Casing Strength and Load Analysis: Collapse Criterion

Casing Collapse Design - API 5C3 Collapse Regimes, Resistance Calculations, and Design Scenarios

The API 5C3 collapse rating for a given casing size and grade is not a single number derived from a single formula. It is the minimum of four separate collapse pressure calculations, each corresponding to a different failure mechanism that governs at different diameter-to-thickness ratios (D/t). For thin-walled casing (high D/t), elastic buckling governs and the collapse resistance is independent of yield strength - only geometry matters. For thick-walled casing (low D/t), yield collapse governs and the collapse resistance scales directly with yield strength. In the transition zones between these extremes, plastic collapse and transition collapse formulas apply. A casing design that uses the elastic formula for thick-walled pipe, or the yield formula for thin-walled pipe, will be wrong by a factor of 2 or more. This guide gives you the correct formulas, the D/t boundaries between regimes, and the worked calculations that determine whether the selected casing can survive the worst-case external pressure load in the well.

1. The Four Collapse Regimes - API 5C3 Framework

1.1 D/t Ratio - The Governing Parameter

The diameter-to-thickness ratio (D/t = OD/wall thickness) determines which collapse mechanism governs. The regime boundaries depend on the grade yield strength and are calculated from API coefficient tables:

Collapse Regime	D/t Range (P-110 example)	Physical Mechanism	Depends On
Yield strength collapse	D/t ≤ 13.85 (P-110)	Wall yields in compression before buckling occurs. Thick-walled pipe.	Yield strength Yp only
Plastic collapse	13.85 - 19.63 (P-110)	Partially plastic failure - yielding initiates but instability follows before full yield.	Yp and D/t
Transition collapse	19.63 - 26.22 (P-110)	Empirical transition between plastic and elastic regimes.	Yp and D/t
Elastic collapse	D/t ≥ 26.22 (P-110)	Buckling instability occurs at stresses below yield. Thin-walled pipe. Classic Euler buckling.	E and D/t only (NOT yield strength)

2. The Four Collapse Formulas - API 5C3

2.1 Elastic Collapse (thin-walled, high D/t)

Elastic collapse pressure (psi):
Pc_elastic = 46.95 x 10^6 / [(D/t) x (D/t - 1)^2]

This is derived from Timoshenko's thin-shell elastic buckling formula with E = 30 x 10^6 psi and nu = 0.3.
Critical point: yield strength does NOT appear. Using higher-grade steel does NOT improve elastic collapse resistance.
Only way to improve: increase wall thickness (reduce D/t).

Example: 13-3/8" 54.5 lb/ft J-55 casing (OD=13.375", t=0.380", D/t = 13.375/0.380 = 35.2):
Pc_elastic = 46.95e6 / [35.2 x (35.2-1)^2] = 46.95e6 / [35.2 x 1,169.6] = 46.95e6 / 41,170 = 1,140 psi

If upgraded to N-80 same OD and weight (same D/t = 35.2):
Pc_elastic = 1,140 psi (unchanged - yield strength makes no difference in elastic regime)

2.2 Yield Strength Collapse (thick-walled, low D/t)

Yield collapse pressure (psi):
Pc_yield = 2 x Yp x (D/t - 1) / (D/t)^2

This is the Lamé equation for thick-walled cylinder yielding under external pressure.

Example: 9-5/8" 53.5 lb/ft P-110 casing (OD=9.625", t=0.625", D/t = 9.625/0.625 = 15.4):
Pc_yield = 2 x 110,000 x (15.4-1) / (15.4)^2
= 2 x 110,000 x 14.4 / 237.16
= 3,168,000 / 237.16 = 13,358 psi yield collapse

If downgraded to N-80 (Yp = 80,000 psi), same D/t = 15.4:
Pc_yield = 2 x 80,000 x 14.4 / 237.16 = 9,714 psi
Grade upgrade from N-80 to P-110 improves yield collapse resistance by 37% (13,358/9,714 = 1.375)

2.3 Plastic Collapse (intermediate D/t)

Plastic collapse pressure (psi):
Pc_plastic = Yp x [A/(D/t) - B] - C

Where A, B, C are API coefficients that depend on grade yield strength (from API Bulletin 5C3 Tables):

For P-110 (Yp = 110,000 psi): A = 3.181, B = 0.0819, C = 2,580
For N-80 (Yp = 80,000 psi): A = 3.071, B = 0.0667, C = 1,156
For J-55 (Yp = 55,000 psi): A = 2.991, B = 0.0542, C = 470

Example: 9-5/8" 47 lb/ft P-110 (OD=9.625", t=0.545", D/t = 9.625/0.545 = 17.66):
D/t = 17.66 falls in plastic collapse range for P-110 (13.85 to 19.63)
Pc_plastic = 110,000 x [3.181/17.66 - 0.0819] - 2,580
= 110,000 x [0.18011 - 0.0819] - 2,580
= 110,000 x 0.09821 - 2,580
= 10,803 - 2,580 = 8,223 psi plastic collapse

Verification: This is the value used in the design check, not the elastic or yield formula.

2.4 Transition Collapse

Transition collapse pressure (psi):
Pc_transition = Yp x [F/(D/t) - G]

For P-110: F = 1.998, G = 0.0425
For N-80: F = 1.998, G = 0.0434
For J-55: F = 1.989, G = 0.0418

Used when D/t falls between the plastic and elastic boundaries. Less commonly encountered in standard casing sizes.

