This study was designed to develop a normalized stiffness-based framework for estimating the FRP thickness required to repair steel pipes with external corrosion defects. The analysis focused on the hoop stress response of an axisymmetrically repaired pipe subjected to operational internal pressure. Since the applied pressure did not induce plastic deformation in the steel pipe, the response remained within the elastic range and was therefore modeled using linear elastic material behavior. The main objective was to determine the required normalized FRP thickness, tF/a, needed to restore the maximum inner-hoop stress of the corroded steel pipe to within a specified tolerance relative to the intact pipe.

The investigated model consisted of a steel pipe containing an external corrosion groove of finite axial length Ld that extended continuously around the full pipe circumference, filled with epoxy and externally wrapped with an FRP repair layer, as illustrated in Fig. 1. In three-dimensional geometric terms, this axisymmetric idealization corresponds to an annular circumferential groove rather than a localized corrosion patch. The parameter Ld therefore represents the axial extent of the groove. This idealization was adopted to represent a conservative circumferential wall loss condition and to allow the repaired pipe to be modeled using an axisymmetric radial–axial cross-section in ABAQUS. The geometric parameters included the pipe diameter D, pipe thickness t, defect depth a, defect length Ld, FRP repair thickness tF, and FRP repair length LF. The pipe diameter and length were kept constant at D = 406.4 mm and L = 4064 mm, respectively, while the pipe's diameter-to-thickness ratio was varied as D/t=10, 20, and 40, corresponding to pipe thicknesses of 40.64, 20.32, and 10.16 mm, respectively.

The normalized corrosion depth was varied as a/t=0.10, 0.20, 0.30, 0.40, 0.50, and 0.60. Previous work showed that increasing the normalized defect length beyond Ld/D=0.50 produced negligible additional influence on the maximum inner-hoop stress (Alhusain, 2026b). Accordingly, the defect length was fixed at Ld/D=0.50 to represent a near-saturated critical defect length condition. The FRP repair length was fixed at LF/Ld=1.00, corresponding to the minimum repair length that fully covered the defect. Previous work also showed that extending the FRP repair beyond the defect length produced only a marginal additional reduction in the maximum inner-hoop stress (Alhusain, 2026a). Therefore, LF/Ld=1.00 was adopted as a conservative full-coverage repair condition. These fixed values allowed the effects of the defect depth, pipe geometry, and FRP orthotropic stiffness level on the required normalized repair thickness to be isolated.

The FRP layer was represented using a normalized orthotropic stiffness model in which the overall stiffness level was varied through the stiffness ratio EF/E, where EF is the FRP hoop direction modulus, and E is the elastic modulus of the steel pipe. Six stiffness ratios were considered: EF/E=0.20, 0.40, 0.60, 0.80, 1.00, and 1.20. The parameter was indexed by the hoop direction modulus, whereas the remaining elastic and shear moduli were scaled proportionally to preserve the relative anisotropy of the reference FRP material. The complete simulation matrix and fixed geometric and/or loading parameters are listed in Table 1.

For each combination of D/t, a/t, and EF/E, the required value of tF/a was determined by iteratively adjusting the FRP thickness until the maximum inner-hoop stress in the repaired steel pipe satisfied the adopted stress tolerance criterion: 1σθ,repairedmax⁡≤1.10σθ,intact, where σθ,repairedmax⁡ is the maximum inner-hoop stress in the repaired steel pipe, and σθ,intact is the corresponding maximum inner-hoop stress in the intact pipe with the same D/t ratio. The 10 % stress tolerance criterion was adopted following previous work by Alhusain (2026a), in which the same criterion was used for preliminary carbon-fiber-reinforced polymer (CFRP) repair sizing of corroded steel pipelines. More generally, assessing repair effectiveness relative to the corresponding intact structural response is consistent with previous FRP rehabilitation studies. For example, George et al. (2021) evaluated repair performance using a strength regain ratio referenced to the intact member and reported full recovery of the intact capacity in most cases and approximately 90 % recovery for the pure axial-compression specimens. Accordingly, the present criterion was adopted as a consistent benchmark requiring substantial recovery toward the intact-pipe stress response rather than as a code-prescribed acceptance requirement.

