seismic-nuclear

name	seismic-nuclear
description	Nuclear facility seismic analysis — ASCE 4 (seismic analysis of safety-related nuclear structures), ASCE 43 (seismic design criteria for structures, systems, and components), in-structure response spectra (ISRS), floor response spectrum generation, seismic qualification of equipment (IEEE 344, ASME QME-1), fragility analysis, HCLPF capacity, soil-structure interaction (SSI), and 10 CFR 50 Appendix S.
metadata	{"priority":7,"promptSignals":{"phrases":["seismic nuclear","nuclear seismic","floor response spectrum","in-structure response spectra","ISRS","seismic qualification nuclear"],"minScore":3}}

Nuclear Facility Seismic Analysis — Complete Skill

Regulatory Framework

US Nuclear Regulatory Commission (NRC) Requirements

10 CFR 50 Appendix A — General Design Criteria: GDC 2: Design bases for protection against natural phenomena (earthquakes) GDC 4: Environmental and dynamic effects design bases

10 CFR 50 Appendix S — Earthquake Engineering Criteria: Design Basis Earthquake (DBE) = Safe Shutdown Earthquake (SSE) — 84th percentile; 1/2,500 yr return Operating Basis Earthquake (OBE): typically 1/2 × SSE (or site-specific) If OBE < 1/3 SSE → NRC allows elimination of OBE from design basis (fatigue not governing)

10 CFR 100 Appendix A: site suitability — defines SSE as Maximum Credible Earthquake

USNRC Regulatory Guides: RG 1.60: Design response spectra for nuclear power plants (standard smooth spectra; anchored to PGA) RG 1.92: Combination of modal responses and spatial components (SRSS, CQC rules) RG 1.122: Development of floor response spectra RG 1.208: Performance-based approach to define SSE (new plants)

Design Standards

ASCE 4: Seismic Analysis of Safety-Related Nuclear Structures and Commentary ASCE 43: Seismic Design Criteria for Structures, Systems, and Components in Nuclear Facilities

ASCE 43 Seismic Design Categories (SDC) and Limit States:

SDC	Performance Goal (HCLPF)	Limit State
SDC-3	1×10⁻⁴/yr	Significant damage (LS-D)
SDC-4	4×10⁻⁵/yr	Controlled damage (LS-C)
SDC-5	1×10⁻⁵/yr	Essentially elastic (LS-B)

HCLPF = High Confidence of Low Probability of Failure (0.95 confidence of <5% failure probability)

Seismic Input Motion

Design Response Spectra

RG 1.60 spectra (horizontal): Anchored to PGA (a_g); peak spectral acceleration at 0.1–0.5 s = 2.5 × a_g (standard shape) Spectra covers 0.1–33 Hz (T = 0.03–10 s); damping: 5% standard (7% for heavy damping systems)

Site-specific PSHA spectra (new plants, RG 1.208): Probabilistic Seismic Hazard Analysis → Uniform Hazard Spectra (UHS) at 10⁻⁴/yr and 10⁻⁵/yr Conditional Mean Spectrum (CMS) for time history selection Vertical spectra: typically 2/3 × horizontal for rock sites; 1/2 for soft soil

Time history input: 3 pairs of horizontal + 1 vertical; statistically independent; spectrum-compatible Criteria: within ±10% of target spectrum from 0.5T₁ to 1.25T₁ (T₁ = fundamental period) ASCE 4 Section 3.2: minimum 3 time histories; use average or maximum for design

In-Structure Response Spectra (ISRS) / Floor Response Spectra

Generation Method

ISRS: response spectra at floor/elevation levels of structure; input to equipment qualification

Method 1 — Time History Analysis:

1. Apply site ground motion time history to base of structure model
2. Calculate acceleration time history at each floor
3. Compute response spectrum from floor acceleration history
4. ISRS = envelope of spectra from multiple ground motions

Method 2 — Direct Spectral Method (ASCE 4 Section 3.3): S_f(ω_e) = H(ω_e) × S_g(ω_e) [S_f = floor spectrum; S_g = ground spectrum; H = structural transfer function] For lightly damped structures: peak floor spectrum near structural frequencies amplified by: A_peak / S_g(ω_structure) ≈ ζ_structure + ζ_equipment) / (ζ_structure) × SD at structural freq.

