Chapter 14 — Seismic Hazard and Liquefaction

Seismic hazard characterization and liquefaction evaluation are critical components of geotechnical services for railroad infrastructure in seismically active regions. Rail corridors operated by UPRR, BNSF, CPKC, CN, and Amtrak traverse some of the highest seismic hazard zones in North America — the Pacific Coast, Cascades, Intermountain West, New Madrid Seismic Zone (NMSZ), and St. Lawrence Valley. Even apparently moderate-seismicity regions crossed by NSR, CSXT, and G&W require assessment for NMSZ influence and localized fault activity.

This chapter provides the analytical framework for: (1) characterizing probabilistic seismic hazard using USGS national hazard maps; (2) classifying site response using V_S30 and ASCE 7 / AASHTO site categories; (3) evaluating liquefaction triggering potential using the Seed-Idriss Simplified Procedure for both SPT and CPT data; (4) quantifying post-liquefaction consequences including lateral spreading, seismic settlement, and residual strength loss; (5) performing Newmark sliding block analysis for seismically induced slope deformation; and (6) applying client-specific seismic performance criteria across all nine railroad clients. All equations are presented in English units.

Earthquake damage to railroad infrastructure manifests through several mechanisms: embankment slope failures, liquefaction-induced track settlement and lateral spreading, bridge foundation movement, retaining wall failure, and disrupted drainage producing post-event flooding. The consequences range from temporary slow orders to multi-week line closures with significant freight revenue loss.

Railroad seismic design philosophy differs from building or highway design in several important ways:

• Operational continuity: Class I railroads require rapid return to service following design-level events. UPRR's Seismic Design Criteria define a three-tier performance objective: (1) Frequent Earthquake Event (FEE, 108-yr return period, 50% PE in 72 years) — no significant damage, no service interruption; (2) Design Earthquake (DE, 475-yr return, 10% PE in 50 yr) — repairable damage, service restored within 72 hours; (3) Maximum Considered Earthquake (MCE, 2,475-yr return, 2% PE in 50 yr) — life safety preserved, service restored within 30 days.
• Distributed infrastructure: A single mainline may traverse hundreds of miles of varying geological conditions. Screening-level assessments must efficiently identify critical exposures warranting detailed analysis.
• Track geometry tolerance: FRA track geometry standards (49 CFR Part 213) define allowable surface deviations that translate directly into post-seismic settlement acceptance criteria. Class 4 mainline track (maximum 60 mph freight) allows surface deviation of 3.0 in. over a 62-ft chord; Class 7 (Amtrak NEC, up to 150 mph) allows 0.75 in.
• Bridge approach sensitivity: Settlement differential between bridge-on-pile-foundation and approach embankment on liquefied ground produces the "bump at the end of the bridge" phenomenon at orders of magnitude greater intensity than under static loading.

Supplemental figures · LEVI Library

Seismic isolation of bridges and train protection

Profillidis frames railway seismic risk in two parts. First, structures, track and subgrade are designed for the regional design acceleration (up to about 10 ft/s² in his text) so that nothing collapses even in the most severe event. In zones of very high seismicity, bridges are fully isolated from their supports with dampers (Figure 14-11). Second, trains are protected during an event by trackside accelerometers that stop traffic above 2.1 ft/s² and reduce speed between 1.3 and 2.1 ft/s² (details in Chapter 4, §4.6).

Figures · click to zoom

After Profillidis (2014), §9.17, Fig. 9.22. Full reference under Supplemental Sources.

For seismically induced slope deformation, the Newmark (1965) sliding block method estimates permanent displacement U_d (in.) by integrating the earthquake acceleration record above the critical (yield) acceleration k_y:

Critical (yield) acceleration:

More rigorously, k_y is determined by reducing the pseudo-static coefficient until FS_pseudo = 1.0 in Bishop or Janbu analysis (Chapter 13).

Newmark permanent displacement — Jibson (2007) regression (preferred for engineering practice):

Where U_d is in inches (ln-normal model; reported as median ± 1σ). Alternatively, use Saygili & Rathje (2008) for two-parameter models including PGV.

