Measuring and Judging One Inch of Differential Settlement on a Ringwall Tank

One inch of what? The five components Annex B separates

Annex B of API 653 is normative and covers evaluation of tank bottom settlement. Its first move is not to judge anything. Clause B.2.2 divides shell settlement into three components: uniform settlement, rigid body tilt described as planar tilt, and out-of-plane settlement. Clause B.2.3 handles edge settlement, where the shell settles sharply around the periphery and deforms the bottom plate near the shell-to-bottom corner. Clause B.2.5 handles localized bottom settlement remote from the shell, meaning depressions and bulges occurring in a random manner.

Each of the five has a different consequence and a different limit. Uniform settlement induces no stress in the tank structure, and Annex B directs attention instead to piping, nozzles and attachments. Planar tilt raises the liquid level on the low side, increasing hoop stress in the shell, and can bind the peripheral seal on a floating roof and inhibit roof travel. Out-of-plane settlement is the component that produces internal stresses in the structure and drives out-of-roundness at the top of the shell.

This is why an owner reporting roughly one inch of differential settlement across two inspection cycles cannot be answered from that number. One inch distributed as planar tilt across a 120 ft tank is a hydraulic and roof-clearance question. One inch of out-of-plane residual on a short, wide tank is inside the criterion. One inch of edge settlement across a narrow band is a repair conversation. The tank inspection interval framework sets when you look; Annex B sets what the looking means.

The survey has to be valid before the number means anything

Clause 12.5.2 defines the point count: N = D/10 with D in feet, rounded up to the next higher even whole number, never fewer than eight, uniformly distributed around the circumference, with maximum spacing of 10 m (32 ft). Figure B.1 repeats those constraints for external shell measurements and requires at least four equally spaced diametrical measurement lines. Figure B.2 governs internal bottom measurements with the tank out of service and adds a maximum spacing of 3 m (10 ft) across the diameter.

Clause B.2.1 adds requirements that decide whether two cycles of data are comparable at all. Measurements are to be performed by personnel experienced in the procedures, using equipment capable of sufficient accuracy to distinguish settlement differences, and settlement measurement locations should be re-used in any future settlement surveys and evaluations. A trend built from points that moved between surveys is not a trend.

B.2.1 also names the systematic error that corrupts shell surveys. Where the bottom is distorted or corroded beyond the shell, measurements taken near bottom lap welds can produce significant errors in measured elevation, and repaired plates, replaced plates or slotted-in bottoms may not sit parallel to the original bottom. The annex suggests surveying the elevation of the weld between the first and second shell courses instead. For bottom and edge measurements, readings taken while the bottom is not in contact with the soil can overestimate or underestimate; where the result is near the allowable, the annex asks for the measurement to be repeated with the bottom forced down onto the soil.

Subtract the two components that do not stress the shell

The construction in Figure B.3 works in a fixed order. The actual settlement is plotted with points around the circumference as the abscissa. The vertical distance from the abscissa to the lowest point on the curve is the minimum settlement, and it is called the uniform settlement component; a line through that point parallel to the abscissa becomes the datum for adjusted settlements. What remains after that subtraction is everything except the uniform component.

The plane of rigid tilt is then represented by the optimum cosine curve fitted through the adjusted data. Vertical distances between the irregular measured curve and that cosine curve are the out-of-plane settlements, written Ui at data point i. Uniform settlement and tilt have been removed by construction, not by judgment, and only what is left is compared against the structural criterion.

That ordering explains why raw survey spreads mislead. A tank with an eight-inch spread between its highest and lowest elevation points can carry almost all of that as uniform settlement and tilt and be structurally comfortable, while a tank with a two-inch spread concentrated at two adjacent points can fail B.3.2.1. Anyone reading a settlement report should look for the fitted cosine curve before reading any headline number, which is one of the checks in our tank inspection support work.

The cosine fit and the R-squared gate

Clause B.2.2.4 e) states the accepted method: solve for constants a, b and c to find the optimum cosine curve of the form Elevpred = a + b cos(theta + c), starting from a least-squares fit chosen to minimize the sum of the squares of the differences between measured and predicted elevations. The curve is only considered valid, meaning it accurately fits the measured data, where R squared is greater than or equal to 0.9, with R squared equal to (Syy minus SSE) divided by Syy.

The annex is explicit about what a low R squared means. Where out-of-plane settlement concentrates in one or two areas, the least-squares fit under-predicts the local settlement and is not conservative, and R squared will typically fall below 0.9. In that situation the annex directs the engineer to more rigorous curve-fitting procedures, or to the alternative procedure in B.2.2.5 where the settlement does not indicate a well-defined rigid tilt plane at all.