For the feasible repaired cases, the selected tF/a values reduced the maximum inner-hoop stress to approximately 9.5 %–10 % above the corresponding intact-pipe stress, confirming that the reported repair thicknesses were close to the target tolerance rather than being substantially over-conservative. An upper bound of tF/a=5 was adopted to delimit the repair thickness search rather than to define an absolute physical feasibility limit. For the deepest defect considered in this study, a/t=0.60, this upper bound corresponds to an FRP thickness equal to 3 times the pipe wall thickness. Therefore, the selected limit provides a sufficiently broad range for preliminary repair sizing while avoiding an excessively large composite buildup. Cases for which the stress recovery criterion was not satisfied within tF/a≤5 were classified as having indeterminate feasibility (IF), indicating that their feasibility beyond the investigated thickness range was not evaluated. The resulting dataset was used to evaluate repair feasibility; quantify the effects of EF/E, a/t, and D/t on the required FRP thickness; and develop a compact empirical correlation for preliminary repair thickness estimation. The complete FE-derived repair thickness data used to construct the design maps are provided in the Supplement.

A structured axisymmetric mesh was generated for the repaired pipe model, as illustrated in Fig. 3. The steel pipe, epoxy filler, and FRP repair layer were discretized using eight-node biquadratic axisymmetric quadrilateral elements (CAX8). These second-order elements were selected to improve the representation of stress gradients through the pipe wall and across the repaired region. A fine mesh was used in the corrosion defect, epoxy filler, and FRP repair regions to capture the local stress gradients near the repaired defect. A magnified view of the repair region is shown in Fig. 3, illustrating the mesh distribution across the steel pipe, epoxy filler, and FRP layer.

A mesh convergence study was performed using a representative repaired pipe model with D/t=20, EF/E=0.4, and a/t=0.60. Four mesh sizes were examined, ranging from 6 to 1 mm, as summarized in Table 4. The convergence assessment was based on the maximum hoop stress at three locations: the inner steel surface, defect end region, and outer steel surface. The defect end stress was included as a local convergence indicator because this region contains the strongest geometric discontinuity and stress gradient in the repaired model. The percentage error was calculated relative to the finest mesh (M4).

The maximum inner-hoop stress was insensitive to mesh refinement and remained constant at 103.9 MPa for all investigated mesh sizes. The defect end hoop stress also showed excellent convergence, with the error decreasing from 0.15 % for the 6 and 4 mm meshes to 0.05 % for the 2 mm mesh. The outer surface hoop stress exhibited the largest mesh sensitivity for the coarsest mesh, with an error of 3.24 % for M1. However, this error decreased to 0.97 % for M2 and only 0.06 % for M3.

Based on these results, a 2 mm mesh was selected for the parametric study. This mesh produced the same maximum inner-hoop stress as the finest 1 mm mesh and resulted in errors of only 0.05 % and 0.06 % for the defect end and outer surface hoop stresses, respectively. Therefore, further refinement to 1 mm provided negligible improvement while increasing the computational cost.

Before conducting the parametric study, the axisymmetric FE model was verified using a closed-form multilayer thick cylinder solution. Verification was performed to confirm that the FE model correctly reproduced the elastic-hoop stress response of a bonded steel–epoxy–FRP system under internal pressure. A three-layer cylindrical configuration consisting of a steel pipe, epoxy filler, and external repair layer was considered. The pipe was treated as open-ended, consistent with the FE boundary conditions, and perfect bonding was assumed between the adjacent layers.

This verification was intended to confirm the implementation of the bonded multilayer elastic cylinder model, including pressure loading, material layering, and interfacial compatibility. It was not used as a validation of the local corrosion defect response because the analytical Lamé solution does not represent geometric wall loss discontinuities.

An analytical solution was obtained using the Lamé thick-cylinder theory (Timoshenko et al., 1970). For each layer, the radial and hoop stresses were expressed as 2σr=A-Br2,3σθ=A+Br2, where r is the radial coordinate, and A and B are the Lamé constants for the corresponding layer. The constants were evaluated using the pressure boundary conditions at the inner and outer radii and the interface pressures between adjacent layers. Since the model represents an open-ended pipe, the radial displacement used for enforcing interfacial compatibility was written as 4u(r)=(1-ν)Ar+(1+ν)B/rE, where E and ν are the elastic modulus and Poisson's ratio of the layer. The unknown interface pressures were obtained by satisfying the displacement continuity at the steel–epoxy and epoxy–FRP interfaces.