Thresholds calibrated to FRA Class 4 track geometry. Amtrak NEC thresholds are 50% of values shown.

Reference graphics

Worked Example 14-1: Liquefaction Triggering — SPT Method (UPRR Bridge, Cascades)

Project: UPRR bridge replacement over Willamette River tributary, Oregon. M_w = 7.0 design earthquake (Cascadia Subduction Zone). PGA = 0.38g at Site Class B/C (USGS 475-yr return). Site Class D (V_S30 = 660 ft/s).

Soil profile at critical elevation (z = 20 ft):

• γ_total = 120 pcf; γ_w = 62.4 pcf; WT at z = 5 ft
• σ_v = 120 × 20 = 2,400 psf
• σ'_v = (120 × 5) + (120 − 62.4) × 15 = 600 + 864 = 1,464 psf
• SPT: N_meas = 14 bpm; E_m = 0.72 (donut hammer, rope-and-cathead); C_B = 1.0; C_R = 0.85; C_S = 1.0

Step 1 — N₆₀:

Step 2 — C_N and (N₁)₆₀:

Step 3 — Fines correction (FC = 18%):

Step 4 — CRR₇.₅:

Step 5 — CSR:

Site Class D F_a = 1.2 → S_MS = 1.2 × 0.38g = 0.456g → a_max = 0.456g (used for CSR).

Step 6 — MSF (M_w = 7.0):

Step 7 — FS_L:

Interpretation: FS_L = 0.67 < 1.2 (UPRR DE minimum). Liquefaction mitigation required. Estimated seismic settlement (Tokimatsu & Seed): ε_v ≈ 2.5% for (N₁)₆₀ = 17, H = 15 ft → S_seismic ≈ 0.025 × 15 × 12 = 4.5 in., exceeding UPRR Class 4 allowable. Stone column or deep soil mixing remediation recommended.

Worked Example 14-2: Lateral Spreading — CSXT Bridge Approach, NMSZ

Project: CSXT mainline bridge over Obion River, western Tennessee. M_w = 7.7, R = 18 mi from New Madrid Fault. PGA = 0.62g (475-yr USGS). Free-face condition; W = 15% (levee height = 25 ft; distance = 165 ft).

Liquefiable layer characteristics:

• T₁₅ = 22 ft (layers with (N₁)₆₀ < 15, cumulative)
• F₁₅ = 12% (average fines content)
• D50₁₅ = 0.008 in.

Step 1 — Modified source distance:

Step 2 — log D_H (free-face):

log D_H = -16.713 + 1.532(7.7) - 1.406 log(34.3) - 0.012(18) + 0.592 log(15) + 0.540 log(22) + 3.413 log(88) - 0.795 log(0.108)

Interpretation: Estimated lateral spreading of 32 ft far exceeds the 3 in. threshold for Class 4 track. This finding is consistent with observed NMSZ lateral spreading up to 50 ft in the 1811–1812 events. CSXT requires deep ground improvement (stone columns or vibro-compaction) to T₁₅ = 0 ft, or alternatively deep pile foundation through liquefiable zone with structural approach slab designed for post-liquefaction differential settlement.

Worked Example 14-3: Newmark Analysis — BNSF Embankment, Pacific Northwest

Project: BNSF embankment slope (H = 28 ft, 2H:1V side slope) at MP 142, Columbia River Gorge. Static FS = 1.65 (Bishop Simplified, drained). PGA = 0.35g (DE, 475-yr). k_y determination required.

Step 1 — Critical acceleration k_y:

Reduce pseudo-static k until FS_pseudo = 1.0:

From Bishop analysis with k_h = 0.0: FS = 1.65. Iterative analysis yields FS_pseudo = 1.0 at k_h = 0.21g → k_y = 0.21g

Step 2 — Newmark displacement (Jibson 2007):

Upper bound (median + 1σ): U_d = 10^{-0.391 + 0.510} = 10^{0.119} = 1.32 in.

