9.1 Minimum Bottom Thickness Formulations (MRT, MRTbottom, MRTlinear)

API 653 Aboveground Storage Tank Inspector Exam

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1 Chapter 1: API 653 Scope, Inspector Certification & Roles

1.1 Scope of API 653, Tank Types & Construction Standards 1.2 Inspector Roles, Responsibilities & Certification Requirements 1.3 Inspection Planning, Safety, Confined Space Entry & Preparation

2 Chapter 2: Tank Shell & Roof Components Inspection

2.1 Fixed Roof Types, Structural Supports & Inspection Practices 2.2 Floating Roofs, Seals, Drainage & Operational Issues 2.3 Shell Courses, Welds, Attachments & Wind Girders 2.4 Tank Appurtenances, Nozzles, Manways & Piping Connections

3 Chapter 3: Tank Bottom & Foundation Inspection

3.1 Tank Bottom Types, Annular Plates & Internal Bottom Inspection 3.2 Foundation Types (Concrete Ringwall, Earth, Asphalt) & Inspection 3.3 Leak Detection Systems, Secondary Containment & Under-Tank Monitoring

4 Chapter 4: Corrosion & Damage Mechanisms in Storage Tanks

4.1 Atmospheric Corrosion, Condensation & External Deterioration 4.2 Corrosion Under Insulation (CUI) & Piping/Nozzle Interfaces 4.3 Soil-Side Corrosion, Under-Bottom Pitting & Microbiologically Induced Corrosion (MIC) 4.4 Product-Side Deterioration: Chemical Attack, Ethanol SCC, Concentration Cell & Sulfuric Acid Corrosion

5 Chapter 5: Materials, Toughness & Brittle Fracture Prevention

5.1 Tank Steels, Material Specifications & Historic Standards 5.2 Brittle Fracture Assessment: Figure 5.1 Decision Tree & Exemption Curves (API 653 Section 5) 5.3 Charpy V-Notch Impact Testing & Minimum Design Metal Temperature (MDMT)

6 Chapter 6: Cathodic Protection & Interior Linings

6.1 Cathodic Protection Principles & Systems for Tank Bottoms (API RP 651) 6.2 CP Criteria, Surveys, Potential Measurements & Interference (API RP 651) 6.3 Tank Bottom Interior Linings, Surface Prep & Inspection (API RP 652)

7 Chapter 7: Corrosion Rates, Remaining Life & Inspection Intervals

7.1 Determining Corrosion Rates (Short-Term vs. Long-Term) 7.2 Remaining Life Calculations & Limiting Components 7.3 Establishing In-Service & Out-of-Service Inspection Intervals (API 653 Section 6)

8 Chapter 8: Tank Shell Minimum Thickness Evaluation

8.1 Shell Minimum Thickness Calculations (tmin for Hydrostatic & Operating Levels) 8.2 One-Foot Method, Variable Design Point & Reconstructed-Tank Shell Thickness 8.3 Joint Efficiency (E) Selection, Missing Data & Radiography Factors 8.4 Evaluation of Pitting, Localized Thin Areas (LTA) & Critical Length (L)

9 Chapter 9: Bottom Plate & Annular Ring Thickness Evaluation

9.1 Minimum Bottom Thickness Formulations (MRT, MRTbottom, MRTlinear) 9.2 Annular Plate Evaluation, Stress Criteria & Critical Zones 9.3 Bottom Pitting Evaluation & Remaining Thickness Before Next Inspection

10 Chapter 10: Tank Repairs & Alterations Standards

10.1 Classification: Repair vs. Alteration vs. Reconstruction (API 653 Section 9) 10.2 Shell Plate Replacement, Lapped Patch Plates & Insert Plates 10.3 Shell Penetrations, Door Sheets & Nozzle Additions 10.4 Hot Tapping Requirements, Limitations & Pre-Engineering (API 653 Section 9.15 & API Publ 2201)

11 Chapter 11: Welding Procedures, Qualifications & Quality Control

11.1 Welding Procedure Specification (WPS) & Procedure Qualification Record (PQR) per ASME IX 11.2 Welder Performance Qualification (WPQ) & Continuity per ASME IX 11.3 Essential, Non-Essential & Supplementary Essential Variables 11.4 Preheating, Post-Weld Heat Treatment (PWHT) & Weld Flaw Remediation