Peak broadening: ISRS peaks are broadened ±15% of frequency (ASCE 4 / RG 1.122) to account for frequency uncertainty Results in wider peaks; equipment must remain qualified over broadened range

Critical ISRS amplification at structural resonance: If equipment frequency ≈ structure frequency: amplification = (1 + β_structure)/(β_structure × β_equipment) × β_equipment For 5% structural damping, 2% equipment: peak ISRS ≈ 5× ground input at that frequency

Envelope for in-structure spectra: For multiple soil cases or ground motions → envelope all spectra → single bounding ISRS for qualification

Structural Analysis Methods

Equivalent Static Analysis

For simple, regular structures only: F_lateral = C_s × W [C_s = seismic coefficient = S_DS/R × I_e for non-nuclear] Nuclear: use ASCE 4 Section 3.3.1; vertical distribution per ASCE 7 (triangular or mode-based) Typically not adequate for nuclear safety-related structures — dynamic required

Response Spectrum Analysis (RSA)

Modal combination rules (RG 1.92): SRSS: S_total = √Σ S_i² [used when all modal frequencies well separated, Δf > 10%] CQC: S_total = √(Σ Σ ρ_ij × S_i × S_j) [for closely spaced modes; ρ_ij = cross-modal coefficient] ρ_ij = 8√(ζ_i × ζ_j) × (ζ_i + r_ij × ζ_j) × r_ij^(3/2) / [(1 - r_ij²)² + 4ζ_iζ_j×r_ij×(1+r_ij²) + 4(ζ_i² + ζ_j²)×r_ij²] [r_ij = ω_j/ω_i]

Spatial combination (3 directions): SRSS: S_total = √(Sx² + Sy² + Sz²) [RG 1.92 Method 1] or 100-40-40: S = ±1.0×Sx ± 0.4×Sy ± 0.4×Sz [take worst combination; RG 1.92 Method 2]

Number of modes: Include sufficient modes to capture ≥ 90% mass participation in each direction Residual rigid response: for modes above ZPA frequency (≥ 33 Hz) — apply algebraically

Time History Analysis (THA)

Direct integration: Newmark β method (β = 0.25, γ = 0.5 for average acceleration; unconditionally stable) α-HHT or Hilber-Hughes-Taylor for better numerical dissipation of high-frequency noise Time step: Δt ≤ T_min / 20 (smallest period of interest); typically 0.002–0.005 s

Nonlinear THA required for: Soil-structure interaction (SSI) in time domain Friction, gap, rocking elements Sliding isolation systems

Soil-Structure Interaction (SSI)

Approaches

Direct Method (coupled): Model soil as finite elements + structure; apply DRM (Domain Reduction Method) or transmitting boundaries Nonlinear soil: equivalent linear (SHAKE2000) or fully nonlinear (FLAC3D, OpenSees) Best accuracy; computationally expensive

Substructure Method (ASCE 4 Section 3.4):

1. Compute foundation impedance functions K(ω) = K_R + iω × C [stiffness + radiation damping]
2. Compute scattering motion (kinematic interaction — input motion to foundation differs from free-field)
3. Apply foundation input motion to structure with soil springs K_R and dashpots C

Foundation impedance functions (surface or embedded circular foundation): K_v = 4GR/(1-ν) [vertical spring; G = shear modulus; R = foundation radius; ν = Poisson] K_h = 8GR/(2-ν) [horizontal] K_r = 8GR³/(3(1-ν)) [rocking] Radiation damping: C_v = 3.4R²ρV_s/(1-ν); C_h = 4.6R²ρV_s/(2-ν) [ρ = soil density; V_s = shear wave speed]