Interpretation: Median displacement of 0.41 in. is below BNSF's 1.0 in. threshold (Table 14-5). Upper-bound value of 1.32 in. falls in the "Monitor post-event" range. BNSF accepts this performance level for DE event with post-event inspection protocol activated. No remediation required; embankment is added to BNSF's post-seismic inspection priority list.

NC = Non-liquefiable ((N₁)₆₀cs ≥ 30). FS_L values < 1.20 flagged for UPRR DE performance requirement.

Figure 14-1: USGS Seismic Hazard Map — PGA at 2% PE in 50 yr (2,475-yr return), Western United States, showing UPRR/BNSF/CPKC mainline corridors highlighted.

Figure 14-2: CSR vs. CRR triggering chart (Youd et al. 2001 boundary curve) with plotted liquefaction assessment data from Table 14-7 (liquefiable vs. non-liquefiable points labeled by boring).

Figure 14-3: Stress reduction factor r_d vs. depth (ft) showing three-segment piecewise equation and scatter bounds from Liao & Whitman (1986).

Figure 14-4: Magnitude Scaling Factor (MSF) vs. M_w curve with data points from NCEER Working Group 1996 and Idriss (1999) relationship.

Figure 14-5: SPT-based CRR boundary curve with fines content correction — (N₁)₆₀ vs. CSR₇.₅ showing FC = 0%, 15%, and 35% boundary curves.

Figure 14-6: CPT-based SBT chart (Robertson 1990) with liquefaction susceptibility zones and I_c contours overlaid on representative CPTu sounding from UPRR Cascade corridor.

Figure 14-7: Lateral spreading displacement D_H vs. T₁₅ (Youd et al. 2002 model) for NMSZ M_w = 7.7 scenario — CSXT Tennessee corridor risk map.

Figure 14-8: Newmark displacement vs. k_y/PGA ratio — Jibson (2007) median and ±1σ bounds with BNSF Columbia Gorge embankment case plotted.

Figure 14-9: Typical cross-section showing liquefaction remediation layout — stone column grid pattern with T₁₅ layer identified and design depth annotations.

Figure 14-10: Post-liquefaction failure mechanism schematic for bridge approach embankment — lateral spreading toward channel, settlement trough in track zone, and residual strength failure surface.

Reference graphics

1. Conduct seismic screening before detailed investigation. Use USGS Unified Hazard Tool to extract PGA at all bridge and embankment locations before mobilizing rigs. Sites with 475-yr PGA < 0.10g (or 0.07g for Amtrak) are typically screened out of detailed liquefaction analysis. This screening step costs nothing and focuses investigation resources on critical exposures.
2. Sample across the full profile to 50 ft for liquefaction analysis. Shallow SPT refusal on dense layers does not preclude liquefaction in interbedded loose sands at intermediate depths. Continuous SPT at 2.5-ft intervals from the groundwater table to 50 ft or refusal (whichever is deeper) is the minimum acceptable program for DE-level liquefaction analysis at UPRR, BNSF, and Amtrak sites.
3. Pair SPT with CPTu soundings for spatial continuity. SPT provides the direct (N₁)₆₀ value needed for triggering analysis, but CPTu provides vertical resolution of thin liquefiable layers (<3 ft) that SPT's 18-in. sample interval can miss. UPRR and Amtrak require minimum one CPTu per 500 ft of alignment in known liquefiable zones.
4. Include seasonal groundwater in all CSR calculations. WT depth controls σ'_v and therefore CSR. NMSZ sites with shallow seasonal WT (5–10 ft depth in spring) may show FS_L 15–25% lower than the same calculation at summer WT. Report CSR at both conditions; govern on worst case. CSXT ES requires both conditions reported in the GDR.
5. Do not rely on Youd lateral spreading model as sole design input. The Youd MLR model carries ±1 order of magnitude uncertainty (standard deviation σ = 0.51 in log-space). For D_H > 3 ft, supplement with numerical analysis (e.g., FLAC or PLAXIS with PM4Sand constitutive model) to narrow the uncertainty band before finalizing remediation scope.
6. Document post-liquefaction residual strength conservatively. Seed & Harder (1990) lower-bound values are appropriate for safety-critical railroad structures (bridges, retaining walls, major embankments). The upper bound of the s_ur envelope is not appropriate for design and should never be used without explicit railroad client approval.
7. Integrate seismic assessment output into GIS deliverables. UPRR and BNSF both require FS_L and estimated seismic settlement tabulated at milepost resolution with GIS shapefile delivery. Structure the liquefaction summary table to feed directly into the client's infrastructure risk management database, using milepost, latitude/longitude, event return period, and remediation priority as key fields.

