3–5 iterations).

Equation 13-3 — Slice Weight:

Wi = γavg,i · hi · bi · 1 ft (per unit width, kips/ft or lb/ft)

Where γ_avg,i = weighted average unit weight of materials in slice i (pcf); h_i = average slice height (ft).

13.3.3 Pore Pressure Ratio (r_u)

For preliminary and parametric analysis, pore pressure is expressed as a fraction of total overburden:

Reference graphics

Groundwater Monitoring for Slope Stability
Groundwater Monitoring for Slope Stability
Equation 13-4 — Pore Pressure Ratio:

ru = u / (γ · h) = pore pressure / total vertical stress

Typical r_u values: 0 for fully drained slope; 0.25–0.35 for partially drained embankment fill; 0.50 for steady-state seepage with phreatic surface at the slope surface (worst case). USACE EM 1110-2-1902 specifies that steady-state seepage with drawdown must be analyzed separately from the static long-term case.

13.3.4 Janbu Simplified (Non-Circular Surfaces)

For a planar or compound failure surface, Janbu Simplified satisfies horizontal force equilibrium:

Equation 13-5 — Janbu Simplified FS:

FS = f₀ · Σ [1/nα,i · (c'i·li + (Wi − ui·bi)·tan φ'i)] / Σ Wi·tan αi

Equation 13-6 — n_α Factor:

nα,i = cos²αi · [1 + (tan αi · tan φ'i)/FS]

Equation 13-7 — Janbu Correction Factor f₀:

f₀ = 1 + b1 · [d/L − 1.4(d/L)²]

Where d = maximum depth of failure surface below a chord connecting the crest and toe (ft); L = horizontal distance of the failure surface (ft); b1 = 0.31 for φ' > 0 soils; 0.50 for φ' = 0 (undrained clay). f₀ corrects for inter-slice shear forces neglected in the simplified formulation.

13.3.5 Tension Crack

In cohesive soils, a tension crack develops at the crest of the failure mass to a theoretical depth:

Equation 13-8 — Tension Crack Depth:

zc = 2c' / (γ · √Ka) = 2su / γ (for φ' = 0, undrained)

Where K_a = tan²(45 − φ'/2). For φ' = 0: z_c = 2s_u / γ. The tension crack reduces the effective length of the failure arc and, when water-filled, adds a destabilizing hydrostatic pressure. USACE EM 1110-2-1902 requires that tension crack analysis be performed for all embankments and cuts in cohesive soils with the crack assumed water-filled in the critical stability case.

Water pressure in tension crack:

Equation 13-9 — Tension Crack Water Force:

Pw = 0.5 · γw · zc² (lb/ft, acts horizontally into failure mass)

Supplemental reference · LEVI Library

Shallow sloughing: the infinite slope check

EM 1110-2-1902 recommends the infinite slope method for slopes of cohesionless material, where the critical surface lies parallel to and just below the face. With c′ = 0, slope angle β and ru = u/γz:

F = (cos2β − ru) tan φ′ / (cos β sin β)

A circular search in the same material converges on a very shallow, large-radius circle with the same FS. USACE cautions that the lowest FS is often such a shallow surface, while deeper surfaces carry the real consequence. For a granular embankment over soft clay, report the deeper surfaces that could take out the track even when a skin slide has a lower FS. In the other direction, shallow fully-softened slides in clay fills (above) are exactly the ones that undercut ballast shoulders.

Source: U.S. Army Corps of Engineers (2003). Slope Stability. EM 1110-2-1902

13.4 Pseudo-Static Seismic Stability Analysis

For railroad slopes in seismically active regions (UPRR western network, BNSF Cascades/Rockies, CPKC Rockies, Amtrak NEC through New York/Connecticut), a pseudo-static horizontal force is applied to the failure mass to represent earthquake loading.

Equation 13-10 — Pseudo-Static Seismic Force:

Feq = kh · W

Where:

  • k_h = horizontal seismic coefficient = a_max / g × 0.5 (USACE EM 1110-2-1902 recommendation; the 0.5 factor accounts for transient nature of earthquake accelerations)
  • a_max = peak ground acceleration (g) from USGS hazard map at the site
  • W = total weight of failure mass (lb/ft)

The pseudo-static force F_eq is added to the driving moments/forces in the Bishop or Janbu equations. USACE EM 1110-2-1902 specifies minimum FS = 1.0 for pseudo-static analysis (the slope should not fail during the design earthquake, even with zero reserve). BNSF EI requires FS ≥ 1.1 pseudo-static.

Equation 13-11 — Bishop Simplified with Pseudo-Static Loading:

FS = Σ [1/mα,i · (c'i·bi + (Wi − ui·bi)·tan φ'i)]

/ Σ (Wi·sin αi + kh·Wi·cos αi · Rm/R)

Where R = failure circle radius (ft) and R_m = moment arm for the pseudo-static force (approximately equal to the height of the centroid of the failure mass above the center of the circle).

13.5 USACE Minimum Factors of Safety

USACE EM 1110-2-1902 (2003) provides the standard minimum FS criteria used across all nine railroad clients as a baseline:

Table 13-1 — Minimum Factors of Safety by Loading Condition (USACE EM 1110-2-1902 and Railroad Client Standards)
Loading ConditionUSACE Min FSCSXT ESNSR ESMBNSF EIAmtrak ESG&W EBCPKC TSCN ES
End-of-construction (undrained)1.31.31.31.41.51.31.31.3
Long-term static (drained)1.51.51.51.51.751.3–1.51.51.4
Steady-state seepage1.51.51.51.51.751.41.51.4
Rapid drawdown1.31.31.31.31.51.31.31.3
Pseudo-static seismic1.01.11.01.11.11.01.11.0
Residual (progressive failure)1.21.31.21.31.51.21.21.2
Emergency repair (temporary)1.11.11.11.11.31.11.11.1

Client-specific deviations from USACE baseline reflect the consequence of failure on high-density operations. Amtrak's FS = 1.75 for long-term static reflects the catastrophic consequence of a slope failure under a 125 mph Acela Express.

Supplemental reference · LEVI Library

What EM 1110-2-1902 actually tabulates

Table 13-1 lists a “USACE Min FS” column, but EM 1110-2-1902 prescribes values only for new earth and rock-fill dams (Table 3-1): 1.3 at end of construction (including staged construction), 1.5 for long-term steady seepage, 1.4 at maximum surcharge pool, and 1.1–1.3 for rapid drawdown (1.1 from maximum surcharge pool, 1.3 from maximum storage pool; 1.4–1.5 where drawdown is routine, as in pumped storage). The manual does not tabulate pseudo-static, residual or emergency-repair values; for earthquake loading it refers to ER 1110-2-1806. Cite those rows to the client standards or to project-specific judgment, not to USACE.

For “other slopes” — and EM 1110-2-1902 names railway embankments explicitly — USACE says FS should reflect both the uncertainty in strength and pore pressure and the consequence of failure. Where both are small, about 1.3 or even less can be acceptable. Where either grows, a larger FS is needed, and “large uncertainties coupled with large consequences of failure represent an unacceptable condition, no matter what the calculated value of the factor of safety.” Typical minimums are about 1.3 for end of construction and multistage loading, 1.5 for long-term loading, and 1.1–1.3 for infrequent rapid drawdown.

Cuts get weaker with time. For excavated slopes, the long-term condition is normally critical because pore pressures rise and the soil swells and weakens after excavation. A cut in low-permeability soil can stand temporarily yet be unstable in the long term; USACE calls this inherently dangerous and allows it only with detailed study and the observational method.

Source: U.S. Army Corps of Engineers (2003). Slope Stability. EM 1110-2-1902

13.6 Residual Strength and Progressive Failure

In overconsolidated clays and clay shales, the post-failure (residual) strength is significantly lower than peak strength. The residual friction angle φ'_r is measured by ring shear test (ASTM D 6467) or repeated direct shear at large displacement.

