Damaging Depth

Damaging Depth

Source: CHESS_Library/Structure_Reponses/Equations/damaging_depth.m (header: "ALPHA VERSION — FOR INTERNAL TESTING ONLY"), with the depth-limited wave height from goda_Hmax.m. Called from compute_structure_response.m. Applies to: All structure types. Enable flag: config.compute_damaging_depth

What it models

Damaging depth is the height of the water column from the offshore bed up to the crest of the controlling wave. It is a hazard metric for flood damage potential at the site, not a measure of how the structure performs: it uses no crest elevation or face slope. From the file header: "Damaging depth = SWL + 0.7·Hc. The controlling wave height, Hc, is defined as the average height of the highest 1-percent of waves during storm conditions. It is limited to the theoretical breaker limit using Goda's breaker equation. 70 percent of the controlling wave height is assumed to lie above the SWL."

Conceptual model

• Water level. SWL is taken to include every storm water level component (surge, tide, wave setup).
• Controlling wave. Hc is the mean of the highest 1% of waves, taken as 1.6·Hm0 (Rayleigh) and capped by the depth-limited breaker height. The breaker height is evaluated 5·Hm0 seaward of the structure, on the toe berm or on the offshore slope (see Breaker height).
• Wave crest. 70% of Hc lies above SWL, reduced by the sheltering coefficient Ks when rows of buildings shield the site.
• Reference bed. The depth is measured from the offshore elevation (positive up, study datum). It comes from the storm database's CHS study grid point nearest the savepoint, or, when the database has none, from the PSE's offshore_elevation row. Every run checks that one of them exists (check_offshore_elevation.m).
• No water column. When the crest elevation is below the offshore elevation (for example an offshore elevation above datum and a low storm), DamDepth is clipped to 0. NaN is kept.

Conceptual diagram

The equations

Hc           = goda_Hmax(Hm0, Ts, 1.6, h, hb, B, tanα_berm, tanα_offshore)   (Ts = Tp, narrow spectrum)
DamDepthElev = SWL + 0.7 · Ks · Hc
DamDepth     = max( DamDepthElev − offshore_elevation , 0 )                  (NaN kept)

Breaker height (goda_Hmax.m)

Shared with Goda Vertical Wall Pressures P1 P2 P3 Pu, which uses a factor of 1.8 instead of 1.6.

x_b = 5·Hm0                                       distance seaward of the structure
depth at x_b:
  toe berm, x_b on the berm crest  →  hb = d
  toe berm, x_b on the berm slope  →  hb = d + tanα_berm·(x_b − B)          slope = tanα_berm
  beyond the berm toe, or no berm  →  hb = h + tanα_offshore·(x_b − x_toe)  slope = tanα_offshore
                                      (x_toe = (h − d)/tanα_berm + B with a berm, 0 without)
hb < 0 → 0

Lo   = g·Ts² / (2π)
Hb   = 0.12 · Lo · (1 − exp(−1.5π · hb/Lo · (1 + 11·tanα^(4/3))))           Goda (breaker index)
Hc   = min( Hb , 1.6·Hm0 )

Parameters

Symbol	Meaning	Units	Source
SWL	Still water level (surge, tide and setup)	m, datum	Project forcing
Hm0	Significant wave height	m	Project forcing
Tp (Ts)	Peak wave period	s	Project forcing
h	Water depth at the toe, SWL − toe_elevation (floodwall without berm: wall bottom)	m	Forcing, structure.toe_elevation
hb (d)	Water depth on the berm crest, SWL − berm_crest_elevation (= h without a berm)	m	Forcing, structure.berm_crest_elevation
B	Berm crest width (0 without a berm)	m	structure.berm_crest_width
tanα_berm	Berm seaward slope, 1/berm_seaward_slope	—	structure.berm_seaward_slope
tanα_offshore	Offshore slope, 1/offshore_slope	—	structure.offshore_slope (template default cot α = 8)
offshore_elevation	Offshore bed elevation, positive up	m, study datum	Storm database study grid, else PSE offshore_elevation
Ks	Sheltering coefficient: 1 for 0–1 rows of buildings, 0.7 for 2–3, 0.5 for 4–5, 0.3 for ≥ 6	—	config.compute_damaging_depth_Ks
g	Gravitational acceleration	m/s²	config.gravity_constant

Outputs

Field	Meaning	Units
DamDepthElev	Elevation of the controlling wave crest	m, datum
DamDepth	Water column from the offshore bed to the wave crest (≥ 0)	m

Notes / limitations

• The file is labelled alpha / internal testing; treat results as provisional.
• Toe berms are hidden for levees, floodwalls and rubble mounds (finalize_structure_config.m), so for those structures hb = h and the breaker depth is always on the offshore slope.
• Elevations are signed (no abs()): a toe below datum zero is entered as a negative elevation, not as a positive depth.

References

• Goda, Y. Depth-limited breaker height, cited in-code as "Goda, 1995" in goda_Hmax.m. The source file gives no title or publisher.
• Damaging depth formulation: Jeffrey A. Melby (JAM), per the file header.