12 Chapter 12: Nondestructive Examination (NDE) Methods

12.1 Visual Examination (VT) & Magnetic Particle Testing (MT) per ASME V 12.2 Liquid Penetrant (PT) & Ultrasonic Thickness Measurement (ASME V Article 6 & SE-797) 12.3 Radiographic Testing (RT): Acceptance Criteria, Film Interpretation & ASME V/API 650

13 Chapter 13: Hydrostatic Testing & Post-Repair Examination

13.1 Hydrostatic Test Triggers, Exemption Criteria & Major Alterations (API 653 Section 12.3) 13.2 Leak Testing: Vacuum Box, Tracer Gas, Diesel & Air Pressure Tests 13.3 NDE Examination Requirements for Shell, Bottom, Roof & Nozzle Welds (API 653 Section 12.1)

14 Chapter 14: Relief Devices, Tank Settlement & Nameplate Records

14.1 Pressure & Vacuum Relief Devices, Venting Principles (API RP 576 & API 2000) 14.2 Tank Settlement Types: Uniform, Tilt, Out-of-Plane & Edge Settlement (API 653 Annex B) 14.3 Evaluating Settlement Limits, Cosine Curve Analysis & Remedial Action 14.4 Tank Marking, Nameplates, Inspection Reports & Recordkeeping (API 653 Section 13)

9.1 Minimum Bottom Thickness Formulations (MRT, MRTbottom, MRTlinear)

Key Takeaways Explain This Topic AI

API 653 Section 4.4.5 mandates evaluating bottom plate integrity using the governing formula: MRT = (minimum of RT_bc or RT_ip) - O_r * (U_r + P_r), ensuring remaining plate thickness satisfies safety thresholds at the next scheduled inspection.

API 653 Table 4.4 sets the minimum bottom plate thickness at the next inspection at 0.10 in. (2.5 mm) where the tank bottom/foundation design gives no means of detecting and containing a bottom leak, and 0.05 in. (1.3 mm) where it does, or where a reinforced tank bottom lining thicker than 0.05 in. has been applied per API RP 652.

An applied reinforced tank bottom lining thicker than 0.050 in. (1.3 mm) conforming to API RP 652 allows an MRT threshold of 0.05 in., and may even tolerate perforation prior to the next inspection if engineered to structurally bridge anticipated perforations without leakage.

The operating interval O_r calculated from linear corrosion rates can in no case exceed 20 years under the prescriptive rules of API 653 Section 6.4.2, and drops to 10 years when corrosion rates are unknown and similar-service experience is unavailable; a formal Risk-Based Inspection assessment per API RP 580 may increase or decrease that figure, bounded by the safeguards credited in API 653 Table 6.1.

Accelerating or non-linear corrosion—triggered by microbial activity (SRB), cathodic protection shielding, water draw failures, or coating breakdown—invalidates linear projections and requires conservative interval down-rating.

Last updated: September 2026

Introduction to Tank Bottom Integrity and Degradation Dynamics

The bottom plate assembly of an aboveground atmospheric storage tank (AST) represents one of its most vulnerable mechanical components. Unlike the cylindrical tank shell, which can be readily inspected from the exterior during normal operations, the tank floor is subjected to simultaneous, unobservable corrosion attack from two opposing environments:

Internal (Product-Side) Corrosion : Driven by corrosive water bottoms, basic sediment and water (BS&W), entrained salts, organic acids, dissolved gases (hydrogen sulfide, carbon dioxide, oxygen), and anaerobic microbiologically influenced corrosion (MIC).

External (Soil-Side / Under-Bottom) Corrosion : Driven by moisture ingress beneath the floor, corrosive native soils or contaminated sand cushions, differential aeration cells, stray electrical currents, and uneven or shielded cathodic protection (CP) distribution.

Because an undetected floor perforation can result in severe environmental contamination, catastrophic product loss, costly soil remediation, and mandatory facility shutdowns, API Standard 653 Section 4.4 establishes rigorous quantitative procedures to determine whether an in-service bottom plate can safely remain in operation until the next scheduled internal turnaround.

