Cathodic Protection Groundbed

Current requirement, anode count and life, groundbed resistance (Dwight, Sunde) and rectifier sizing for impressed-current systems, and anode output and life for galvanic systems.

1. What this check does

Finds the protective current from surface area, current density and coating breakdown (or a measured value), the number of anodes needed to carry that current and to last the design life, the resistance of a vertical, horizontal or deep-well groundbed, and the rectifier voltage and current with a margin.

2. Inputs used

Surface area, design current density and coating breakdown factor — or a known current requirement.
Soil resistivity at the groundbed; anode or backfill column length and diameter; spacing; burial depth for horizontal beds.
Anode mass, consumption rate, utilization factor and maximum current per anode; design life.
Cable and structure-to-earth resistance, back EMF (default 2 V) and rectifier margin (default 1.25).

3. Formulas and assumptions

Current and anodes (impressed current)

Current

I = A \cdot \dfrac{i}{1000}\cdot f

A in m², i in mA/m², f coating breakdown.

Anodes

N = \max\left(\left\lceil \dfrac{I}{I_{\max}} \right\rceil,\ \left\lceil \dfrac{I\,C\,Y}{m\,U} \right\rceil\right) \qquad Y = \dfrac{N\,m\,U}{C\,I}

C consumption kg/A·yr, U utilization, m anode mass, Y life.

Groundbed resistance

Vertical, one

R = \dfrac{\rho}{2\pi L}\left(\ln\dfrac{8L}{d} - 1\right)

Dwight. Also used for a deep-well active column.

Vertical, N

R = \dfrac{\rho}{2\pi N L}\left(\ln\dfrac{8L}{d} - 1 + \dfrac{2L}{S}\ln(0.656\,N)\right)

Sunde. S anode spacing.

Horizontal

R = \dfrac{\rho}{2\pi L}\left[\ln\dfrac{4L^2 + 4L\sqrt{s^2 + L^2}}{d\,s} + \dfrac{s}{L} - \dfrac{\sqrt{s^2 + L^2}}{L} - 1\right]

Dwight. L = (N − 1)·S + anode length, s = 2 × depth.

Rectifier

V = I\,\bigl(R_{\text{bed}} + R_{\text{cable}} + R_{\text{structure}}\bigr) + E_{\text{back}}

Rating = V × margin, I × margin.

Galvanic anodes

Driving voltage

\Delta V = \lvert E_{\text{anode}} \rvert - \lvert E_{\text{protection}} \rvert

e.g. 1.75 − 0.85 = 0.90 V for high-potential magnesium.

Per anode

I_a = \dfrac{\Delta V}{R_a + R_{\text{lead}}} \qquad N = \left\lceil \dfrac{I}{I_a} \right\rceil \qquad Y = \dfrac{m\,U}{C\,I_a}

Life is set by one anode’s own output.

Symbols

$A,\ i,\ f$	Protected surface area; current density; coating breakdown factor	m², mA/m², —
$I,\ I_{\max}$	Required protection current; maximum output per anode	A
$C,\ U,\ m$	Anode consumption rate; utilization factor; anode mass	kg/A·yr, —, kg
$N,\ Y$	Number of anodes; design life	—, yr
$\rho,\ L,\ d$	Soil resistivity; anode (or backfill column) length and diameter	Ω·m, m, m
$S,\ s$	Anode spacing; twice the burial depth (horizontal bed)	m
$R_{\text{bed}},\ R_{\text{cable}},\ R_{\text{structure}}$	Groundbed, cable and structure-to-earth resistance	Ω
$E_{\text{back}}$	Back EMF of the anode–structure cell	V
$E_{\text{anode}},\ E_{\text{protection}}$	Anode open-circuit potential; protection criterion (−0.85 V CSE)	V
$\Delta V,\ R_a,\ I_a$	Driving voltage; galvanic anode resistance; output per anode	V, Ω, A

Circuit sketch: rectifier positive to anode groundbed, current through soil to buried pipe or tank, return to rectifier negative. — **Figure 1.** Impressed-current system: rectifier, anode bed, soil and the protected structure.