The verification was carried out for D/t=10, 20, and 40 while keeping the pipe diameter constant at D = 406.4 mm. The corresponding pipe thicknesses were 40.64, 20.32, and 10.16 mm, respectively. For the verification analysis, both the epoxy and FRP layer thicknesses were set to be equal to 20 % of the pipe wall thickness. The FE model retained the orthotropic FRP properties corresponding to EF/E=0.40, with a hoop direction modulus of E3=EF = 82 400 MPa. For the analytical multilayer-cylinder solution, the FRP layer was represented using an equivalent isotropic elastic modulus of 82 400 MPa and a Poisson's ratio of 0.30. This equivalent isotropic representation was used only in the analytical calculation; the FRP material in the FE model remained orthotropic. The inner and outer surface hoop stresses in both the steel pipe and FRP layer were extracted from the FE model and compared with the analytical results.

As shown in Fig. 4, the FE predictions were in close agreement with the analytical solution for all investigated D/t ratios. The hoop stresses on the inner and outer surfaces of the steel pipe were nearly identical between the two approaches, and a similar agreement was observed for the FRP layer. This agreement confirms that the axisymmetric FE model accurately captures the elastic stress distribution and load transfer in the bonded multilayer systems. Therefore, the verified model was used for the subsequent parametric investigation of the required normalized FRP repair thickness.

To provide an additional literature-based validation for a repaired pipe containing actual wall thinning, the validation procedure previously reported by Alhusain (2026a) was adopted, in which selected axisymmetric composite-repair cases from Saeed et al. (2014) were reproduced. Two zero-live-pressure cases with circumferential wall thinning of 30 % and 40 % were reproduced using the pipe geometry, repair thicknesses, composite properties, and design pressure reported in the reference study. Saeed et al. employed a two-dimensional axisymmetric FE model and evaluated the composite response at a design pressure of 27.25 MPa. The present FE model predicted maximum FRP hoop strains of approximately 0.200 % and 0.211 % for the 30 % and 40 % wall-thinning cases, respectively. The corresponding analytical values were approximately 0.199 % and 0.210 %, while the digitized literature FEA values were approximately 0.203 % and 0.223 %, as shown in Fig. 4c. The present FE predictions therefore differed from the digitized literature values by approximately 1.5 % and 5.4 %, respectively, indicating a reasonable agreement. Although the analytical and literature-based benchmarks do not reproduce the finite defect end geometry, the local stress response was assessed through the mesh convergence study in Sect. 2.3, where the selected 2 mm mesh differed from the finest 1 mm mesh by only 0.05 % in the defect end hoop stress.

After determining the required FRP thickness from the FE simulations, the resulting dataset was used to develop a compact empirical correlation for estimating the normalized repair thickness, tF/a. The correlation was formulated in terms of the three main non-dimensional parameters considered in the parametric study: the FRP-to-steel-stiffness ratio EF/E, the normalized defect depth a/t, and the pipe diameter-to-thickness ratio D/t. The objective was to define a design-oriented functional form that captures the main FE trends and that can be used for the preliminary estimation of the required FRP repair thickness.

The proposed functional form was selected based on the trends observed in the FE results. The required normalized repair thickness decreased with increasing EF/E, increased with increasing a/t, and varied with D/t in a manner dependent on the defect depth. Accordingly, the following general correlation was adopted: 5tFa=CEFEna/t0.20pD/t20q[(a/t)-0.20], where C, n, p, and q are the fitting constants. The reference values a/t=0.20 and D/t=20 were used to normalize the correlation around representative values within the investigated parameter range.

The fitting constants were obtained using MATLAB by minimizing the difference between the FE-derived and predicted values of tF/a. Only feasible repaired cases were included in the fitting dataset. Cases classified as no repair were excluded because they correspond to tF/a=0, while IF cases were excluded because the stress recovery criterion was not achieved within the investigated upper limit of tF/a=5. The shallowest defect cases with a/t=0.10 were also excluded from the fitting and error evaluation because several of these cases required no repair or very small repair thicknesses, which can distort a power-law correlation intended for finite repair demand.