The Governing Minimum Remaining Thickness (MRT) Formulation

API 653 Section 4.4.5.1 provides the fundamental mathematical model for evaluating bottom plate degradation and predicting the plate thickness that will remain at the end of a projected operating interval. +-------------------------------------------------------------------------+

• | API 653 BOTTOM THICKNESS EVALUATION |
• | |
• | Top-Side (Product) Metal Loss |
• | [ Rate = U_r ] |
• | ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
• | ====================+=========================+==================== |
• | | | Internal Pitting | | |
• | | | (RT_ip) | | |
• | | +------------v------------+ | |
• | | | |
• | | +------------^------------+ | |
• | | | Soil-Side Pitting | | |
• | | | (RT_bc) | | |
• | ====================+=========================+==================== |
• | ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
• | Soil-Side (Foundation) Metal Loss |
• | [ Rate = P_r ] |
• +-------------------------------------------------------------------------+

The governing formula for the Minimum Remaining Thickness ( M R T MRT MRT ) at the end of the operating interval is: M R T = ( minimum of R T b c or R T i p ) − O r ( U r + P r ) MRT = (\text{minimum of } RT_{bc} \text{ or } RT_{ip}) - O_r (U_r + P_r) MRT = ( minimum of R T b c ​ or R T i p ​ ) − O r ​ ( U r ​ + P r ​ )

Where:

M R T MRT MRT : Minimum remaining thickness of the bottom plate (in inches or millimeters) at the completion of the future operating period O r O_r O r ​ .

R T b c RT_{bc} R T b c ​ : Minimum remaining thickness from bottom-side (external/soil-side) corrosion after deducting bottom metal loss (in inches or millimeters).

R T i p RT_{ip} R T i p ​ : Minimum remaining thickness from internal (product-side) corrosion or pitting after deducting internal metal loss (in inches or millimeters).

O r O_r O r ​ : Planned in-service operating period until the next internal inspection (in years).

U r U_r U r ​ : Maximum expected rate of internal (product-side) corrosion (in inches/year or mm/year).

P r P_r P r ​ : Maximum expected rate of external (soil-side/bottom) corrosion (in inches/year or mm/year).

When metal loss is relatively uniform and pitting is not isolated to separate distinct faces, the formulation simplifies to the linear remaining thickness model ( M R T l i n e a r MRT_{linear} MR T l in e a r ​ ): M R T l i n e a r = t a c t u a l _ m i n − O r ( U r + P r ) MRT_{linear} = t_{actual\_min} - O_r (U_r + P_r) MR T l in e a r ​ = t a c t u a l _ min ​ − O r ​ ( U r ​ + P r ​ )

where t a c t u a l _ m i n t_{actual\_min} t a c t u a l _ min ​ represents the lowest validated ultrasonic thickness reading obtained on the bottom plate during the inspection.

Determining the Maximum Operating Interval ( O r O_r O r ​ )

Rearranging the governing equation allows the Authorized Inspector to solve directly for the maximum allowable run time before the bottom plate reaches its code-mandated thickness threshold ( M R T t h r e s h o l d MRT_{threshold} MR T t h res h o l d ​ ): O r = min ⁡ ( R T b c , R T i p ) − M R T t h r e s h o l d U r + P r O_r = \frac{\min(RT_{bc}, RT_{ip}) - MRT_{threshold}}{U_r + P_r} O r ​ = U r ​ + P r ​ min ( R T b c ​ , R T i p ​ ) − MR T t h res h o l d ​ ​

Important

Per API 653 Section 6.4.2, the calculated operating interval O r O_r O r ​ establishes the maximum calendar interval between out-of-service internal inspections. Under the prescriptive rules, O r O_r O r ​ shall in no case exceed 20 years , and shall not exceed 10 years when corrosion rates are not known and similar-service experience is not available. A formal Risk-Based Inspection assessment conducted in accordance with API RP 580 may increase or decrease that interval — including the 20-year figure — with the permissible extension bounded by the tank safeguards credited in API 653 Table 6.1 . The RBI assessment must be approved by an Authorized Inspector and a knowledgeable engineer and re-reviewed at intervals not exceeding 10 years.