Reference graphics

Landslides After Rain
Landslides After Rain
Equation 13-12 — Residual Strength Envelope:

τ_r = c'_r + σ'_n · tan φ'_r

For Cretaceous clay shales (CPKC prairie territory; NSR Pocahontas district): c'_r ≈ 0 psf; φ'_r = 8°–14° (Skempton 1985; ring shear data). This is dramatically lower than peak φ' = 24°–30°, meaning a slope designed at FS = 1.5 using peak strength may fail over decades at FS < 1.0 using residual strength as progressive straining reduces the mobilized angle along the surface.

CPKC TS requires that all cut slopes in clay shale be analyzed using residual strength parameters with FS ≥ 1.2 minimum. NSR ESM requires the same in Appalachian shale territory. The consultant must confirm whether the soil has experienced previous shearing (by identifying pre-existing slickensides in core samples or split spoon) — if slickensides are present, residual strength governs.

Supplemental reference · LEVI Library

Fully softened strength — the step between peak and residual

Section 13.6 moves directly from peak to residual strength. The intermediate fully softened strength (FSS) — close to the peak strength of the soil in a normally consolidated state — is the one that governs first-time slides in two situations common on railroads: (1) cuts in overconsolidated, fissured clays and clay shales, and (2) compacted clay embankments exposed to wet–dry cycles. The USACE/ASCE white paper notes that 3H:1V–4H:1V slopes 15–25 ft high routinely compute FS > 1.5 (often > 2) with peak strengths, yet many have failed, implying FS ≈ 1. One case describes a compacted fill slope that failed after about six years on a shallow surface, with back-analysis matching the FSS.

  • Softening process: stress relief opens joints and fissures, water infiltrates, the clay swells and weathers, and repeated cycles bring it toward a normally consolidated state. Softening develops faster and deeper in sloping ground than in level ground, and faster in uncovered slopes.
  • Depth: first-time slip surfaces in heavily overconsolidated clay ranged from 4 to about 65 ft deep (Skempton, 1977), with most case histories at 20–25 ft. Apply FSS to at least that depth in such clays. Most clay embankment failures are shallow (< 10 ft).
  • FSS vs. residual: the gap between φ′FSS and φ′r reaches about 16° for LL of 80–140% and is smaller (< 8° at 1,000 psf and < 6° at 8,300 psf) for LL < 50% (Figure 13-S3). It is larger at low normal stress, i.e., for shallow surfaces. Where the gap is large, check two cases: FS > 1.5 with FSS, and FS > 1.0 with residual strength on any pre-existing or slickensided surface.
  • Nonlinear envelope: the FSS envelope is curved, so a linear c′–φ′ fit over-predicts strength at the low normal stresses of shallow slides. The paper recommends a power function τ = a(σ′)b, with average b ≈ 0.96 for clay-size fraction CF ≤ 20%, 0.905 for 20–45%, and 0.852 for CF ≥ 50%. Do not add an apparent cohesion from a linear fit.
  • Temporary cuts may use a strength above FSS because there is not enough time to soften fully.

Source: Stark, T. D. et al. (2016). Development and Use of Fully Softened Shear Strength in Slope Stability Analyses, Third Draft. USACE / ASCE FSS Subcommittee

Supplemental figures · LEVI Library
(a) Deep slide in shale bedrock in an area of no known prior landsliding; (b) slickensided shale along the failure surface &mdash; the condition that calls for residual rather than fully softened strength.
Supplemental Figure 13-S2. (a) Deep slide in shale bedrock in an area of no known prior landsliding; (b) slickensided shale along the failure surface — the condition that calls for residual rather than fully softened strength. Source: Stark, T. D. et al. (2016). Development and Use of Fully Softened Shear Strength in Slope Stability Analyses, Third Draft. USACE / ASCE FSS Subcommittee, p. 19.
Difference between secant fully softened and residual friction angles as a function of liquid limit at effective normal stresses of 1,040 and 8,350 psf (Stark et al., 2015).
Supplemental Figure 13-S3. Difference between secant fully softened and residual friction angles as a function of liquid limit at effective normal stresses of 1,040 and 8,350 psf (Stark et al., 2015). Source: Stark, T. D. et al. (2016). Development and Use of Fully Softened Shear Strength in Slope Stability Analyses, Third Draft. USACE / ASCE FSS Subcommittee, p. 20.
13.7 Cut Slope Design in Rock

For rock cut slopes along NSR Appalachian routes, BNSF Montana/Idaho territory, and CPKC Rocky Mountain corridor, kinematic analysis of joint and bedding plane orientations governs slope geometry over soil mechanics methods.

Reference graphics

Rockfall Mitigation and Slope Stabilization
Rockfall Mitigation and Slope Stabilization
Rock Bolt vs Soil Nail
Rock Bolt vs Soil Nail
Cable Anchoring of Rock Slopes
Cable Anchoring of Rock Slopes
Steel Cable Mesh on Slopes — Rockfall Protection
Steel Cable Mesh on Slopes — Rockfall Protection
Equation 13-13 — Planar Rock Slide FS (Drained):

FS = (c'_j · A + (W·cos αp − U − V·sin αp) · tan φ'_j)

/ (W·sin αp + V·cos αp)

Where:

  • c'_j = joint cohesion (psf; often 0 for clean joints)
  • A = area of failure plane per unit width (ft²/ft)
  • W = weight of sliding block (lb/ft)
  • U = water uplift force on failure plane = 0.5 γ_w h_w A (lb/ft); h_w = water height in tension crack
  • V = water force in tension crack = 0.5 γ_w z_w² (lb/ft); z_w = water depth in crack
  • α_p = dip angle of failure plane (°)
  • φ'_j = joint friction angle (°)
Table 13-2 — Typical Rock Joint Strength Parameters for Railroad Cut Slopes
Rock Typec'_j (psf)φ'_j (°)Notes
Clean sandstone joint0–50028–35NSR WV, BNSF MT
Clay-filled shale parting0–2008–16NSR/CPKC clay shale; use residual
Limestone bedding plane0–1,00032–40G&W Gulf Coast carbonate
Granite exfoliation joint035–42UPRR Sierra Nevada
Weathered basalt0–50025–32BNSF Pacific Northwest

Kinematic feasibility of planar, wedge, and toppling failure must be evaluated by stereographic projection (stereonet analysis) using joint orientation data collected during field mapping. This analysis is beyond scope here but must be performed for every rock cut slope on NSR, BNSF, and CPKC projects per their respective standards.

Supplemental reference · LEVI Library

Kinematic screening before stability analysis

Section 13.7 leaves stereonet analysis out of scope. The screening rules are short enough to apply to every railroad rock cut. Following Wyllie and Mah (2004), with face dip ψf and dip direction αf:

  • Planar sliding is possible when the plane daylights (ψp < ψf), dips more steeply than its friction angle (ψp > φj), and its dip direction is within about ±20° of the face. Outside ±20°, intact rock at one end of the block provides enough restraint.
  • Wedge sliding is possible when the line of intersection daylights (ψi < ψf) and plunges more steeply than φ. Its daylight envelope is wider than that for planes because two planes provide release.
  • Toppling requires steep planes dipping into the face, striking within about 10° of it, and satisfying (90° − ψf) + φj < ψp (Goodman and Bray, 1976).
  • The friction cone (radius φ) plotted on the same stereonet gives a first stability check for gravity loading only. It ignores water pressure and bolt forces, so kinematically possible blocks then go to the limit-equilibrium analysis of Eq. 13-13.

Wyllie and Mah note it is rarely possible to change an alignment enough to avoid an adverse structure; the choice is usually to flatten that face or reinforce it.

Why rock falls happen on transportation corridors

A California study of 308 highway rock falls (McCauley et al., 1985, reported by Wyllie and Mah) found that water-related causes account for 68% (rain 30%, freeze–thaw 21%, snowmelt 8%, channeled runoff 7%, plus differential erosion, springs and tree roots), and 85% when adverse geology is added. On a major western Canadian railroad, about 70% of 25 years of recorded falls occurred in winter, and falls smaller than about 1.3 yd³ occurred up to 50 times a year, while 13,100 yd³ slides recurred every 10–50 years. Many railroad cuts were blasted more than a century ago with techniques that damaged the rock, and have since weathered. Schedule scaling and inspection for late fall and early spring, and treat drainage as a primary rock-fall control.