This is a gate, not a formality. A report that presents a cosine curve without stating R squared has not demonstrated that the tilt plane it subtracted was real, and every out-of-plane number downstream of that fit inherits the doubt. Obtaining a statistically valid curve may require more measurement points than the Figure B.1 minimum, which is a survey planning decision, not a desk exercise after the fact.

S is not the settlement you measured

The single most misread step in Annex B is the difference between Ui and Si. Ui is the out-of-plane settlement at point i, the vertical distance from the measured curve to the fitted cosine curve. Si is the out-of-plane deflection at that point, and Figure B.3 defines it as Si = Ui minus the average of its two neighbors: for point 11, S11 = U11 minus one half of U10 plus one half of U12.

Si is what gets compared against the permissible value. A uniform sag spread evenly around several adjacent points produces large Ui values and small Si values, because each point's neighbors have moved with it. A single sharp local dip produces a large Si. The criterion is about local curvature of the shell, and reporting Ui as though it were Si will fail tanks that are fine.

The note to B.2.2.4 e) closes a second trap. Adding measurement points improves the cosine fit, but feeding all of them into the B.3.2.1 equation shortens the arc length L and shrinks the allowable. The annex permits all points to be used for the curve fit while a subset spaced no further than 32 ft, with eight as the minimum, is used to calculate Si and Smax, provided the subset includes the points furthest from the fitted curve. With 16 points taken at 15 ft spacing where 8 are required, the equation becomes Si = Ui minus one half of Ui-2 plus one half of Ui+2.

The out-of-plane limit, and why height beats diameter

Clause B.3.2.1 gives the permissible out-of-plane deflection where a cosine curve approach was used: Smax equals 11 times L squared times Y, divided by 2EH, with Smax and L in feet, Y the yield strength of the shell material in psi, E Young's modulus in psi and H the tank height in feet. API attributes the equation to Marr, Ramos and Lambe, published by ASCE in 1982.

Combine that with the point-count rule and a non-obvious result falls out. Since N = D/10, the arc length L is pi times D divided by N, which reduces to about 31.4 ft for every tank of 80 ft diameter or larger. Diameter cancels. For any large tank the permissible out-of-plane deflection is a function of shell height and material yield alone, which is why the table above shows a 200 ft by 64 ft tank with a tighter limit than an 80 ft by 32 ft tank. Below 80 ft diameter the eight-point minimum takes over, L shrinks with diameter, and small tanks end up with the tightest limits of all.

Run it once for the tank in question. A 100 ft diameter, 40 ft tall tank in A36 material gives L = 31.4 ft, and Smax = 11 times 986 times 36,000 divided by (2 times 29,000,000 times 40), which is 0.168 ft, or 2.02 in. In A283 Grade C at 30,000 psi the same tank permits 1.68 in. An inch of local out-of-plane deflection on that tank is inside the criterion with margin, and the conversation moves to the edge and the bottom.

When there is no tilt plane: B.2.2.5 and the K equation

Clause B.2.2.5 applies where a well-defined rigid tilt plane cannot be determined, or where the B.3.2.1 limit is exceeded and the owner wants an alternative to rigorous analysis or repair. Instead of a fitted curve, B.2.2.5.1 works from the plotted profile: an initial settlement arc length Sarc and maximum settlement are read from the points where the settlement slope changes direction, and additional measurement points halfway between those points refine both the arc length and the location and magnitude of the maximum. The refinement step may be repeated.

Clause B.2.2.5.3 adds a rule for one specific pattern: where the plot indicates a fold pattern about a diameter of the tank, the maximum out-of-plane settlement should be determined using a settlement arc length of 50 percent of the tank circumference.

Clause B.3.2.2 then supplies the acceptance equation: Smax equals the lesser of K times Sarc times D divided by H times Y divided by E, and a fixed ceiling of 100 mm (4 in.). K is tabulated by diameter band and roof type, running from 28.7 for open-top tanks of 50 ft diameter or less down to 2.4 for open-top tanks between 240 and 300 ft, and from 10.5 down to 2.3 for fixed roof tanks, which the table covers only to 180 ft. Above 300 ft diameter no K is given. Clause B.3.2 also excludes several geometries from both criteria, including abrupt ridges, discontinuities such as low nozzles in the settled region, fold patterns in cone roof tanks where the fold line runs adjacent to or through a line of roof columns, and combined shell and edge settlement patterns.

Edge settlement is where an inch usually fails

Clause B.2.3.3 splits the allowable in two. Bew is the allowable where the settled area contains a bottom lap weld essentially parallel to the shell, within plus or minus 20 degrees, and it is read from Figure B.11. Be is the allowable for areas with no bottom welds, with butt welds, or with lap welds essentially perpendicular to the shell within plus or minus 20 degrees, read from Figure B.12. Both charts plot allowable settlement in inches against R, the radius of the settled area, with curve families for tank diameters from 20 ft up to 160 ft and larger. Since Bew is the more conservative of the two, the annex suggests evaluating every settled area against Bew first and only splitting them out if that fails.