Regulatory MRT Thresholds per API 653 Section 4.4.5

The minimum thickness threshold that the tank bottom plate must maintain at the end of the projected operating cycle ( M R T t h r e s h o l d MRT_{threshold} MR T t h res h o l d ​ ) is strictly governed by the tank's leak mitigation systems and protective barriers. API 653 Section 4.4.5 categorizes tank bottoms into three distinct operating configurations: +-------------------------------------------------------------------------+

• | API 653 SECTION 4.4.5 MRT THRESHOLDS |
• +---------------------------------------------+---------------------------+
• | Tank Bottom Operating Configuration | Minimum Allowable MRT |
• +---------------------------------------------+---------------------------+
• | 1. No means of detecting and containing a | 0.10 in. (2.5 mm) |
• | bottom leak, and no qualifying lining | |
• +---------------------------------------------+---------------------------+
• | 2. Tank bottom/foundation design provides | 0.05 in. (1.3 mm) |
• | a means to detect AND contain a leak | |
• +---------------------------------------------+---------------------------+
• | 3. Applied reinforced tank bottom lining | 0.05 in. (1.3 mm) |
• | thicker than 0.050 in., per API RP 652 | (Or perforation allowed |
• | | if structurally designed) |
• +---------------------------------------------+---------------------------+

1. No Leak Detection/Containment and No Qualifying Lining ( M R T ≥ 0.10 in. MRT \ge 0.10\text{ in.} MRT ≥ 0.10 in. )

For bare steel tank floors resting directly on an earthen, sand, or gravel pad with no secondary barrier or internal protective coating, the minimum acceptable remaining thickness at the conclusion of the operating interval is 0.10 in. (2.5 mm) . If calculations show that corrosion will erode the steel below 0.10 in. before the next scheduled turnaround, the owner-user must repair the thinned plates, shorten the inspection interval, or install mitigating barriers.

2. Leak Detection and Containment Provided ( M R T ≥ 0.05 in. MRT \ge 0.05\text{ in.} MRT ≥ 0.05 in. )

A Release Prevention Barrier (RPB) is defined in the API 653 Section 3 definitions as a secondary barrier erected beneath or around the tank bottom that diverts any leaking fluid to an accessible detection point and prevents soil and groundwater contamination. Recognized RPBs include:

Impervious flexible synthetic liners (e.g., HDPE or elastomer membranes) installed beneath the foundation.

Double-bottom constructions with an interstitial drainage space.

Concrete slabs with radial leak detection channels.

Because an RPB (or an applied reinforced tank bottom lining thicker than 0.05 in. per API RP 652) provides an additional layer of defense against unmonitored loss of containment, API 653 Table 4.4 allows the bottom steel to corrode down to 0.05 in. (1.3 mm) at the next inspection. A thin-film lining of 20 mils does not qualify — Table 4.4 names a reinforced lining thicker than 0.05 in.

3. Applied Reinforced Bottom Lining Thicker Than 0.05 in. (API RP 652)

Where an owner-user installs a thick-film fiberglass-reinforced epoxy or polyester lining system with a dry film thickness exceeding 0.050 in. (1.3 mm) in accordance with API RP 652 , the structural threshold remains M R T ≥ 0.05 in. MRT \ge 0.05\text{ in.} MRT ≥ 0.05 in. .

Furthermore, API 653 Section 4.4.5.2 and 4.4.5.3 incorporate a critical engineering allowance: perforation of the steel plate may be permitted prior to the next inspection if the thick-film reinforced lining is structurally engineered and verified to bridge and span the maximum anticipated perforation diameter without deflection, rupture, or leakage under full hydrostatic head.

Linear vs. Non-Linear and Accelerating Corrosion Modeling

In standard engineering assessments, corrosion rates ( U r U_r U r ​ and P r P_r P r ​ ) are modeled as linear constants derived from historical ultrasonic data: Corrosion Rate = t p r e v i o u s − t a c t u a l t e l a p s e d _ t i m e \text{Corrosion Rate} = \frac{t_{previous} - t_{actual}}{t_{elapsed\_time}} Corrosion Rate = t e l a p se d _ t im e ​ t p re v i o u s ​ − t a c t u a l ​ ​

While linear extrapolation is mathematically straightforward, operating conditions frequently trigger non-linear or accelerating corrosion kinetics that render simple linear models dangerously non-conservative. Plate Thickness

• ^
• | Linear Projection

t_0 +.................................