Three cross-sections: vertical anodes in backfill columns, horizontal anodes in a backfill trench at depth, and a deep-well column of anodes. — **Figure 2.** Groundbed types: vertical, horizontal and deep well.

Magnesium anode connected to a buried pipe; a potential scale shows the anode at −1.75 V and the protected pipe at −0.85 V versus CSE. — **Figure 3.** Galvanic anode: the potential difference drives the current.

Uniform soil resistivity at the groundbed; use the value measured over the anode depth.
Backfill is treated as part of the electrode (its diameter and length are used); backfill resistance itself is ignored.
Default back EMF 2 V and rectifier margin 1.25 are RokBench assumptions.
Galvanic anodes cannot be regulated: each one delivers ΔV / R whatever the demand, so adding anodes raises the current but does not extend their life.
Galvanic defaults are typical alloy values used by RokBench: open-circuit potential −1.75 V (high-potential magnesium), −1.55 V (standard magnesium), −1.10 V (zinc) versus CSE; consumption 7.9 kg/A·yr for magnesium and 11.2 kg/A·yr for zinc; utilization 0.85; protection potential −0.85 V CSE. The manufacturer data sheet takes precedence.
Current density, coating breakdown, consumption rate and utilization are your design inputs; UFC 3-570-01 and anode manufacturers publish typical values.

4. What is NOT checked

Protection criteria such as −850 mV CSE (AMPP/NACE SP0169) and polarization.
Current attenuation along pipelines and the need for multiple groundbeds.
Interference with foreign structures and stray current.
Interaction between closely spaced galvanic anodes and anode-to-structure distance.

5. Reference standards

Pointers only; consult the edition adopted by your authority having jurisdiction.

UFC 3-570-01 Cathodic Protection — U.S. DoD, approved for public release
AMPP (NACE) SP0169 — control of external corrosion on buried piping
H. B. Dwight, Calculation of Resistances to Ground (1936)
E. D. Sunde, Earth Conduction Effects in Transmission Systems (1949)

6. Validation cases

These worked examples run through the engine on every change; the expected values come from the cited source. All cases: Validation.

Galvanic anodes, high-potential magnesium, 1 A in 30 Ω·m soil cathodic/galvanic · Hand calculation

Pass

Source: Hand calculation from Dwight's single vertical electrode equation and the galvanic anode output and life equations — ΔV = 1.75 − 0.85 = 0.90 V; Ra = 30/(2π·1.5)·(ln(8·1.5/0.2) − 1) = 9.8496 Ω; Ia = 0.9/9.8496 = 0.09137 A; N = ⌈1/0.09137⌉ = 11; life = 14.5·0.85/(7.9·0.09137) = 17.07 years.

Quantity	Expected	RokBench	Error	Result
anodeResistanceOhm	9.8496	9.85	0.004%	Pass
outputPerAnodeA	0.09137	0.0914	0.033%	Pass
anodes	11	11	0%	Pass
lifeYears	17.07	17.1	0.176%	Pass

ICCP, 10 A, seven vertical anodes at 5 m in 30 Ω·m soil cathodic/iccp · Hand calculation

Pass

Source: Hand calculation from Sunde's multiple vertical anode equation and the anode life equation — I = 10000·10·0.1/1000 = 10 A; N = max(⌈10/2⌉, ⌈10·0.5·20/(20·0.8)⌉) = 7; R = 30/(2π·7·2.1)·(ln(8·2.1/0.25) − 1 + (4.2/5)·ln(0.656·7)) = 1.4578 Ω; V = 10·(1.4578 + 0.3) + 2 = 19.58 V.

Quantity	Expected	RokBench	Error	Result
currentA	10	10	0%	Pass
groundbedOhm	1.4578	1.458	0.014%	Pass
lifeYears	22.4	22.4	0%	Pass

7. Known issues and changes

See the Engineering Notes. Try the tool: Cathodic Protection Groundbed.