Question 9-1: A SPT boring in southern Illinois (NMSZ zone, M_w = 7.7, PGA = 0.50g at rock, Site Class D, F_a = 1.2) shows N_meas = 10 blows/ft at z = 15 ft. Total unit weight γ = 118 pcf; WT at z = 4 ft. Hammer energy E_m = 0.72; C_B = 1.0; C_R = 0.85; C_S = 1.0. FC = 20%. Compute FS_L.

Answer 9-1:

• σ_v = 118 × 15 = 1,770 psf; σ'_v = (118 × 4) + (118 − 62.4) × 11 = 472 + 612 = 1,084 psf
• N₆₀ = 10 × (0.72 × 1.0 × 0.85 × 1.0)/0.60 = 10 × 1.02 = 10.2
• C_N = √(2,117/1,084) = 1.40; (N₁)₆₀ = 1.40 × 10.2 = 14.3
• ΔN = exp[1.63 + 9.7/20.01 − (15.7/20.01)²] = exp[1.63 + 0.485 − 0.616] = exp[1.499] = 4.48
• (N₁)₆₀cs = 14.3 + 4.5 = 18.8
• CRR₇.₅ = 1/(34 − 18.8) + 18.8/135 + 50/[233]² − 1/200 = 0.0658 + 0.139 + 0.001 − 0.005 = 0.201
• a_max = 0.50g × 1.2 = 0.60g; r_d = 1.0 − 0.00765 × 15 = 0.885
• CSR = 0.65 × (1,770/1,084) × 0.60 × 0.885 = 0.65 × 1.633 × 0.531 = 0.564
• MSF (M_w = 7.7) ≈ 10^2.24 / 7.7^2.56 = 173.8/97.6 = 1.78 → Wait: recalculate: 7.7^2.56 = e^(2.56 × ln 7.7) = e^(2.56 × 2.041) = e^5.225 = 186.1; MSF = 173.8/186.1 = 0.934 — note: for M_w > 7.5, MSF < 1.0, meaning higher-magnitude earthquakes generate more cycles and are more damaging; MSF = 0.934.
• CSR₇.₅ = 0.564/0.934 = 0.604 (divided by MSF < 1.0 → increases adjusted CSR, conservative)
• FS_L = 0.201/0.604 = 0.33 → Highly liquefiable. FS_L << 1.2 CSXT minimum. Emergency ground improvement warranted.

Question 9-2: A BNSF site in central Washington has V_S30 = 780 ft/s. What is the ASCE 7-22 site class? If S_S = 1.25g and F_a = 1.0 (Site Class D), what is S_DS?

Answer 9-2:

• V_S30 = 780 ft/s falls between 530 and 850 ft/s → Site Class D (Stiff Soil), ASCE 7-22 Table 20.3-1.
• S_MS = F_a × S_S = 1.0 × 1.25g = 1.25g
• S_DS = (2/3) × 1.25g = 0.833g
• This exceeds BNSF's threshold requiring site-specific ground response analysis for new bridge structures at this site.

Question 9-3: A Amtrak NEC embankment (Class 7 track) overlies 8 ft of loose sand (FS_L = 0.72, (N₁)₆₀ = 9) at z = 10–18 ft. Estimate seismic settlement using Tokimatsu & Seed (1987). Is this acceptable for Amtrak service?