To assess the predictive robustness of the proposed correlation form, 5-fold cross-validation was performed using the 74 eligible FE cases. The cases were randomly divided into five approximately equal groups, G1–G5, containing 14–15 cases each. In each run, four groups were used to refit the correlation coefficients C, n, p, and q, while the remaining group was withheld for validation, as summarized in Table 5. This procedure ensured that every case was used once for validation. The overall cross-validation statistics were calculated from the combined held-out predictions. Detailed group assignments, fold-specific fitted coefficients, and validation statistics are provided in the Supplement. The fold-specific coefficients were used only for cross-validation, whereas the final correlation reported in Sect. 3.4 was fitted using the complete set of 74 eligible FE cases.

The optimized constants and predictive performance of the final correlation are presented in Sect. 3.4. The proposed correlation was developed for the parameter ranges investigated in this study and is intended as a preliminary thickness estimation tool for elastic-hoop stress recovery. Therefore, its use should be limited to the fitted parameter range and should not be interpreted as a substitute for detailed design checks involving FRP failure, interfacial debonding, installation constraints, or long-term durability.

The overall repair response was first examined by comparing the representative hoop stress distributions before and after repair. Figure 5 shows the hoop stress contours for the case D/t=20 and a/t=0.4, including the unrepaired pipe and two repaired configurations with different FRP stiffness ratios. The unrepaired pipe exhibited a significantly higher hoop stress field near the corrosion defect, confirming the stress amplification caused by the local wall thickness reduction. After repair, the steel-hoop stress was substantially reduced, and the two repaired cases produced similar stress distributions despite using different FRP stiffness ratios and repair thicknesses.

For the repaired cases shown in Fig. 5, the lower-stiffness repair with EF/E=0.4 required a larger normalized thickness of tF/a=2.50, whereas the higher-stiffness repair with EF/E=1.2 required only tF/a=0.75. The similarity between the repaired stress fields indicates that comparable elastic repair performances can be obtained using different FRP systems when the repair thickness is adjusted according to the FRP stiffness. Therefore, EF/E primarily controls the amount of repair thickness required to achieve the target stress reduction, which is consistent with previous findings that composite stiffness governs load sharing in repaired steel pipes (Chen et al., 2021; Dumitrescu et al., 2021). In the present cases, once the same stress recovery criterion was satisfied, the repaired steel stress distributions remained broadly similar despite the different stiffness–thickness combinations.

The complete feasibility map is shown in Fig. 6. This figure summarizes the required tF/a values for all of the investigated combinations of D/t, a/t, and EF/E. Cases marked as NR indicate that the unrepaired corroded pipe already satisfied the 10 % stress tolerance criterion and therefore did not require an FRP repair. Cases marked as IF indicate indeterminate feasibility, meaning that the criterion was not satisfied within the investigated upper limit of tF/a≤5. This classification distinguishes between cases in which repair is unnecessary, cases in which the criterion can be satisfied within the investigated thickness range, and cases for which the feasibility beyond this range remains undetermined. Accordingly, the NR and IF classifications are specific to the adopted 10 % stress tolerance criterion and tF/a≤5 search limit and should not be interpreted as absolute classifications independent of these thresholds. The feasibility map also shows that low-stiffness FRP systems are more likely to reach the investigated upper thickness limit for deeper defects than high-stiffness FRP systems.

The influence of FRP stiffness was particularly evident at EF/E=0.2, where the stress recovery criterion was satisfied within the investigated thickness range for fewer parameter combinations as the defect depth increased. In contrast, higher stiffness ratios expanded the range of configurations for which the criterion was satisfied and reduced the required normalized thickness over a wider range of a/t and D/t. These results demonstrate that the ability to satisfy the adopted stress recovery criterion within the investigated thickness range depends on the combined effects of defect severity, pipe geometry, and FRP stiffness.

