Home / Tools / Missile Barrier N · Protective

Concrete Barrier Against Hard-Missile Impact — Penetration, Scabbing, Perforation

Required reinforced-concrete barrier thickness against a non-deforming missile, by the nuclear-safety design methods: modified NDRC penetration (Kennedy 1976), Chang scabbing and Degen perforation (the NEI 07-13 / DOE-STD-3014 set), with NDRC/ACE and CEA-EDF for comparison and a code-dependent design factor. For protective design of shelters, barriers and nuclear-plant structures.

Missile

Mass M kg

Diameter d m

Impact velocity V₀ m/s

Nose shape (N)

Barrier

f′c MPa

Concrete density kg/m³

Barrier thickness H (optional) m

Design factor

High-strength / UHPC (f′c above calibration)

Design formula set

Results

NDRC G · branch · N—

Penetration depth x (x/d)—

Required thickness (with design factor)—

Parça çapraz kontrolü (v526)Bu aracın Kennedy-NDRC uygulaması, UFC 3-340-02'nin standart birincil parça denklemleriyle (Dusenberry (ed.) 2010, Denk. 8.28–8.29; 4 000 psi) karşılaştırıldı: UFC denklemleri %7–12 daha derin penetrasyon verir (daha muhafazakâr; NDRC saçılımı ±%25 içinde). Kitabın ağırlık biçimli denklemleri parça ağırlığını ONS cinsinden ister. Kitabın √(4 000/f′c) dayanım düzeltmesi derin penetrasyonda NDRC ile tutarlı, sığ penetrasyonda fazla güçlüdür (yüksek dayanımlı betonda sığ penetrasyonu küçük gösterir).

NDRCG = 3.8×10⁻⁵·N·M/(d·√f′c)·(V₀/d)^1.8 with f′c in Pa; x/d = 2√G for G ≤ 1, G + 1 for G > 1 (one review prints this inequality inverted).

Scabbing / perforationNDRC/ACE: h_s/d = 7.91x/d − 5.06(x/d)² (x/d ≤ 0.65), 2.12 + 1.36x/d; e/d = 3.19x/d − 0.718(x/d)² (x/d ≤ 1.35), 1.32 + 1.24x/d. Degen: e/d = 2.2x/d − 0.3(x/d)² (x/d < 1.52), 0.69 + 1.29x/d. Chang: e/d = (61/V₀)^0.25(MV₀²/(d³f′c))^0.5, h_s/d = 1.84(61/V₀)^0.13(MV₀²/(d³f′c))^0.4. CEA-EDF: e/d = 0.82M^0.5V₀^0.75/(ρ_c^0.125f′c^0.375d^1.5).

VerifyNuScale turbine-missile barrier (NRC submittal): t_s 26.1 → 31.3 in, t_p 22.9 → 27.5 in — reproduced. EPRI/Calspan pipe tests (MCEER-17-0004): NDRC predicted/measured ratios reproduced with flat nose N = 0.72. IRIS P1 (0.25 m slab, 136 m/s): every formula predicts perforation, as observed. Main source: Li, Reid, Wen & Telford (2005), Int. J. Impact Eng. 32:224–284.

UHPCThe formulas are calibrated for normal-strength concrete. Above the limit the calculation uses the limit strength by default (no credit for high-strength or UHPC). Evidence is regime-dependent: shallow-impact tests (same projectile, 41–162 MPa) show penetration falling as f′c^−0.43, faster than the f′c^−0.25 of NDRC, so NDRC is conservative there; one deep-penetration UHPC data set (160 MPa) shows the opposite and remains unresolved.

AccuracyNo empirical formula is better than about ±20–40% (Sliter 1980: NDRC ±25% for x/d > 0.6) — hence the design factor and the envelope option.

Visual explanation

Penetration resistance: UHPC versus normal concrete. Steel-fibre UHPC shows much shallower penetration and less rear-face damage; thinner protection suffices — **Figure 50.** Penetration resistance: UHPC versus normal concreteSource: Modified NDRC (C30, C80); Máca et al. (2014) UHPFRC trends. UHPC fibre factor is representative.

Required protective thickness against hard-missile impact. Modified NDRC limits: penetration, perforation and scabbing; the scabbing limit governs the protected volume — **Figure 52.** Required protective thickness against hard-missile impactSource: Kennedy (1976); Li et al. (2005). Computed for a reference hard missile.

Preliminary calculation tool. Final design requires the full text of the referenced standard (see the sources on this page) and review by a licensed PE.