Answer 9-3:

• For (N₁)₆₀ = 9 and FS_L = 0.72 (liquefiable), volumetric strain ε_v ≈ 2.5–3.0% (from Tokimatsu & Seed 1987, Figure 2, for cyclic shear strain γ_c ≈ 2–3%).
• Seismic settlement: S = 0.028 × 8 ft × 12 in./ft ≈ 2.7 in. (using ε_v = 2.8% midpoint).
• Amtrak NEC Class 7 allowable seismic settlement = 0.50 in. (Table 14-5).
• 2.7 in. >> 0.50 in. — Not acceptable. Amtrak ES requires ground improvement (deep soil mixing or grouting) to raise (N₁)₆₀ to ≥ 30 blows/ft. Alternatively, pile-supported track structure (concrete slab track) may be specified to bypass the liquefiable layer.

Question 9-4: A slope at a CPKC Rockies location has k_y = 0.15g and PGA = 0.30g at the DE level. Using Jibson (2007), compute the median Newmark displacement and assess acceptability.

Answer 9-4:

• CPKC DE performance threshold: 1.0 in. (Class 4 mainline per Table 14-5 analog).
• 0.88 in. < 1.0 in. — Acceptable at the median level. Upper bound: 10^(−0.057 + 0.510) = 10^0.453 = 2.84 in., which exceeds the threshold. Recommend post-event inspection protocol and slope instrumentation (inclinometer) per CPKC TS Geohazard Management Program.

Question 9-5: A CPTu sounding at a CSXT Mississippi Delta site shows q_c = 25 tsf (526,000 psf), f_s = 0.30 tsf (6,300 psf), u₂ = 0.04 tsf (840 psf), at z = 12 ft with σ_v = 1,380 psf, σ'_v = 840 psf. Compute I_c (initial iteration, n = 1.0) and assess soil behavior type.

Answer 9-5:

• Correct q_t: q_t = q_c + u₂(1−a) ≈ 526,000 + 840(1−0.80) = 526,000 + 168 ≈ 526,168 psf (a = 0.80 typical; q_t ≈ q_c for this sounding)
• Q_t = [(526,168 − 1,380)/2,117] × (2,117/840)^1.0 = (524,788/2,117) × 2.520 = 247.9 × 2.520 = 624.7 → This is very high, indicating very dense/stiff material or shallow rock.
• F_r = [6,300/(526,168 − 1,380)] × 100 = 6,300/524,788 × 100 = 1.20%

• I_c = 1.46 < 1.64 → Gravelly sand to sand (SBT Zone 7) — non-liquefiable by SBT classification alone. However, F_r = 1.2% and I_c = 1.46 suggest clean to slightly silty sand at very high relative density. (q_c1N)_cs >> 160 → Non-liquefiable. CSXT recommendation: no liquefaction mitigation required at this depth.

End of Chapter 14 — Seismic Hazard and Liquefaction

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)
• ASCE 7-22
• AASHTO Guide Specifications for LRFD Seismic Bridge Design (2011, 2nd ed.)
• Youd, T. L. et al. (2001). Liquefaction resistance of soils. ASCE J. Geotech. Geoenviron. Eng.
• Robertson and Wride (1998); Tokimatsu and Seed (1987); Seed and Harder (1990)

Supplemental sources (LEVI Library)

• Towhata, I. (2008). Geotechnical Earthquake Engineering. Springer
• Elnashai, A. S. and Di Sarno, L. (2008). Fundamentals of Earthquake Engineering. Wiley
• Ooms, M. The Effect of EPS Geofoam Backfill on the Seismic Performance of Integral Abutment Bridges. M.S. thesis, Rutgers University
• Partner Engineering and Science, Inc. Seismic Zone Map of the United States (after the 1997 Uniform Building Code)
• Bolt, B. A., Horn, W. L., Macdonald, G. A. and Scott, R. F. (1977). Geological Hazards: Earthquakes, Tsunamis, Volcanoes, Avalanches, Landslides, Floods, 2nd ed. Springer-Verlag

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