Crest Velocity Exceedance u1p

1%-Exceedance Crest Overtopping Velocity (u1%)

Source: CHESS_Library/Structure_Reponses/Equations/u1p_calc.m, called from van_gent_Dn50_leeside_stability.m (Van Gent Leeside Armor Stone Stability Dn50), leeside_armor_stone_damage.m (Leeside Armor Damage Progression LCS CSR), and directly from chess_csr_dpa.m (a separate, diagnostic-only pre-loop computation — see Leeside Armor Damage Progression LCS CSR for the distinction). Applies to: struc_type = 3 (Rubblemound) only — this is a helper function used exclusively within the leeside/LCS-CSR family of equations, not dispatched from compute_structure_response.m. Enable flag: None of its own; it runs whenever its caller runs (config.compute_dn50_leeside for the Van Gent Dn50 path, or config.csr_call_dpa for the CSR-DPA path).

What it models

u1p_calc.m computes the flow velocity across the structure crest, exceeded by only 1% of the incident waves, given the 1%-exceedance run-up elevation from Wave Runup Exceedance z1p. Physically, it represents how fast the overtopping "sheet" of water is moving as it crosses the crest — the excess of run-up above the freeboard (z1% − Rc) drives the flow, while a wider crest attenuates it. This crest velocity is the direct forcing term for the leeside/rear-side armor stability and damage equations (Van Gent Leeside Armor Stone Stability Dn50, Leeside Armor Damage Progression LCS CSR), since it is the velocity of water descending the leeside slope that determines whether the rear-side armor stones are dislodged.

As with Wave Runup Exceedance z1p, the slope argument this function's surf-similarity/friction-factor calculation depends on is supplied by the caller — every current call site (Van Gent Dn50, CSR-DPA leeside damage, and chess_csr_dpa.m's diagnostic pre-loop call) supplies the seaside slope; see that page's "What it models" section for the full breakdown.

Conceptual model

• Velocity from the overshoot. The water that runs up past the crest (z1% − Rc) falls across it; the higher it overshoots, the faster it flows: u ∝ √(g·H)·√((z1% − Rc)/(γf·H)).
• A wide crest slows it down. The 1 + 0.1·B/H term reduces the velocity at the landward edge as the flow loses energy crossing the crest.
• Roughness uses the same built-in rock factor γf as Wave Runup Exceedance z1p.
• No flow (u1% = 0) when the run-up does not reach the crest, when z1% = 0 (low freeboard), or when the relative freeboard Rc/H < 0.3 (outside the Van Gent and Pozueta range, added 2026-02-23).

Conceptual diagram

The equation

Source: no independent header/citation in u1p_calc.m itself (the file has no header block at all, unlike most other equation files in the library). One inline comment ties a specific restriction to the Van Gent & Pozueta paper — see below and References.

Local wave conditions and surf similarity parameter, computed the same way as in Wave Runup Exceedance z1p (spectral mean period Tm-1,0, here named Tmm1):

L_m-1,0 = grav · Tmm1² / (2π)
som     = H / L_m-1,0
SSPm    = 1 / Sslp / √som                (surf-similarity parameter)

Friction factor (same piecewise form as z1p_calc.m, written slightly differently but numerically equivalent):

γf = 0.55                              if SSPm ≤ 2
γf = 0.05625·(SSPm − 2) + 0.55         if 2 < SSPm < 10
γf = 1                                  if SSPm ≥ 10

gam_crest = γf                          (duplicate of γf, used as-is in the velocity formula)

Crest velocity:

u1pNum   = √((z1% − Rc) / γf / H)
u1pNum   = 0                            where z1% = 0   (no run-up ⇒ no overtopping flow)

u1pDenom = 1 + 0.1 · wdth / H            (crest-width attenuation term; wdth = crest_width)

u1% = √(grav · H) · 1.7 · √(gam_crest) · u1pNum / u1pDenom

Validity restrictions applied after the fact:

u1% = 0   where (z1% − Rc) < 0            (no overtopping reaching the crest)
u1% = 0   where Rc / H < 0.3              (JAM in-code comment: "from v&P paper" — see References)

Parameters

Symbol	Meaning	Units	Source
wdth	Structure crest width	m	structure.crest_width
Rc	Freeboard: crest_elevation − SWL (or an artificially raised freeboard under a caller's cutoff correction)	m	Passed in by the caller
z1p (z1%)	1%-exceedance run-up elevation	m	Output of Wave Runup Exceedance z1p, computed immediately before this call
Tmm1	Spectral mean wave period (Tm-1,0)	s	Passed in by the caller
H	Significant wave height at the structure toe	m	Passed in by the caller
Sslp	Cotangent of the slope used in the surf-similarity/friction-factor calculation — the seaside slope, at every current call site	—	structure.seaside_slope
grav	Gravitational acceleration	m/s²	config.gravity_constant
γf (gam_crest)	Friction factor, computed internally from SSPm (same formula as in z1p_calc.m)	—	Computed internally

Notes / limitations

• u1p_calc.m has no license/header/purpose comment block at all — unlike every other equation file surveyed in this wiki, which at minimum carry the standard CHESS file header. This makes independent verification of authorship or intended scope harder than for its sibling z1p_calc.m.
• The Rc/H < 0.3 restriction carries an explicit in-code attribution: %JAM added on 2/23/26 from v&P paper — i.e., a developer (JAM) added this specific validity guard citing the Van Gent & Pozueta paper. This is the strongest direct evidence in either z1p_calc.m or u1p_calc.m tying the run-up/velocity formulation to that source (see References).
• gam_crest is set equal to γf with no further transformation — the duplicate variable name suggests the code may once have distinguished a separate "crest" friction factor from a general one, but in the current implementation they are identical.
• This function has no independent config.compute_* enable flag; it always runs as part of whichever caller invokes it, immediately after that caller's own z1p_calc call.

References

• No title, author, or year is stated anywhere in u1p_calc.m itself beyond the inline initialed comment described above.
• Van Gent, M. R. A., and B. Pozueta. 2005. "Rear-Side Stability of Rubble Mound Structures." Coastal Engineering 2004, 3481–93. World Scientific Publishing Company. — cited in full by chess_csr_dpa.m's reference list (see Leeside Armor Damage Progression LCS CSR) and independently corroborated for this specific function by the in-code comment % from v&P paper attached to the Rc/H < 0.3 restriction. This is the best-supported attribution available for u1p_calc.m, but note it confirms only that one restriction line, not the full velocity formula, as sourced from that paper.
• Van Gent, M., and B. Pozueta. 2004. Cited by title in the header of leeside_armor_stone_damage.m as Proc. of Coastal Structures 2003, ASCE, Reston, VA (see Leeside Armor Damage Progression LCS CSR) — the same likely lineage, not independently confirmed within u1p_calc.m.