3. D/t Regime Boundaries for Common Grades

Grade	Yp (psi)	Yield → Plastic (D/t)	Plastic → Transition (D/t)	Transition → Elastic (D/t)
J-55 / K-55	55,000	16.00	26.73	42.64
N-80	80,000	14.44	21.93	30.88
L-80 / C-90	80,000 / 90,000	14.44 / 14.14	21.93 / 20.93	30.88 / 29.18
P-110	110,000	13.85	19.63	26.22
Q-125	125,000	13.44	18.37	24.16

Practical implication from the table: J-55 casing is in the elastic collapse regime for D/t above 42.64 - where yield strength makes zero difference. A 13-3/8" surface casing with D/t = 35 is still in the transition regime for J-55 but already in the elastic regime for P-110. Upgrading grade makes sense only when the D/t puts the casing in the yield or plastic regime for both grades being compared.

4. Collapse Load Cases - What External Pressure to Design Against

4.1 The Three Standard Collapse Scenarios

Scenario	External Pressure	Internal Pressure	Net Collapse Load
Full evacuation (most severe)	Full mud hydrostatic outside: rho_mud x 0.052 x TVD	Zero (gas filled or empty)	= External hydrostatic
Partial evacuation (production string)	Mud or pore pressure on outside	Reduced internal pressure from production drawdown or partial fluid level drop	= External - Internal at each depth
Cementing collapse	Cement slurry hydrostatic on outside during pumping	Drilling fluid inside = mud hydrostatic	= Cement hydrostatic - mud hydrostatic (can be significant for heavy cement)

4.2 Full Evacuation Collapse - Complete Design Calculation

Design scenario: 9-5/8" production casing, 14 ppg mud, full evacuation to gas, TVD = 12,000 ft

Step 1 - Net collapse pressure at shoe (maximum):
P_collapse = External - Internal = (14.0 x 0.052 x 12,000) - 0 = 8,736 psi

Step 2 - Select candidate casing and calculate D/t:
Option A: 9-5/8" 47 lb/ft P-110 (t = 0.545", D/t = 9.625/0.545 = 17.66)
Option B: 9-5/8" 53.5 lb/ft P-110 (t = 0.625", D/t = 9.625/0.625 = 15.40)

Step 3 - Identify collapse regime:
Option A: D/t = 17.66 → P-110 plastic range (13.85 to 19.63) → use plastic formula
Option B: D/t = 15.40 → P-110 plastic range (13.85 to 19.63) → use plastic formula

Step 4 - Calculate collapse resistance:
Option A: Pc = 110,000 x [3.181/17.66 - 0.0819] - 2,580 = 8,223 psi
Option B: Pc = 110,000 x [3.181/15.40 - 0.0819] - 2,580
= 110,000 x [0.2065 - 0.0819] - 2,580
= 110,000 x 0.1246 - 2,580 = 13,706 - 2,580 = 11,126 psi

Step 5 - Safety factor check:
Option A: SF = 8,223 / 8,736 = 0.94 → FAILS (minimum 1.00)
Option B: SF = 11,126 / 8,736 = 1.27 → PASSES

Decision: Select 9-5/8" 53.5 lb/ft P-110. The 47 lb/ft fails by 6%. Upgrading to 53.5 lb/ft (only 6.5 lbs/ft additional) provides a 27% safety margin - adequate for the full evacuation design load.

5. Effect of Wear on Collapse Resistance

5.1 Wall Thickness Reduction from Casing Wear

During drilling operations, the rotating drill string wears the inside of the casing at dogleg locations. This reduces the wall thickness and therefore the collapse resistance of the worn section. The collapse resistance degrades approximately as the square of the remaining wall thickness fraction:

Collapse resistance after wear:
Pc_worn / Pc_new ≈ (t_worn / t_nominal)^2 (approximate for yield and plastic regimes)

Example: 9-5/8" 53.5 lb/ft P-110, nominal t = 0.625", casing wear of 20% wall loss at dogleg:
t_worn = 0.625 x (1 - 0.20) = 0.500"
D/t_worn = 9.625 / 0.500 = 19.25 (still in plastic regime for P-110)

Pc_worn = 110,000 x [3.181/19.25 - 0.0819] - 2,580
= 110,000 x [0.16526 - 0.0819] - 2,580
= 110,000 x 0.08336 - 2,580 = 9,170 - 2,580 = 6,590 psi worn collapse resistance

Original: 11,126 psi → After 20% wear: 6,590 psi → 41% reduction in collapse resistance

New SF against 8,736 psi design load: 6,590 / 8,736 = 0.75 → FAILS

Conclusion: 20% wall loss at a high-DLS dogleg on the intermediate casing converts an adequate collapse design to a failure condition during production phase when internal pressure drops. This is why casing wear monitoring and multi-finger caliper surveys are critical before completing the well.

Conclusion

The elastic collapse example in this article demonstrates the most important and most frequently misunderstood aspect of collapse design: upgrading from J-55 to P-110 on a 13-3/8" surface casing with D/t = 35 provides zero improvement in collapse resistance because the failure mechanism is elastic buckling, which depends only on geometry. The casing designer who upgrades grade to improve collapse resistance on thin-walled casing has spent money on additional yield strength that the collapse mechanism does not use. The correct intervention is to increase wall thickness - moving to a heavier weight per foot in the same OD.

The wear analysis shows that collapse design cannot be evaluated only at installation. A 9-5/8" production casing that passes the collapse check at the time of cementing with SF = 1.27 fails the same check after 20% wall loss at a dogleg with SF = 0.75. The production period - when internal pressure drops due to depletion, creating the highest net external collapse load - is when the worn casing is most at risk. The design should account for the expected wear at the end of the drilling program, not just the initial unworn condition.

Want to access our API 5C3 collapse calculator with all four regime formulas, D/t boundary check, and wear correction, or discuss collapse design for a specific casing string? Join our Telegram group for casing design discussions, or visit our YouTube channel for step-by-step tutorials on API casing collapse calculations.