• | \
• | \
• | \
• MRT + - - - - - -\ - - - - - - - - - - [Code Threshold]
• | \
• | Accelerating \ <--- (CP failure, MIC breakout, water draw loss)
• | Corrosion \_ _ _
• 0 +-----------------------+---------> Time
• O_r
• Key Triggers of Non-Linear Acceleration

Microbiologically Influenced Corrosion (MIC) : In anaerobic water bottoms, colonies of Sulfate-Reducing Bacteria (SRB, e.g., Desulfovibrio ) produce localized biogenic hydrogen sulfide ( H 2 S H_2S H 2 ​ S ). Under mature biofilms, pitting rates can rapidly surge from a baseline of 2 mpy ( 0.002 in./yr 0.002\text{ in./yr} 0.002 in./yr ) to over 40 mpy ( 0.040 in./yr 0.040\text{ in./yr} 0.040 in./yr ), penetrating 1/4-in. plate within 3 to 5 years.

Cathodic Protection System Failure : A tank floor may experience near-zero soil-side corrosion while an impressed current cathodic protection (ICCP) system is operational. If rectifiers trip, positive anode cables disconnect, or reference cells drift, the soil-side corrosion rate can jump instantaneously to the unmitigated environmental rate (often 5 to 15 mpy).

Operational Lapses in Water Bottom Drainage : When automated or manual water-draw schedules are neglected, stagnant water layers accumulate. Stratified acidic water containing chlorides and dissolved oxygen sets up severe concentration cells, tripling internal metal loss rates.

Protective Coating Degradation : Internal epoxy linings typically follow an S-curve degradation model. For years, the lining provides total isolation ( U r = 0 U_r = 0 U r ​ = 0 ). Once blistering, under-film corrosion, or mechanical damage occurs, localized attack concentrates at pinholes (holidays), generating intense galvanic pitting.

When evidence of accelerating mechanisms exists, the Authorized Inspector must utilize upper-bound or non-linear corrosion rates, or establish an abbreviated inspection frequency.

• Step-by-Step Worked Numerical Examples
• Example 1: Verifying MRT for a Prescriptive 10-Year Interval

An unlined carbon steel crude oil storage tank resting on an earthen pad without an RPB was inspected out of service. Ultrasonic floor scanning identified the following limiting parameters:

Original nominal bottom thickness ( t n o m i n a l t_{nominal} t n o mina l ​ ): 0.250 in. 0.250\text{ in.} 0.250 in.

Minimum remaining thickness from soil-side corrosion ( R T b c RT_{bc} R T b c ​ ): 0.185 in. 0.185\text{ in.} 0.185 in.

Minimum remaining thickness from internal pitting ( R T i p RT_{ip} R T i p ​ ): 0.170 in. 0.170\text{ in.} 0.170 in.

• Maximum internal corrosion rate ( U r U_r U r ​ ): 0.003 in./year 0.003\text{ in./year} 0.003 in./year
• Maximum soil-side corrosion rate ( P r P_r P r ​ ): 0.004 in./year 0.004\text{ in./year} 0.004 in./year

Proposed operating interval until next internal inspection ( O r O_r O r ​ ): 10 years 10\text{ years} 10 years

Calculation Steps :

Identify the limiting baseline thickness : min ⁡ ( R T b c , R T i p ) = min ⁡ ( 0.185 , 0.170 ) = 0.170 in. \min(RT_{bc}, RT_{ip}) = \min(0.185, 0.170) = 0.170\text{ in.} min ( R T b c ​ , R T i p ​ ) = min ( 0.185 , 0.170 ) = 0.170 in.

Calculate total combined annual corrosion rate : U r + P r = 0.003 + 0.004 = 0.007 in./year U_r + P_r = 0.003 + 0.004 = 0.007\text{ in./year} U r ​ + P r ​ = 0.003 + 0.004 = 0.007 in./year

Calculate expected metal loss over the 10-year operating interval : Total Metal Loss = O r × ( U r + P r ) = 10 × 0.007 = 0.070 in. \text{Total Metal Loss} = O_r \times (U_r + P_r) = 10 \times 0.007 = 0.070\text{ in.} Total Metal Loss = O r ​ × ( U r ​ + P r ​ ) = 10 × 0.007 = 0.070 in.