Source: Wyllie, D. C. and Mah, C. W. (2004). Rock Slope Engineering: Civil and Mining, 4th ed. Spon Press

Supplemental reference · LEVI Library

Surface support: high-tensile mesh and grouted reinforcement

Active high-tensile mesh. Draped mesh only guides falling rock to the ditch; a pretensioned mesh pinned with a grid of soil or rock nails actively holds the surface layer. The Geobrugg TECCO system (presented at the Appalachian geohazards conference) uses wire of more than 256 ksi, giving mesh tensile strength of about 10.2 kips/ft, compared with about 3 kips/ft for common steel wire mesh and 2.75 kips/ft for a PET geogrid. The design (RUVOLUM concept) checks (1) sliding of the surface layer parallel to the slope and (2) local failure between nails, and sets the maximum nail spacing. It does not replace a global stability analysis (e.g., Bishop) of deeper surfaces. The presentation cites failed alternatives — shotcrete facing replaced after about 10 years and soft geogrid facing that failed by creep, cutting at sharp edges and overload.

Load transfer in grouted bolts and cables. Wang, Hagan and Cao (2016) summarize laboratory work on fully grouted reinforcement:

  • Cable strands rarely rupture. Failure is more likely at the cable–grout interface (or the grout–rock interface), so capacity depends on load transfer, not steel strength. Modified strands (bulbed, indented) transfer load much better than plain strand because the geometry increases normal pressure at the interface.
  • Rebar bolts fail either by parallel shear on a cylindrical surface (smooth bars, closely spaced ribs, short embedment in stiff confinement) or by dilational slip on a conical surface. The optimum rib profile depends on grout properties and confining pressure.
  • Push tests overstate performance compared with pull tests (the bar expands under compression instead of necking). Verify bolt and anchor capacity with pull tests that load the bar in tension as in service.

Source: Amend, F. Slope Stabilization with High Tensile Wire Mesh. Geohazards in Transportation in the Appalachian Region Conference, Geobrugg North America · Wang, S., Hagan, P. C. and Cao, C. (2016). Advances in Rock-Support and Geotechnical Engineering. Butterworth-Heinemann

Rockfall management: stabilize, protect, warn

Table 13-6. Rock-slope management strategies and indicative costs
StrategyMethodsNotes
StabilizingDrainage, trimming, scaling, shotcrete, bolting; retaining walls; stabilizing berms; horizontal drainsHighest safety and reliability impact; cost varies; scaled-rock disposal can be a problem
ProtectingCatchment nets; barrier walls; lock blocks; rock sheds (~$1–10M); tunnels (~$3–50M); flumes (~$600K); rock mesh (~$100–250K)Nets for confined chutes and unscalable sources; keep catch ditches and wall accumulation zones clean
WarningSlide-detector fences; mercury and tip-over switches; temporary radio unitsA warning layer, not a fix: about 90% of trips prove passable; maintenance burden and false positives

A Jasper near-miss shows the limit of warning devices: the fence tripped as designed, but the train could not stop on the grade. Use engineering-grade concrete for lock blocks and source matching keys. Mark already-documented fallen rocks with an X.

Figures · click to zoom

Figure 13-16. Scaling crew on a cliff above the right-of-way.
Figure 13-16. Scaling crew on a cliff above the right-of-way.
Figure 13-17. A catchment net stopping a boulder.
Figure 13-17. A catchment net stopping a boulder.
Figure 13-18. Barrier wall at the base of a cliff.
Figure 13-18. Barrier wall at the base of a cliff.
Figure 13-19. Rock mesh controlling raveling.
Figure 13-19. Rock mesh controlling raveling.
Figure 13-20. Interlocking lock blocks with an uphill slide detector.
Figure 13-20. Interlocking lock blocks with an uphill slide detector.
Figure 13-21. Slide-detector fence along a cutting.
Figure 13-21. Slide-detector fence along a cutting.

After Geotechnology for Railroaders Program, Module 6.4; §02–04. Full reference under Supplemental Sources.

13.8 Rapid Drawdown Analysis

UPRR Missouri River territory and BNSF river crossing embankments are subject to rapid drawdown — when a river in flood recedes quickly, the phreatic surface within the embankment lags behind the external water level, creating a destabilizing outward seepage gradient.

The three-stage approach per USACE EM 1110-2-1902 Appendix F:

  1. Analyze embankment at full pool (phreatic surface at top of bank); compute total and effective stresses.
  2. Instantly lower the pool; the phreatic surface remains at its high position.
  3. Analyze with consolidated-undrained (CU) strength of the embankment materials after consolidation at full pool, but with the external water pressure removed.

For materials with k > 10⁻³ ft/day (sands and gravels), drained strengths can be used at the lowered pool because drainage occurs faster than drawdown. For clays with k < 10⁻⁵ ft/day, CU strengths apply throughout.

Rapid drawdown in the field: the 12–24 hour window

While a pond is high, its weight helps hold the slope despite saturation. When it drops quickly, that support disappears while the fill is still saturated, and seepage reverses outward. Field guidance is that the slope stays at its least stable for about 12 hours after drawdown, recovering over 12–24 hours as the bank drains. Monitor for at least that long, and for at least three days where the drop is 2 ft or more. Beaver-dam or culvert releases create the same condition. The Nakina derailment of 1992, in which two employees were killed, was a rapid-drawdown failure beneath a moving train.

Figures · click to zoom

Figure 13-22. Rapid-drawdown embankment failure beneath a train after an uphill lake level dropped.
Figure 13-22. Rapid-drawdown embankment failure beneath a train after an uphill lake level dropped.
Figure 13-23. Standing water pressed against an embankment (illustrative risk rating: Severe).
Figure 13-23. Standing water pressed against an embankment (illustrative risk rating: Severe).

After Geotechnology for Railroaders Program, Module 7.1, Module 4, Module 6.5; Module 7.1 §06; Module 4 §10. Full reference under Supplemental Sources.

Case study: 13.16.1 Flood drawdown failures along the Brisbane River (Look 2023), in §13.16 Case Studies.

13.9 Representative Data Table
Table 13-3 — Representative Slope Stability Input Parameters by Client Territory
ClientTerritorySoil/Rockc' (psf)φ' (°)φ'_r (°)γ (pcf)s_u (psf)Design FS
CSXTCoastal GA/SCSoft CH clay foundation0——100–105400–800≥1.3 (EOC)
NSRWV PocahontasResidual silty clay2002212115—≥1.5 (LT)
NSRVA AppalachianWeathered shale0149130—≥1.2 (res.)
G&WGulf Coast LASoft CL/CH0——105600–1,200≥1.3
UPRRNE LoessLoess (ML)30028—110—≥1.5
BNSFMT MountainDense glacial till50032—135—≥1.5
CPKCSK PrairieCretaceous clay shale0106125—≥1.2 (res.)
AmtrakNEC CT/NYStiff marine clay10026—1201,500–2,500≥1.75
CNON/QCLeda quick clay0——115200–600≥1.4 (staged)
13.10 Figure Placeholders
  1. Figure 13-1: Rotational failure geometry — slice numbering, weight W_i, base angle α_i, piezometric line.
  2. Figure 13-2: Bishop Simplified iteration convergence — FS vs. iteration number chart.
  3. Figure 13-3: Non-circular failure surface through weak clay layer — Janbu slice geometry.
  4. Figure 13-4: Tension crack diagram — cohesive slope crest with water-filled crack, force vectors.
  5. Figure 13-5: Pseudo-static seismic force application — horizontal F_eq on failure mass centroid.
  6. Figure 13-6: USACE FS vs. loading condition matrix — graphical summary of Table 13-1.
  7. Figure 13-7: Progressive failure concept — peak to residual strength along failure surface.
  8. Figure 13-8: Planar rock slide geometry — tension crack, water uplift U, slide block weight W.
  9. Figure 13-9: Rapid drawdown stages — pool level, phreatic surface at drawdown, seepage force.
  10. Figure 13-10: Staged construction approach — fill lifts, pore pressure dissipation, FS vs. time.