The influence of the FRP-to-steel-stiffness ratio, EF/E, on the required normalized repair thickness is shown in Fig. 7. For all of the investigated D/t ratios, increasing EF/E reduced the required tF/a. This trend is expected because a stiffer FRP layer provides greater circumferential resistance to pressure-induced deformation, allowing the target reduction in steel-hoop stress to be achieved with a smaller repair thickness. This behavior is consistent with previous findings, which show that the stiffness of the composite repair layer governs load sharing between the steel pipe and the external repair system (Ansari Sadrabadi et al., 2022; Duell et al., 2008; Lim et al., 2019).

For D/t=10, the repair demand was highly dependent on both the defect depth and FRP stiffness, as shown in Fig. 7a. Shallow defects with a/t=0.1 did not require repair because the unrepaired pipe already satisfied the 10 % stress tolerance criterion. For larger defects, however, the required tF/a decreased markedly as EF/E increased. For example, at a/t=0.2, the required thickness decreased from tF/a=3.30 at EF/E=0.2 to tF/a=0.47 at EF/E=1.2. For deeper defects, some low-stiffness cases exhibited indeterminate feasibility within the investigated upper limit of tF/a≤5, indicating that increasing repair stiffness becomes increasingly important as the defect severity increases.

A similar reduction in the required repair thickness was observed for D/t=20, as shown in Fig. 7b. For this geometry, feasible repairs were obtained over a wider range of defect depths and stiffness ratios. The required tF/a decreased consistently with increasing EF/E for all defect depths. At a/t=0.4, the required normalized thickness decreased from tF/a=2.50 at EF/E=0.4 to tF/a=0.75 at EF/E=1.2. This behavior confirms that higher-stiffness FRP systems can substantially reduce the repair thickness required to satisfy the same stress criterion.

For D/t=40, shown in Fig. 7c, the effect of EF/E remained clear, but the reduction in tF/a became more gradual at higher stiffness ratios. The curves show a steep decrease between EF/E=0.2 and 0.6, followed by smaller reductions as EF/E increased further. This indicates that the benefit of increasing the FRP stiffness is strongest when moving from low-stiffness to moderate-stiffness repair systems, while further increases in stiffness produce progressively smaller reductions in the required normalized thickness.

Overall, Fig. 7 confirms that EF/E is one of the dominant parameters controlling the required repair thickness. The decrease in tF/a with increasing EF/E was consistent across all pipe geometries and defect depths. However, the magnitude of this reduction depended on a/t and D/t, showing that FRP stiffness cannot be evaluated independently from defect severity and pipe geometry. These results support the use of a normalized stiffness-based correlation, in which EF/E, a/t, and D/t are considered simultaneously.

The effect of the pipe diameter-to-thickness ratio, D/t, on the required normalized FRP thickness is shown in Fig. 8. Unlike the effect of FRP stiffness, the influence of D/t was more dependent on the defect depth and stiffness ratio. This indicates that pipe slenderness affects the repair demand through its influence on the stress recovery target and the remaining wall stiffness. Previous numerical work on FRP-reinforced steel pipes has similarly shown that pipe dimensions, including diameter and wall thickness, influence the effectiveness of composite reinforcement (Elchalakani et al., 2017; Li et al., 2022; Sebeay and Ahmed, 2023).

For low FRP stiffness, the effect of D/t was more pronounced, and the feasible repair region was limited. At EF/E=0.2, shown in Fig. 8a, several deeper-defect cases exhibited indeterminate feasibility within the investigated upper thickness limit. For the feasible cases, the required tF/a did not vary monotonically in the same way for all defect depths. For shallow defects, the thicker-pipe case was less demanding and could even require no repair. However, for larger defects, the stress recovery criterion was not achieved for some low-stiffness configurations within the investigated thickness range.

As the stiffness ratio increased, the influence of D/t decreased. For EF/E=0.4 and 0.6, shown in Fig. 8b and c, the required tF/a generally decreased as D/t increased for moderate and deep defects. This trend suggests that, within the investigated range, thinner-walled pipes require smaller normalized repair thicknesses once the repair is feasible. However, this does not imply that thinner pipes are less stressed in terms of absolute values. Instead, it reflects how the normalized repair thickness required to restore the stress to the corresponding intact-pipe baseline changes with the wall slenderness.