Clause B.3.4.4 handles welds at an arbitrary angle by interpolation: B equals Be minus (Be minus Bew) times sine of the angle of the weld to a tank centerline. Clauses B.3.4.1 and B.3.4.3 set an inspection trigger well below the allowable. Where measured settlement B exceeds 75 percent of the allowable, all shell-to-bottom welds and bottom welds should be examined visually and with magnetic particle or liquid penetrant methods, and all indications repaired or evaluated for risk of brittle fracture and fatigue before the tank returns to service. Clause B.3.4.2 extends visual examination to any welds within 300 mm (12 in.) of either side of the breakover area.

Clause B.3.4.6 states the basis and the limits of these charts: they were developed for typical 6 mm (1/4 in.) thick bottoms with minimal corrosion, can be applied with reasonable accuracy to 8 mm and 10 mm bottoms, and can be applied to generally corroded bottoms provided areas near all welds remain thicker than 5 mm (3/16 in.). For locally corroded bottoms, thin areas below 5 mm within the settled zone must be smaller than 300 mm (12 in.) across and must not include a weld. A corroded lap-welded floor around the periphery puts the tank outside the chart basis, and that is an engineering evaluation, not a chart lookup.

Localized depressions and bulges: the 0.37R rule

Clause B.3.3 covers depressions and bulges remote from the shell with a single equation: BB = 0.37R, where BB is the maximum height of the bulge or depth of the local depression in inches and R is the radius of the inscribed circle in the bulged or depressed area in feet. In SI the same relationship is written BB = 0.031R with both terms in millimeters. Figure B.10 presents it graphically, with the caption stating that repairs or a rigorous assessment should be conducted where the observed depth or height sits above the line.

The geometry input is the inscribed circle radius, not the width of whatever the crew measured across. A shallow dish 20 ft across permits 0.37 times 10, or 3.7 in. of depth. The same depth over a 3 ft inscribed radius permits only 1.1 in. and fails. Clause B.2.5.2 notes that acceptability depends on localized stresses in the bottom plate, the design and quality of the lap welds as single-pass or multi-pass, and voids below the bottom plate, and that the limits apply to bottoms with single-pass lap-welded joints.

Figure B.10 carries two curve families, one for a depression or bulge anywhere in the bottom and one for a partial ring-type depression or bulge at the edge only. Reading the wrong family is a common error in reports, and it is one of the items worth catching during independent review of an inspection report rather than during the next turnaround.

What triggers repair, and the trap in a two-cycle trend

Clause B.3.1 frames the whole annex honestly: the methods are not mandatory and approximate the maximum permissible settlement, and experience has shown that where settlements exceed them, further assessment or repair is required. Clause B.3.2.4 preserves the alternative, allowing a more rigorous evaluation by an engineer experienced in tank settlement analysis in place of repair. Clause B.4.2 describes what repair means when it is required: plate exceeding acceptable strains, typically 2 to 3 percent, should be replaced, re-leveling will not remove the plastic strain, welds in high-strain areas should be removed and replaced or subjected to a fitness-for-service evaluation, and the condition that caused the settlement should be corrected. Jacking and leveling are done in conjunction with plate and weld replacement, not instead of it.

Now the part that decides the reader's case. Clause B.3.4.5 states the usual practice of comparing measured edge settlement against the allowable without adding an allowance for further settlement, on the presumption that most settlement occurred in the first few years. It then names the exception: where significant additional settlement is expected, an engineer experienced in tank settlement evaluation should evaluate the settlement expected at the next inspection against the B.3.4 limits, and the annex calls this analogous to a corrosion allowance. An inch accumulated across two inspection cycles is evidence of active settlement, which puts the tank squarely in that exception. The comparison has to be made against the projected value at the next due date, not against today's reading. Clause B.3.4.5 also flags erosion of the pad adjacent to the tank as a cause that will continue until the pad is repaired.

One number keeps this in proportion. Clause 10.5.6.2 sets the construction tolerance for a foundation true to a horizontal plane: where concrete ringwalls are provided, the top of the ringwall shall be level within plus or minus 3 mm (1/8 in.) in any 9 m (30 ft) of circumference and within plus or minus 6 mm (1/4 in.) over the total circumference measured from the average elevation. An inch is four times the total construction tolerance and a fraction of the in-service acceptance limit, which is exactly why it alarms operators and why the decomposition, not the headline number, settles the question. Where the projection crosses a limit, the route forward is a fitness-for-service evaluation under API 579 or a defined repair, and the survey interval belongs in the plan alongside the external inspection clocks. We review settlement surveys and the evaluations built on them; send the data and we will tell you which component the inch belongs to.

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