Reference graphics

Slope Stability
Slope Stability
Slope Failure Mechanisms
Slope Failure Mechanisms
Rock Bolt vs Soil Nail
Rock Bolt vs Soil Nail
Impact of Excavation on Hydrogeologic Regime and Slope Stability
Impact of Excavation on Hydrogeologic Regime and Slope Stability
13.11 Worked Calculation Examples
Example 13.1 — NSR Appalachian Embankment over Residual Clay (Bishop Simplified)

Project context: Norfolk Southern Pocahontas District, WV. Proposed 20-ft high railroad fill over residual CL soil derived from shale. Soil profile: embankment fill (c' = 100 psf, φ' = 30°, γ = 120 pcf); foundation CL residual clay (c' = 200 psf, φ' = 22°, γ = 115 pcf). Phreatic surface at 1/3 height of embankment from base. Trial circular failure surface: radius R = 38 ft; circle center 15 ft above embankment crest. NSR ESM requires FS ≥ 1.5. Divide failure mass into 5 slices.

Step 1 — Slice geometry and weights (per unit width)

Sliceb (ft)h_avg (ft)Materialγ (pcf)W = γ·h·b (lb/ft)α (°)u (psf)
164.0Fill1202,880−150
2812.0Fill12011,52000
3818.5Fill+Fdn11817,464+12375
4814.0Fdn Clay11512,880+28624
566.0Fdn Clay1154,140+420

Pore pressure u = γ_w × h_w: at Slices 3 and 4, h_w ≈ 6 ft and 10 ft respectively; u = 62.4 × 6 = 374 ≈ 375 psf; 62.4 × 10 = 624 psf.

Step 2 — Driving moment (Σ W_i sin α_i)

Slice 1: 2,880 × sin(−15°) = 2,880 × (−0.259) = −746 lb/ft

Slice 2: 11,520 × sin(0°) = 0

Slice 3: 17,464 × sin(12°) = 17,464 × 0.208 = 3,633 lb/ft

Slice 4: 12,880 × sin(28°) = 12,880 × 0.469 = 6,041 lb/ft

Slice 5: 4,140 × sin(42°) = 4,140 × 0.669 = 2,770 lb/ft

Σ Wi·sin αi = −746 + 0 + 3,633 + 6,041 + 2,770 = 11,698 lb/ft

Step 3 — Resisting forces — iterate to FS = 1.52 (trial)

For each slice compute m_α = cos α [1 + (tan α · tan φ') / FS]:

Using φ' = 22° (foundation) for Slices 3–5; φ' = 30° (fill) for Slices 1–2; c' = 200 psf (fdn), 100 psf (fill); assume FS = 1.52.

Slicec'b (lb/ft)(W−ub) tan φ' (lb/ft)Numerator (lb/ft)cos αtan α · tan φ' / FSm_αNum/m_α
1100×6=600(2,880−0)×0.577=1,6622,2620.966(−0.268×0.577)/1.52=−0.1020.966×0.898=0.8672,609
2100×8=800(11,520−0)×0.577=6,6477,4471.00001.0007,447
3200×8=1,600(17,464−375×8)×0.404=(17,464−3,000)×0.404=5,8357,4350.978(0.213×0.404)/1.52=0.0570.978×1.057=1.0347,190
4200×8=1,600(12,880−624×8)×0.404=(12,880−4,992)×0.404=3,1914,7910.883(0.532×0.404)/1.52=0.1410.883×1.141=1.0084,754
5200×6=1,200(4,140−0)×0.404=1,6732,8730.743(0.900×0.404)/1.52=0.2390.743×1.239=0.9213,120

Σ (Num/m_α) = 2,609 + 7,447 + 7,190 + 4,754 + 3,120 = 25,120 lb/ft

Step 4 — Computed FS

FS = 25,120 / 11,698 = 2.15

The trial FS (1.52) does not match the computed FS (2.15). This is a single-trial demonstration; in practice, the critical circle is found by systematically moving the circle center and radius to minimize FS. The minimum FS for the critical circle at this site would be reported after searching over hundreds of trial circles in SLOPE/W or SLIDE. The computed FS of 2.15 for this trial surface indicates adequate stability; the critical surface will produce a lower value. For this example, assume the critical circle yields FS = 1.72, which meets NSR ESM's FS ≥ 1.5 requirement.

Conclusion: The 20-ft embankment design with 2H:1V side slopes over the residual CL clay provides adequate long-term stability per NSR ESM. NSR requires submission of SLOPE/W output (minimum 50 trial circles) to the NSR Geotechnical Engineering group for independent review before construction authorization.

Example 13.2 — BNSF Staged Construction Embankment — Undrained (φ = 0) Analysis

Project context: BNSF siding extension, Crescent, WA. Proposed 12-ft embankment over soft saturated CH (s_u = 700 psf undrained, γ = 103 pcf). End-of-construction (undrained) analysis required; BNSF EI requires FS ≥ 1.4 at EOC. Check 1.5H:1V embankment slopes.

Simplified φ = 0 analysis (Taylor's stability chart):

For φ' = 0 soils, the critical circular failure surface passes through the toe for D_f/H ≤ 1 (where D_f = depth of firm layer) and is characterized by the stability number N_s:

Equation 13-14 — Taylor Stability Number:

FS = Ns · su / (γ · H)

N_s is a function of slope angle β and depth factor D = D_f/H. For 1.5H:1V slope (β ≈ 34°) and no firm layer immediately below (deep failure), N_s ≈ 5.52 (from Taylor's chart, Coduto 2001).

FS = 5.52 × 700 / (103 × 12)

= 3,864 / 1,236

= 3.13 ≥ 1.4 ✓

However, the soft CH must be checked for base failure (Prandtl/Terzaghi bearing capacity of the foundation clay):

q_ult = Nc · su = 5.14 × 700 = 3,598 psf

q_applied = γ_fill × H = 120 × 12 = 1,440 psf

FS_base = 3,598 / 1,440 = 2.50 ≥ 1.4 ✓

Staged construction: If s_u were 300 psf (very soft), FS = 5.52 × 300 / 1,236 = 1.34 < 1.4. BNSF EI would require staged construction — place first 6-ft lift, wait for consolidation-induced strength gain before placing the second lift. Settlement plates and piezometers (Chapter 15) monitor the consolidation progress; the fill rate is restricted until FS ≥ 1.4 is reestablished after each stage.

Conclusion: For s_u = 700 psf, the 1.5H:1V embankment at 12 ft height provides FS = 3.13 at EOC, well above BNSF EI's 1.4 minimum. BNSF EI requires that the foundation strength be confirmed by at least two CPTu soundings at every embankment location greater than 8 ft over soft ground (Chapter 7 correlation used for s_u). If CPTu reveals zones of s_u < 500 psf, staged construction with instrumentation must be implemented.

Example 13.3 — CPKC Prairie Clay Shale Cut Slope — Residual Strength

Project context: Canadian Pacific Kansas City (CPKC) Mainline, Saskatchewan. New 25-ft railway cut in Cretaceous clay shale. Residual ring shear data: c'_r = 0 psf, φ'_r = 9°. Peak parameters: c' = 300 psf, φ' = 22°. Unit weight = 130 pcf. Water table at cut bench level (worst case). Check proposed 2H:1V cut slope (β = 26.6°) using both peak and residual strengths.

Step 1 — Infinite slope analysis for shallow translational slide (0–5 ft depth)

For a shallow translational failure along a plane parallel to the slope at depth z = 4 ft:

Equation 13-15 — Infinite Slope FS (Drained):

FS = (c' + γ'·z·cos²β·tan φ') / (γ_sat·z·sin β·cos β)

With WT at surface: γ' = γ_sat − γ_w = 130 − 62.4 = 67.6 pcf; γ_sat = 130 pcf; β = 26.6°; z = 4 ft.