For higher stiffness ratios, EF/E=0.8, 1.0, and 1.2, shown in Fig. 8d–f, the curves became flatter for most defect depths. This indicates that increasing the FRP stiffness reduces the sensitivity of the required thickness to D/t. At high stiffness ratios, the FRP layer provides sufficient circumferential stiffness such that the required tF/a becomes controlled more by the defect depth than by pipe slenderness. Nevertheless, the deepest defect cases still showed visible sensitivity to D/t, especially for a/t=0.5 and 0.6.

The shallow-defect cases exhibited different behaviors compared to the deeper defects. For a/t=0.1, some configurations required no repair, particularly for D/t=10. This occurs because the remaining steel wall is sufficiently stiff for shallow corrosion, such that the unrepaired pipe can remain close to the 10 % stress tolerance criterion. As D/t increases, the same normalized defect depth corresponds to a thinner pipe wall, and the no-repair condition becomes less common. This explains why the shallow-defect curves may increase slightly with D/t, while deeper-defect curves generally decrease or become less sensitive as D/t increases.

Overall, Fig. 8 shows that D/t has a secondary but important influence on the repair thickness. Its effect is strongest for low-stiffness FRP systems and deeper defects, where the feasibility of repair can change depending on the pipe geometry. At higher FRP stiffness ratios, the required thickness becomes less sensitive to D/t, supporting the conclusion that repair stiffness can reduce the geometric dependence of the required FRP thickness.

The fitting procedure described in Sect. 2.5 was applied to the FE-derived repair thickness dataset to obtain the constants for the proposed empirical correlation. The optimized constants were obtained as C=0.577, n = -1.063, p=0.876, and q = -1.850. Therefore, the final proposed correlation is expressed as 6tFa=.577EFE-1.063a/t0.200.876×D/t20-1.850[(a/t)-0.20].

The correlation structure reflects the main trends observed in the FE results. The negative exponent of EF/E indicates that the required normalized repair thickness decreases as the FRP stiffness increases. Because this exponent is close to -1, the required repair thickness is approximately inversely related to the overall orthotropic stiffness level represented by EF/E. The positive exponent of a/t confirms that deeper defects require larger normalized repair thicknesses. The final term accounts for the interaction between D/t and the defect depth, allowing the effect of pipe slenderness to vary with a/t rather than being treated as a constant scaling factor.

Figure 9 compares the FE-derived tF/a values with the values predicted by the proposed correlation for D/t=10, 20, and 40. The markers represent the FE results, and the solid lines represent the proposed correlation. For visual continuity, the correlation curves are extended below a/t=0.20; however, this portion lies outside the fitted correlation domain and was not included in the fitting or error evaluation. For D/t=10, the correlation captures the rapid increase in the required repair thickness with increasing a/t, particularly for low stiffness ratios. For D/t=20, the proposed equation follows the FE trends over a wider range of defect depths and stiffness ratios. For D/t=40, the correlation captures the more gradual increase in required thickness for moderate and high stiffness ratios, as well as the stronger nonlinear response observed for low-stiffness repair systems.

The overall predictive performance of the proposed correlation was further evaluated using the parity plot shown in Fig. 10. Most data points were located close to the one-to-one reference line, indicating good agreement between the FE-derived and predicted tF/a values. The agreement was strongest in the moderate repair thickness range, where most feasible cases were found. Larger deviations occurred mainly near the upper repair thickness range, where the response became more sensitive to the low FRP stiffness and proximity to the investigated upper thickness limit.

The predictive accuracy of the final correlation against the complete fitting dataset was quantified using the coefficient of determination (R2), mean absolute error (MAE), root-mean-square error (RMSE), and mean absolute percentage error (MAPE). The correlation achieved R2 = 0.90, MAE = 0.13, RMSE = 0.34, and MAPE = 7.36 %, indicating good overall agreement with the FE-derived repair thicknesses. To further assess the predictive performance on held-out cases, five-fold cross-validation was performed as described in Sect. 2.5. The combined held-out predictions yielded R2 = 0.86, MAE = 0.14, RMSE = 0.38, and MAPE = 6.71 %. The fold-specific MAPE ranged from 5.41 % to 8.49 %. The comparable error levels obtained for the complete fitting dataset and the held-out cases indicate that the proposed correlation form retains good predictive capability within the investigated parameter space. Detailed cross-validation results are provided in the Supplement.