Calculate Minimum Remaining Thickness at end of interval ( M R T MRT MRT ) : M R T = 0.170 − 0.070 = 0.100 in. MRT = 0.170 - 0.070 = 0.100\text{ in.} MRT = 0.170 − 0.070 = 0.100 in.

Determine code compliance :

Since the tank has no lining and no RPB, the mandatory threshold per API 653 Section 4.4.5 is M R T t h r e s h o l d = 0.100 in. MRT_{threshold} = 0.100\text{ in.} MR T t h res h o l d ​ = 0.100 in. . Because the projected M R T = 0.100 in. ≥ 0.100 in. MRT = 0.100\text{ in.} \ge 0.100\text{ in.} MRT = 0.100 in. ≥ 0.100 in. , the tank bottom strictly satisfies code requirements for a 10-year run.

Example 2: Determining Maximum Inspection Interval ( O r O_r O r ​ ) with and without an RPB

Using the identical tank data from Example 1 ( min ⁡ ( R T ) = 0.170 in. \min(RT) = 0.170\text{ in.} min ( RT ) = 0.170 in. , U r + P r = 0.007 in./yr U_r + P_r = 0.007\text{ in./yr} U r ​ + P r ​ = 0.007 in./yr ), determine the absolute maximum allowable operating interval O r O_r O r ​ :

Case A: Without RPB and Without Lining ( M R T t h r e s h o l d = 0.100 in. MRT_{threshold} = 0.100\text{ in.} MR T t h res h o l d ​ = 0.100 in. ) O r = 0.170 − 0.100 0.007 = 0.070 0.007 = 10.0 years O_r = \frac{0.170 - 0.100}{0.007} = \frac{0.070}{0.007} = 10.0\text{ years} O r ​ = 0.007 0.170 − 0.100 ​ = 0.007 0.070 ​ = 10.0 years

Conclusion : The tank cannot operate a day beyond 10.0 years without violating API 653 thickness limits.

Case B: Retrofitted with an HDPE Release Prevention Barrier providing leak detection and containment ( M R T t h r e s h o l d = 0.050 in. MRT_{threshold} = 0.050\text{ in.} MR T t h res h o l d ​ = 0.050 in. ) O r = 0.170 − 0.050 0.007 = 0.120 0.007 ≈ 17.14 years O_r = \frac{0.170 - 0.050}{0.007} = \frac{0.120}{0.007} \approx 17.14\text{ years} O r ​ = 0.007 0.170 − 0.050 ​ = 0.007 0.120 ​ ≈ 17.14 years

Conclusion : Installing an RPB expands the allowable operating interval from 10.0 years to 17.1 years (well within the 20-year code maximum), deferring major turnaround capital expenditure by over 7 years.

Comparison Table: Bottom Configurations and Inspection Strategy

Parameter No leak detection/containment, no qualifying lining Leak detection and containment provided (RPB) Applied reinforced lining > 0.05 in. per API RP 652

Governing Code Section API 653 Section 4.4.5.1 API 653 Section 4.4.5.2 API 653 Section 4.4.5.2 / API RP 652

Table 4.4 MRT Threshold 0.10 in. 0.10\text{ in.} 0.10 in. ( 2.5 mm 2.5\text{ mm} 2.5 mm ) 0.05 in. 0.05\text{ in.} 0.05 in. ( 1.3 mm 1.3\text{ mm} 1.3 mm ) 0.05 in. 0.05\text{ in.} 0.05 in. ( 1.3 mm 1.3\text{ mm} 1.3 mm )

Perforation Allowed Before Next Inspection? Strictly Prohibited Strictly Prohibited Permitted if structurally verified to span hole

Prescriptive Max Interval Lesser of calculated O r O_r O r ​ and 20 years (10 years if rates unknown) Lesser of calculated O r O_r O r ​ and 20 years Lesser of calculated O r O_r O r ​ and 20 years

Max Interval with RBI Set by the RBI assessment, bounded by the Table 6.1 safeguards Set by the RBI assessment, bounded by the Table 6.1 safeguards Set by the RBI assessment, bounded by the Table 6.1 safeguards

Primary Mitigation Mechanism Structural steel thickness margin Secondary containment / dielectric barrier High-build reinforced bridging composite