Peak strength:

FS_peak = (300 + 67.6×4×cos²26.6°×tan22°) / (130×4×sin26.6°×cos26.6°)

= (300 + 67.6×4×0.797×0.404) / (130×4×0.447×0.894)

= (300 + 87.1) / (207.8)

= 387.1 / 207.8 = 1.86 ≥ 1.5 ✓ (peak)

Residual strength (c'_r = 0, φ'_r = 9°):

= (67.6×4×0.797×0.1584) / 207.8

= 34.2 / 207.8 = 0.165 << 1.0 ✗

Step 2 — Interpretation

The residual strength analysis yields FS = 0.165 — the slope is in a state of impending failure at residual. This is the well-known behavior of clay shale slopes: they appear stable at first cut but fail progressively over months to years as weathering and swelling reduce the mobilized strength toward residual. CPKC TS requires that cut slopes in clay shale be designed with either: (a) gentle slopes (4H:1V to 5H:1V) that achieve FS ≥ 1.2 at residual, or (b) engineered drainage (horizontal drains) to reduce pore pressures to near-zero, or (c) slope reinforcement (soil nails, piles) to maintain stability.

Step 3 — Required slope angle for FS = 1.2 at residual (c'_r = 0)

For infinite slope with c' = 0:

This is impractically flat for a 25-ft deep railway cut.

Conclusion: Drainage is the most economical solution — reduce pore pressures by installing horizontal drains at the slope face. With u = 0 (fully drained): γ = 130 pcf (no buoyancy reduction), γ_sat replaced by γ in both numerator and denominator:

Even fully drained, FS < 1.0 at residual for a 2H:1V cut in this clay shale. A 3.5H:1V slope is the practical minimum for FS = 1.2 at residual with full drainage:

tan β = tan(9°)/1.2 = 0.132

β = 7.5° → 3H:1V + berms at 15-ft height intervals

CPKC TS requires geotechnical instrumentation (surface monuments, inclinometers) for all clay shale cuts exceeding 15 ft depth, with annual monitoring and reporting to CPKC Track Geometry Engineering.

13.12 Practical Recommendations
  1. Search the critical failure surface systematically: The minimum FS may not occur at the toe; for embankments over soft clay, the critical circle often exits through the foundation rather than the embankment slope face. Use a grid search over at least 200 trial centers and 5 radii per center in SLOPE/W or equivalent.
  2. Never use peak strength for clay shale or Appalachian weathered shale: Identify pre-existing slickensides in the boring core before selecting design strength. A single set of slickensides on a joint dipping toward the cut is sufficient to require residual-strength analysis. CPKC TS and NSR ESM both require written confirmation of slickenside inspection in the geotechnical report.
  3. Always include the tension crack in cohesive slope analyses: A water-filled tension crack at the crest reduces FS by 5–15% and is the most commonly omitted factor in routine slope analyses. USACE EM 1110-2-1902 requires it; so do CSXT ES and Amtrak ES.
  4. Staged construction requires real-time instrumentation and a trigger plan: Specifying staged construction in a geotechnical report without a corresponding instrumentation plan and construction trigger criteria (maximum pore pressure ratio, minimum settlement rate before next lift) is incomplete and creates construction-phase liability. BNSF EI and CN ES require the trigger criteria to be included in the geotechnical special provisions (GSP).
  5. Rapid drawdown is often the governing condition for river-crossing embankments: UPRR Missouri River and BNSF Platte River embankments have been subject to drawdown failures after spring flood recession. The rapid drawdown case per USACE EM 1110-2-1902 Appendix F must be analyzed for any embankment adjacent to a river or reservoir with seasonal water level fluctuation > 5 ft.
  6. Report FS for all loading conditions — not just the critical one: CSXT ES and NSR ESM require the geotechnical report to tabulate FS for end-of-construction, long-term static, steady-state seepage, and seismic (where applicable) — even when some conditions clearly are not critical. This demonstrates due diligence and aids the client's Bridge/Track Engineering review.
  7. Coordinate with drainage design: Most railroad slope failures occur after prolonged rainfall that raises pore pressures above the design phreatic surface. The slope stability analysis should be accompanied by a drainage design recommendation (ditch grades, blanket drains, horizontal drains) that maintains pore pressures at or below the assumed steady-state seepage condition.

Reference graphics

Measures to Prevent Landslides
Measures to Prevent Landslides
Highway Slope Stabilization Using Soil Nails & Shotcrete
Highway Slope Stabilization Using Soil Nails & Shotcrete
Micropile installation on a highway slope
Micropile installation on a highway slope
Slope Stability Radar
Slope Stability Radar

The slope remediation toolbox, in order

Consider remedial measures in this order: (1) drainage and subdrainage; (2) geometry, meaning a toe berm, flattening or moving the track; (3) structural support; (4) improving soil properties. Warning devices supplement these.

  • Slopes flattened to 2H:1V are generally very stable. A toe berm about 1/3 of slope height and 12–15 ft wide adds substantial stability; a 30-ft slope needs a berm about 10 ft high. Fill left “hanging” on the shoulder reduces stability.
  • Never leave riprap or fill at the top of an unstable slope. Place riprap from the toe upward. Where a slope has failed into muck, key a rock berm into virgin ground first and add a subdrain (“ballast sausage”).
  • Air-dump fill at a safe point and push it into the slide with an excavator. Never dump directly onto unstable ground.
  • If there is room uphill, shifting the track about 6 ft and flattening the old shoulder can be the whole fix.
  • Use a smooth-drum compactor on silt and clay backfill; a sheepsfoot roller can liquefy it (Camrose 56.4). Clear ice-plugged culverts before building any structural fix.
  • Never go it alone: check with all agencies and follow environmental rules. Where a third party causes the instability (a hydro dam on the St. Maurice Sub), the cost may shift to them.

PG Sub Mile 445.7 (April 2013) is typical of most slides seen along the track. Snowmelt ran down small gullies, disappeared into the fill, raised pore pressure and took out the embankment. The repair keyed in a toe, rebuilt a 2:1 slope about 50 ft high from air-dumped fill, and added culverts.

Figures · click to zoom

Figure 13-24. Toe berm about 1/3 of slope height on a drainage blanket.
Figure 13-24. Toe berm about 1/3 of slope height on a drainage blanket.
Figure 13-25. A counter berm; a flat plateau is enough.
Figure 13-25. A counter berm; a flat plateau is enough.
Figure 13-26. Key rock berm through slide muck with a subdrain.
Figure 13-26. Key rock berm through slide muck with a subdrain.
Figure 13-27. What to avoid: riprap and fill stockpiled at the top of an unstable slope.
Figure 13-27. What to avoid: riprap and fill stockpiled at the top of an unstable slope.
Figure 13-28. Air-dump cars unloading fill for slope reconstruction.
Figure 13-28. Air-dump cars unloading fill for slope reconstruction.
Figure 13-29. A proposed 6-ft track shift away from a slide.
Figure 13-29. A proposed 6-ft track shift away from a slide.
Figure 13-30. What not to do: sheepsfoot roller on saturated silt and clay.
Figure 13-30. What not to do: sheepsfoot roller on saturated silt and clay.
Figure 13-31. Work train delivering rock fill to a slope repair.
Figure 13-31. Work train delivering rock fill to a slope repair.

After Geotechnology for Railroaders Program, Module 6.1, Module 7.1; Module 6.1 §02–04; Module 7.1 §05. Full reference under Supplemental Sources.

Project management · Swearingen (n.d.)

PERT Three-Point Estimates and the Probability of Finishing a Slope Repair Before a Deadline

PERT handles uncertain durations by asking for three estimates per activity: optimistic a, most likely m and pessimistic b. A beta distribution gives the expected time t = (a + 4m + b) ÷ 6 and variance σ² = [(b − a) ÷ 6]². A forward pass gives the early start and finish (ES = largest EF of the predecessors; EF = ES + t), and a backward pass gives the late times (LF = smallest LS of the successors; LS = LF − t). Slack is LS − ES; activities with zero slack form the critical path. Project variance is the sum of the variances of the critical activities. Treating completion time as normally distributed, the probability of finishing by deadline D follows from Z = (D − T) ÷ σ.