Overall, Figs. 9 and 10 show that the proposed correlation provides a reasonable preliminary estimate of the required normalized FRP thickness within the investigated parameter range. The correlation is applicable for feasible repair cases within 0.20≤EF/E≤1.20, 0.20≤a/t≤0.60, and 10≤D/t≤40, with Ld/D=0.50 and LF/Ld=1.00. It should be used as a preliminary thickness estimation tool for elastic-hoop stress recovery, while detailed design should also consider strength limits, FRP failure, interfacial debonding, installation constraints, and long-term durability. Accordingly, the correlation should be interpreted as an interpolation tool within the investigated parameter domain since its predictive accuracy outside these ranges has not been established.

The FE-based results presented in this study provide a normalized map of the FRP thickness required to reduce the maximum inner-hoop stress of a corroded steel pipe to within 10 % above the corresponding intact-pipe value. The maps are intended to show how the required normalized repair thickness, tF/a, changes with the defect depth, pipe diameter-to-thickness ratio, and FRP orthotropic stiffness level. Therefore, the main use of the results is to support preliminary repair assessment by identifying whether a given corrosion severity can be repaired within a practical thickness range and how the required repair thickness changes when a lower- or higher-stiffness FRP system is used for repair.

The feasibility classification used in this study should be interpreted within the adopted repair criterion and the investigated thickness range. Cases marked as no repair indicate that the unrepaired corroded pipe satisfied the 10 % stress tolerance criterion. Cases marked as IF indicate indeterminate feasibility, meaning that the criterion was not achieved within the investigated upper limit of tF/a=5. This classification does not imply that repair is physically infeasible beyond this limit; rather, repair thicknesses exceeding this range were not considered. In practice, the maximum acceptable repair thickness may depend on the installation method, available wrapping systems, allowable diameter increase, accessibility, and project-specific requirements.

The findings are applicable within the parameter range investigated in the FE study: 0.20≤EF/E≤1.20, 0.10≤a/t≤0.60 for the FE maps, and 10≤D/t≤40. The defect length and repair length were fixed at Ld/D=0.50 and LF/Ld=1.00, respectively. These values were selected based on previous parametric studies rather than as arbitrary fixed conditions. A defect length of Ld/D=0.50 represents a near-saturated critical condition because further increases in defect length produced negligible additional influence on the maximum inner-hoop stress (Alhusain, 2026b). Similarly, LF/Ld=1.00 represents the minimum full-coverage repair condition, while extending the FRP beyond the defect length produced only marginal additional stress reduction (Alhusain, 2026a). Nevertheless, because Ld/D and LF/Ld were not varied in the present parametric matrix, the thickness maps and correlation should be applied directly only to these fixed ratios. Application to substantially different defect lengths, partial-coverage repairs, or other repair length ratios requires additional analysis.

Several modeling assumptions must be considered. The analysis was limited to the elastic-hoop stress recovery under internal pressure. The present thickness maps were developed specifically for open-ended pipes, for which no closed-end axial pressure load was applied. Accordingly, the predicted tF/a values are directly applicable to this loading condition. Closed-ended pipes additionally develop a pressure-induced axial membrane stress, which could modify the local multi-axial stress state and should therefore be assessed separately. The steel pipe and epoxy filler were modeled as linear elastic materials, and the FRP layer was represented using an orthotropic-elastic-stiffness model. Perfect bonding was assumed at the steel–epoxy and epoxy–FRP interfaces; therefore, interfacial debonding, adhesive failure, slip, and installation defects were not included. Such interfacial imperfections could reduce load transfer to the FRP layer and may therefore increase the repair thickness required to satisfy the same steel-hoop stress criterion. The repaired configuration was also modeled as axisymmetric with a continuous external FRP layer; therefore, localized three-dimensional corrosion shapes, nonuniform repair thickness, wrinkles, voids, and imperfect surface preparation were outside the scope of this study.

Accordingly, the thickness maps and proposed correlation presented in this study should be used as preliminary design support tools for elastic stress recovery and not as final repair design rules. The final repair design should include checks for FRP tensile capacity, adhesive stresses, bond durability, environmental degradation, installation constraints, safety factors, and relevant repair code requirements.