Layered soil: CLASSI, SASSI2010, SASSI-H software; frequency-dependent impedance from half-space solution

Seismic Qualification of Equipment and Components

Qualification Methods (IEEE 344, ASME QME-1)

Method 1 — Analysis: Static: apply equivalent static force F = a_g × W × K_am [K_am = amplification factor; typically 1.5–3.0] Dynamic: model equipment; apply ISRS; verify stresses/functionality Applicable for simple geometry; conservative for complex equipment

Method 2 — Shake Table Testing (IEEE 344): Subject equipment to test response spectra (TRS) ≥ Required Response Spectra (RRS) RRS = ISRS × amplification (typically ISRS × 1.0 with some margin) TRS must envelop RRS from 1.1–33 Hz Equipment must function before, during, and after test (active/passive classification)

Method 3 — Comparison to Experience Data: Use SQUG (Seismic Qualification Utility Group) experience database Equipment demonstrated to function at historical earthquake shaking (if in experience data) Caveat verification checklist: anchorage, spatial interaction, proximity to other equipment

Seismic Category I equipment: safety-related; must maintain function during/after SSE Seismic Category II: not safety-related but could affect Cat I if it falls; qualified to not collapse

Fragility Analysis (ASCE 43, EPRI NP-6728)

Fragility Curve Parameterization

Lognormal fragility model: F(a) = Φ[(ln(a/A_m)) / β_c] [probability of failure vs. peak ground acceleration a] A_m = median capacity [g]; β_c = composite logarithmic standard deviation

Composite uncertainty: β_c = √(β_R² + β_U²) [β_R = randomness (aleatory); β_U = uncertainty (epistemic)] Typical: β_R = 0.20–0.35; β_U = 0.20–0.35; β_c = 0.30–0.50

HCLPF (High Confidence of Low Probability of Failure): HCLPF = A_m × exp(-1.65 × β_c) [5% failure probability at 95% confidence] Or equivalently: HCLPF = A_m × exp(-2.326 × β_c) [1% fail at 95% — less common definition] Typical HCLPF for well-designed structures: 0.5–2.0g PGA

Capacity estimation: A_m = R × F_Sa [R = capacity-to-demand ratio from code design; F_Sa = demand at design point] R = SR × SF [SR = strength ratio from material; SF = ductility factor; typical R = 2.0–5.0]

Standards and References

Standard	Scope
ASCE 4-16	Seismic analysis of safety-related nuclear structures
ASCE 43-05	Seismic design criteria for nuclear SSCs
IEEE 344-2013	Seismic qualification of equipment for nuclear power plants
ASME QME-1	Qualification of active mechanical equipment
10 CFR 50 Appendix S	NRC seismic criteria (new plants)
NUREG-0800 SRP 3.7	NRC Standard Review Plan — seismic analysis
EPRI NP-6728	Seismic fragility of nuclear power plant structures

Output

Provide: facility type (NPP/research reactor/fuel facility; regulatory basis: 10 CFR 50 or equivalent), seismic hazard (SSE/DBE PGA [g]; spectral accelerations from PSHA or RG 1.60; site class; soil profile), structural model (fixed-base frequencies [Hz]; mode shapes; mass participation %; soil-structure interaction: method used), ISRS generation (method: TH or direct spectral; elevations analyzed; peak ISRS [g] at equipment mounting levels; frequency broadening applied ±15%), modal combination (SRSS/CQC; closely spaced modes threshold; spatial combination rule: SRSS or 100-40-40), member demands (maximum shear, moment, axial [kN, kN·m]; comparison with capacity; D/C ratio), equipment qualification (method: analysis/shake table/experience; RRS from ISRS; TRS vs. RRS check; functionality verified), SSI effects (if included: foundation impedance K_R [kN/m], C; kinematic interaction; base mat flexibility), fragility (A_m [g]; β_c; HCLPF [g]; SDC target HCLPF comparison), and applicable standard (ASCE 4/43; IEEE 344; 10 CFR 50 Appendix S; NUREG-0800).