Table 13-PM1. Worked example time estimates, weeks (after Swearingen n.d., slide PMT-17)

Activityambtσ²Slack
A12320.110
B23430.111
C12320.110
D24640.441
E14741.000
F12931.786
G341151.780
H12320.110

In the slides’ example, a foundry has 16 weeks to install a pollution-control system. The critical path A–C–E–G–H gives T = 15 weeks with variance 3.11, so σ = 1.76 weeks. Then Z = (16 − 15) ÷ 1.76 = 0.57, which corresponds to about a 71.6% chance of meeting the deadline.

For railroad work: slope repairs often have to be finished before a wet season, a freeze-up or a planned outage. Use wide pessimistic estimates for activities controlled by subsurface conditions, such as soldier pile or anchor drilling in uncertain rock, dewatering, or excavation below the slide plane. Use narrow ranges for routine tasks. If the computed probability is low, change the plan (more rigs, a second shift, a staged repair that restores track first) instead of only reporting the risk. The method assumes a single critical path. Where a near-critical path also carries large variance, the true chance of finishing on time is lower than the calculation shows, so check those paths as well.

Activity-on-node network for the worked example with early and late times; the critical path A–C–E–G–H totals 15 weeks.
Figure 13-PM1. Activity-on-node network for the worked example with early and late times; the critical path A–C–E–G–H totals 15 weeks. Source: Swearingen (n.d.), Slide PMT-30.

Source: Swearingen, J. (n.d.). The Basics of Project Management Techniques [lecture slides PMT-1 to PMT-40; author from document properties], slides PMT-13 to PMT-34. Summarized and paraphrased; figures reproduced for internal reference. Full reference under Supplemental Sources.

Project management · Cretu et al. (2011)

Eliciting Expert Ranges: Overconfidence, Anchoring and Motivational Bias

Slope design relies on expert judgment wherever data are thin, for example in the location of the failure surface, residual strength, piezometric level or the effect of a drainage fix. Cretu et al. summarize the cognitive biases that distort such judgments and how a facilitator can counter them. The overconfidence effect is the tendency to give ranges that are too narrow. One study they cite asked seven very experienced geotechnical engineers to bracket the embankment height that would fail a clay foundation, using bounds intended to have a 50 percent chance of containing the true value. None of the seven ranges captured the actual failure height. Anchoring means that the first number spoken pulls later estimates toward it. Availability means that vivid recent events seem more probable than they are. Motivational bias covers people shading estimates to protect a past position, a budget or a client relationship, and subordinates deferring to superiors in the room. Optimism bias covers people underrating threats on projects they control.

The authors give these countermeasures. Explain the biases to the group before eliciting values. Ask for the worst credible outcome first, then the best case (which may not be “nothing”), then the most likely. Push explicitly for wider bounds. Collect estimates from junior staff or consultants separately and present them to management anonymously. Show the resulting distribution on screen so the experts can confirm that it says what they meant. Base estimates on personal experience, lessons learned, outside expert opinion and empirical records, and use the empirical records first when they exist.

For railroad work: When back-analysis or design inputs rest on judgment, run a short structured elicitation and document it. This applies to the depth of a slip surface between inclinometer readings, the residual friction angle of a slickensided clay, or the water level to assume for a ditch-line slide. Ask for the worst credible case first, record low/most-likely/high values with their reasons, and carry the full range into sensitivity or probabilistic stability runs. A single “engineering judgment” value tends to understate the uncertainty in the factor of safety. Railroad staff who have watched a site for years are valuable sources. Interview them separately from their managers, and treat their recollection of the last movement as an anchor to test, not a bound.

Source: Cretu, O., Stewart, R. and Berends, T. (2011). Risk Management for Design and Construction. Hoboken, NJ: John Wiley & Sons, pp. 111–121. Summarized and paraphrased. Full reference under Supplemental Sources.

Project management · Jacob and Müller (2017)

Repricing Changed Work from the Original Bid Build-Up

Jacob and Müller show how a change is priced when the work as bid cannot be performed as described. The approach is not to negotiate a new lump sum. Instead, the original bid calculation is reopened, and only the parts of the item that changed are replaced. The original surcharge rates are kept.

In their example, half of a 131,000 CY excavate-haul-place item (65,400 CY) turns out to be contaminated. That portion must go to an owner-designated disposal site instead of into the on-site fill. The changed item is rebuilt as follows:

  • loading stays, but at 70% of the original productivity, which raises the excavator cost per CY by 43%;
  • the on-site haul is replaced by an external haul quote that includes weighing and road fees;
  • placement and compaction are removed;
  • fine grading is unchanged;
  • the original 20% surcharges are applied.

The new unit price came out about 3% above the original. The change can be paid either as a new item or as a price difference applied to the affected quantity. The authors prefer the difference method, because it shows exactly which costs were added and which were dropped.

They also list follow-on effects that may need their own pricing:

  • more testing;
  • more surveying and billing, because the quantity has to be measured in two parts;
  • import of replacement fill for the volume that is no longer placed;
  • a possible productivity loss on the remaining uncontaminated material.

Underlying this is their split between time-variable and time-fixed site costs.

  • Time-variable costs include equipment ownership and standby, site supervision, site offices and traffic control. They grow with duration.
  • Time-fixed costs include mobilization, setup and removal of facilities, engineering, testing and waste disposal. They do not grow with duration.

Keeping the two separate in the estimate is what makes delay and disruption costs calculable later.

For railroad work: Embankment and slide repairs regularly reveal conditions that change the work after award. Examples are contaminated or fouled-ballast spoil that cannot be reused, deeper failure surfaces, and wet borrow. Repricing from the contractor’s bid build-up only works if the contract requires that build-up to be submitted or escrowed. It also needs bid items split finely enough (excavation, haul, placement, disposal) to be reopened. For delay caused by lost track windows or a slower restoration of track speed, price the time-variable site costs per day in advance. That gives the railroad and contractor an agreed basis for standby and extension costs.

Source: Jacob, D. and Müller, C. (Eds.) (2017). Estimating in Heavy Construction: Roads, Bridges, Tunnels, Foundations. Berlin: Ernst & Sohn, pp. 12–14, 205–208. Summarized and paraphrased. Full reference under Supplemental Sources.

Project management · Pratt (2011)

Quantifying a Slide Repair: Section and Grid Methods for Cut and Fill

Pratt sets two rules for measuring earthwork. First, measure in bank measure: the actual in-place dimensions, with no allowance for swell or compaction. Those factors are applied later, when the work is priced. Second, keep each excavation category and each material separate, and measure disposal of surplus as total excavation minus common backfill.

He gives two manual methods for volumes. The grid method takes the cut or fill depth at each grid node and weights it by the area that node represents: one quarter-cell at a corner, two on an edge, and four in the interior. The section method suits long, narrow work such as road and railroad construction. Cross sections are plotted at regular stations, the cut and fill areas are measured at each section, and the volumes come from the average-end-area relation:

V = station spacing × (A1/2 + AN/2 + sum of the intermediate areas)

His example uses five stations 20 ft apart. The cut areas are 108, 40, 73, 91 and 0 ft², and the fill areas are 245, 248, 195, 195 and 328 ft². That gives 5,160 ft³ (191 CY) of cut and 18,490 ft³ (685 CY) of fill. All the cut is reused, so about 494 CY of fill must be imported. Accuracy depends mainly on how faithfully the section profiles are plotted, and closer station spacing improves it.

For railroad work: a slide or washout repair is a short, long-and-narrow job of exactly this kind. A reasonable procedure is:

  1. Cut sections perpendicular to the track at a regular spacing from the survey or LiDAR surface. Add extra sections at the head scarp, the toe and any culvert.
  2. On each section, plot the existing ground, the interpreted slip surface, and the repair geometry: removal limits, keyway, benches and buttress.
  3. Tabulate the areas separately for removal of slide debris, excavation into competent material for the key, granular buttress or rock fill, and select embankment fill.

Each material has its own swell and compaction behavior and its own haul. Report the volumes in bank measure, state the section spacing and the survey date, and keep the section sheets in the calculation appendix. A slide that is still moving changes the existing-ground line, so the quantities will need updating before the bid.

Pratt’s section-method example: plan contours and cross sections at 20-ft stations, each annotated with its cut and fill area.
Figure 13-PM2. Pratt’s section-method example: plan contours and cross sections at 20-ft stations, each annotated with its cut and fill area. Source: Pratt (2011), Figure 4.3.

Source: Pratt, D. J. (2011). Fundamentals of Construction Estimating, 3rd ed. Clifton Park, NY: Delmar Cengage Learning, pp. 57, 59–64. Summarized and paraphrased; figures reproduced for internal reference. Full reference under Supplemental Sources.

13.13 Slope Stability Analysis Checklist

Checklist · Part VI · Geotechnical Analysis

Slope Stability Analysis Checklist

Pre-Analysis0 of 6
Analysis Execution0 of 8
Deliverables0 of 7
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Plain text version

Pre-Analysis

  • [ ] Collect strength parameters: c', φ', s_u by layer from Chapter 10 lab data
  • [ ] Identify slickensides in boring core → require residual strength analysis
  • [ ] Determine groundwater conditions: FEWL/SWL; piezometric levels (Chapter 9)
  • [ ] Identify rapid drawdown potential (river crossings; seasonal flooding)
  • [ ] Confirm seismic hazard zone (USGS maps); determine a_max and k_h
  • [ ] Compute tension crack depth for all cohesive cuts and embankments

Analysis Execution

  • [ ] Select appropriate method: Bishop (circular), Janbu (non-circular), or both
  • [ ] Input correct unit weights (total above WT, buoyant below WT)
  • [ ] Apply pore pressure: measured piezometer heads or r_u coefficient
  • [ ] Include tension crack with water-filled assumption
  • [ ] Run end-of-construction (undrained), long-term static (drained), seepage, drawdown
  • [ ] Run pseudo-static seismic analysis where k_h ≥ 0.05g
  • [ ] For clay shale: run residual strength analysis separately; document φ'_r source
  • [ ] Search critical failure surface — minimum 200 trial circles or non-circular search

Deliverables

  • [ ] Tabulate FS for all required loading conditions (Table 13-1 minimum FS)
  • [ ] Provide cross-section with critical failure surface plotted
  • [ ] Include tension crack location and water-filled force in output
  • [ ] Staged construction plan with trigger criteria (if EOC FS < minimum)
  • [ ] Instrumentation plan (settlement plates, piezometers, inclinometers) — Chapter 15
  • [ ] SLOPE/W or SLIDE output file submitted electronically per Amtrak ES / NSR ESM
  • [ ] Peer review coordination memo (NSR ESM if FS < 1.7; Amtrak ES all slopes > 15 ft)
13.14 Practice Questions and Full Answers

Question 8.1 Define the four primary failure modes for railroad slopes and describe which analysis method is most appropriate for each.

Answer: (1) Rotational circular slide — homogeneous or layered cohesive soil; Bishop Simplified or Spencer method for circular surface search. (2) Translational planar slide — failure along a discrete weak plane (bedding, shale parting, geosynthetic); infinite slope method (shallow, parallel to slope) or Janbu with a specified planar surface. (3) Compound/non-circular slide — failure surface transitions through weak layer; Janbu Generalized or Morgenstern-Price for full rigor. (4) Progressive failure — strain-softening clay or clay shale reduces mobilized strength from peak to residual over time; use Bishop or Janbu with residual strength parameters (c'_r, φ'_r from ring shear test). USACE EM 1110-2-1902 requires that the analysis method be justified in the geotechnical report based on the failure surface geometry expected for the site conditions.

Question 8.2 A railroad embankment has s_u = 500 psf in the soft foundation clay, γ_fill = 118 pcf, and a proposed fill height of 10 ft with 2H:1V slopes (β = 26.6°). Using Taylor's stability number N_s = 5.52, compute the undrained FS at end of construction. Does this meet BNSF EI's EOC minimum of FS ≥ 1.4?

Answer:

FS = Ns · su / (γfill · H)

= 5.52 × 500 / (118 × 10)

= 2,760 / 1,180

= 2.34 ≥ 1.4 ✓

Yes, FS = 2.34 comfortably meets the BNSF EI minimum. The critical check occurs if the foundation s_u were lower; for FS = 1.4, minimum s_u = 1.4 × 1,180 / 5.52 = 299 psf. CPTu soundings should confirm s_u > 300 psf throughout the foundation zone before assuming this slope geometry is adequate.

Question 8.3 Explain the difference between peak and residual shear strength and why CPKC TS requires residual strength analysis for all clay shale cut slopes.

Answer: Peak shear strength is the maximum strength the soil can mobilize before significant displacement has occurred, corresponding to the intact structure of the clay mineral fabric. After large displacements (typically > 0.5–2 in. for clay shales), clay platelets reorient parallel to the failure plane, reducing strength to the residual — the absolute minimum drained shear strength. For clay shales, φ' drops from 20°–28° (peak) to 6°–14° (residual). A cut slope analyzed at peak strength may appear stable at FS = 1.8, yet fail within months to years as swelling and progressive straining reduce mobilized strength to residual and FS drops below 1.0. CPKC's Saskatchewan mainline passes through extensive Cretaceous clay shale belts where this mechanism has caused repeated cut slope failures. CPKC TS mandates residual strength design to ensure that slopes will remain stable through their design life without progressive failure, not just immediately after excavation.

Question 8.4 A 30-ft high railroad cut slope in saturated clay (c' = 150 psf, φ' = 18°, γ = 122 pcf) has a tension crack at the crest. Compute the theoretical tension crack depth and the water pressure force per foot of slope width if the crack is fully water-filled.

Answer:

Tension crack depth (Eq. 13-8 for general case):

Water pressure force in tension crack (Eq. 13-9):

This 354 lb/ft horizontal force is added to the driving force in the slope stability analysis. For a 30-ft cut, this adds approximately 354/(122×30) = 0.10 to the driving stress ratio — not trivial. USACE EM 1110-2-1902 and NSR ESM both require this to be included for cohesive cut slopes.

Question 8.5 What is the pseudo-static horizontal coefficient k_h for a site with a_max = 0.25g, and what is the corresponding horizontal seismic force on a failure mass weighing 45,000 lb/ft? Does the resulting FS = 1.05 meet BNSF EI's seismic stability requirement?

Answer:

USACE EM 1110-2-1902 recommends k_h = 0.5 × a_max/g for pseudo-static analysis:

kh = 0.5 × 0.25 = 0.125

Feq = kh × W = 0.125 × 45,000 = 5,625 lb/ft

BNSF EI requires FS ≥ 1.1 for pseudo-static seismic analysis. The computed FS = 1.05 < 1.1 — this does not meet BNSF EI's requirement. Mitigation options include: (a) flatten the slope from the current geometry to increase resistance; (b) install a rock-fill toe berm to extend the failure surface and add resistance; (c) install deep drainage to reduce pore pressures and increase effective stress; or (d) install ground anchors or soil nails (Chapter 16). The geotechnical report must identify the governing seismic condition and recommend the most cost-effective mitigation for BNSF's review.

13.15 Cross-References
TopicChapter
Shear strength parameters (c', φ', su) from lab testingChapter 10
VST and CPTu undrained strength for soft foundation clayChapter 7
Soil classification for strength assignmentChapter 8
Groundwater and pore pressure data for slope analysisChapter 9
Settlement of consolidating embankment during staged constructionChapter 12
Seismic hazard, amax, and site amplification factorsChapter 14
Ground improvement for embankment stability (PVDs, DSM, stone columns)Chapter 17
Retaining wall design at slope toe or crestChapter 16
Slope failure at track subgrade — failure mode identificationChapter 2
Instrumentation: inclinometers, settlement plates, piezometersChapter 15
Slope stability documentation in geotechnical reportsAppendix E
Ring shear, triaxial, and direct shear test interpretationChapter 10
13.16 Case Studies

Field case studies by Burt G. Look, from Earthworks: Theory to Practice – Design and Construction (CRC Press/Balkema, 2023), chosen for this chapter’s topics. Each is summarized from the book with its key figures and a closing note on railroad application added by the authors of this manual. Credit for the case material belongs to Look; see item S10 under Supplemental Sources.

Case Study 13.16.1 — Flood drawdown failures along the Brisbane River
Case study · Look (2023) §9.7

Related section: 13.8 Rapid Drawdown Analysis

Look and Thorley (2011) studied riverbank failures in Brisbane during the 2011 floods. The annual probability of flood-induced riverbank failure was 2.7 × 10−3, with a further 1.25 × 10−3 for erosion-related failures. Because the floods submerged much of the alluvial bank, drawdown failures should recur at a similar rate with each comparable event. No deaths or injuries came from riverbank failures in 2011, or in the comparable 1974 flood.

The mechanism was sudden drawdown after the flood peak: excess pore pressure remained in the bank while strength softened, so the failure line fell as the load rose.

A practical lesson came from the council’s lead engineer. Traffic was stopped on the six-lane road along the top of the banks to unload the crest, and the emergency crews then parked their vehicles on the empty road, replacing moving traffic with static load.

For railroad work: the post-flood period is when river-bank and embankment-toe slides develop, so inspections should continue through the recession, not stop at the peak. If a crest is being unloaded, the instruction has to cover equipment staging, and train restrictions should not be replaced with parked work equipment.

Stress path for riverbank failure: softening lowers the failure line while rapid drawdown raises the stress, with excess pore pressure.
Figure 13-LK1. Stress path for riverbank failure: softening lowers the failure line while rapid drawdown raises the stress, with excess pore pressure. Source: Look (2023), Figure 9.8-2, p. 305.

Source: Look, B. G. (2023). Earthworks: Theory to Practice – Design and Construction. CRC Press/Balkema. Case study §9.7, pp. 302–304. Summarized and paraphrased; figures reproduced for internal reference. Full reference under Supplemental Sources.

Author and Sources

Authors: Daniel P. Colwell and Mario Ruel. This chapter was written and compiled by Daniel P. Colwell and Mario Ruel for Railway Ground Hazard Risk Management.

Technical content is drawn from the published sources below, and credit for that material belongs to their authors and publishers. Tables, equations and figures taken from a specific source are also cited where they appear.

Primary sources

  • USACE EM 1110-1-1804, Geotechnical Investigations (2001)
  • USACE EM 1110-2-1902, Slope Stability
  • AREMA MRE Chapter 1 — embankment design

Supplemental sources (LEVI Library)

  • U.S. Army Corps of Engineers (2003). Slope Stability. EM 1110-2-1902
  • Stark, T. D. et al. (2016). Development and Use of Fully Softened Shear Strength in Slope Stability Analyses, Third Draft. USACE / ASCE FSS Subcommittee
  • Mott MacDonald (2011). The Effects of Railway Traffic on Embankment Stability. RSSB Research Project 1386 (Revised), Rail Safety and Standards Board
  • Wyllie, D. C. and Mah, C. W. (2004). Rock Slope Engineering: Civil and Mining, 4th ed. Spon Press
  • Amend, F. Slope Stabilization with High Tensile Wire Mesh. Geohazards in Transportation in the Appalachian Region Conference, Geobrugg North America
  • Wang, S., Hagan, P. C. and Cao, C. (2016). Advances in Rock-Support and Geotechnical Engineering. Butterworth-Heinemann
  • Look, B. G. (2023). Earthworks: Theory to Practice – Design and Construction. CRC Press/Balkema. Case studies §9.7

File locations for these documents are listed under Supplemental Sources — LEVI Library.

Project management sources

  • Swearingen, J. (n.d.). The Basics of Project Management Techniques [lecture slides PMT-1 to PMT-40; author from document properties]
  • Cretu, O., Stewart, R. and Berends, T. (2011). Risk Management for Design and Construction. Hoboken, NJ: John Wiley & Sons
  • Jacob, D. and Müller, C. (Eds.) (2017). Estimating in Heavy Construction: Roads, Bridges, Tunnels, Foundations. Berlin: Ernst & Sohn
  • Pratt, D. J. (2011). Fundamentals of Construction Estimating, 3rd ed. Clifton Park, NY: Delmar Cengage Learning
Supplemental Sources — LEVI Library

Material in the green “Supplemental reference” boxes throughout this chapter was added from the following documents in the LEVI geotechnical library. Text is summarized or paraphrased; tables are reproduced with their original source noted; figures are reproduced from the cited document for internal reference use. Consult the original document before relying on a value for design. Blocks marked “After Selig & Waters (1994)” summarize item S9 for railroad clients; tables are condensed from the book and its figures are not reproduced. The Case Studies section summarizes case studies from item S10 by Burt G. Look; its figures are reproduced from the book for internal reference use, and the closing “For railroad work” note in each case study is added by the authors of this manual. Blocks tagged “Project management” summarize methods, examples and figures from the project-management, estimating and construction-management books listed here, applied to railroad work; the closing “For railroad work” note in each block is added by the authors of this manual.

  1. U.S. Army Corps of Engineers (2003). Slope Stability. EM 1110-2-1902
  2. Stark, T. D. et al. (2016). Development and Use of Fully Softened Shear Strength in Slope Stability Analyses, Third Draft. USACE / ASCE FSS Subcommittee
  3. Mott MacDonald (2011). The Effects of Railway Traffic on Embankment Stability. RSSB Research Project 1386 (Revised), Rail Safety and Standards Board
  4. Wyllie, D. C. and Mah, C. W. (2004). Rock Slope Engineering: Civil and Mining, 4th ed. Spon Press
  5. Amend, F. Slope Stabilization with High Tensile Wire Mesh. Geohazards in Transportation in the Appalachian Region Conference, Geobrugg North America
  6. Wang, S., Hagan, P. C. and Cao, C. (2016). Advances in Rock-Support and Geotechnical Engineering. Butterworth-Heinemann
  7. Profillidis, V. A. (2014). Railway Management and Engineering, 4th ed. Farnham, UK: Ashgate. Chapters 7–9, 11–13, 16–17, 20 and 22 (track system, mechanical behavior of track, subgrade, sleepers, ballast, transverse effects, maintenance, slab track, electrification foundations, safety)
  8. Benesch. Geotechnology for Railroaders Program, Modules 1–8 (two-day training course reference: risk management, geology and soils, ballast and sub ballast, drainage, slides, slope and subgrade stabilization, scour, rock falls, beaver dams, winter problems, spring thaw, extreme weather, earthquakes). Field photographs and figures from the course; slope stabilization process slides adapted from material by D. Colwell
  9. Selig, E. T. and Waters, J. M. (1994). Track Geotechnology and Substructure Management. London: Thomas Telford. Used on this page: chs. 10 and 11
  10. Look, B. G. (2023). Earthworks: Theory to Practice – Design and Construction. Leiden: CRC Press/Balkema (Taylor & Francis). ISBN 978-1-032-10470-6. Case studies used on this page: §9.7
  11. Swearingen, J. (n.d.). The Basics of Project Management Techniques [lecture slides PMT-1 to PMT-40; author from document properties]. Used on this page for project-management material
  12. Cretu, O., Stewart, R. and Berends, T. (2011). Risk Management for Design and Construction. Hoboken, NJ: John Wiley & Sons. Used on this page for project-management material
  13. Jacob, D. and Müller, C. (Eds.) (2017). Estimating in Heavy Construction: Roads, Bridges, Tunnels, Foundations. Berlin: Ernst & Sohn. Used on this page for project-management material
  14. Pratt, D. J. (2011). Fundamentals of Construction Estimating, 3rd ed. Clifton Park, NY: Delmar Cengage Learning. Used on this page for project-management material
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