How Burial Design Drives Slow Crack Growth Risk in HDPE Pipelines
By T. VILLABON, J. VALDERRAMA, P. GARZON, C. RODRÍGUEZ and G. ALVAREZ, Universidad Nacional de Colombia, Bogotá, Colombia
(Editor’s note: This installment is the second in a two-part series. The first part was published in the November issue.)
(P&GJ) — Part 2 will present the outcomes from analyzing 4,536 unique combinations of study variables. To illustrate these interactions, the authors employ a dual-diagram approach for each study variable: trends in failure probabilities as a function of time are depicted alongside box-and-whisker and half-violin plots. These visuals are designed to show when combinations exceed the defined thresholds of 10–3 for medium and 10–2 for high probability of failure (PoF).
This format aims to streamline visualization and analysis, facilitating a clear understanding of how each study variable influences the probability of failure and, by extension, pipeline reliability.
Diameter. In the analysis of the study variable diameter, the line graph in FIG. 3 (Part 1) provides a clear average trend across the dataset. On average, high-density polyethylene (HDPE) pipes with larger diameters exceed critical SCG failure probability thresholds, marked as medium PoF (> 10−3) and high PoF (> 10−2), more quickly than pipes with smaller diameters.15
For instance, on average, pipes with a 12-in. diameter exceed the medium failure probability threshold about 18 yrs earlier and reach the high failure probability level approximately 25 yrs sooner than those with a 3-in. diameter. This pattern indicates an increased probability of SCG for larger pipes over a shorter time frame.
However, the box-and-whisker plots, coupled with the half-violin diagrams, reveal a wide variation in the times when these thresholds are exceeded, which could lead to significant implications for pipeline management. The considerable spread in the data shows that, while the average trend suggests a higher probability of SCG failure for larger diameters, there are instances where this may not be the case.
Proper selection of other study variables could potentially mitigate the time it takes to exceed these PoF thresholds, particularly in situations where changing the diameter is not feasible due to flowrate or capacity requirements of the pipeline system.
Bedding angle. The analysis of the impact of the bedding angle on pipeline reliability, examining a comprehensive range of angles, reveals critical insights. Both the line graph and the half-violin and box-and-whisker diagrams in FIG. 4 indicate that changes in bedding angle beyond 90° are less significant compared to shifts from 0° to 90°. For instance, transitioning to a medium PoF (> 10−3) occurs 24 yrs earlier for pipelines with a 0° bedding angle compared to those at 90°.
However, the difference in reaching a medium PoF between 90° and 180°angles is merely 5 yrs, suggesting that changes within lower angles have a more pronounced effect on the PoF. This observation highlights the importance of selecting appropriate bedding angles in pipeline installations. It is particularly advisable to avoid configurations that result in bedding angles < 90°, as they significantly accelerate the onset of medium and high PoF.
This guidance is supported by the trend analysis over time and distribution patterns observed in the diagrams, underscoring the need for careful consideration of bedding angles to enhance pipeline durability and reliability.
Additionally, the graphs illustrate that following this recommendation, pipelines on average would exceed the medium PoF threshold (> 10−3) after 50 yrs, aligning with the expected lifespan of HDPE pipes, thus further substantiating the advisability of avoiding lower bedding angles.
Depth of cover. Analyzing the effect of the depth of cover on pipeline reliability, the line graph in FIG. 5 clearly indicates an average trend where pipes buried at 120 cm reach medium (> 10−3) and high (> 10−2) PoF sooner than those at shallower depths. On average, pipelines at this depth transition to a medium PoF earlier and to a high probability of earlier failure than those buried at 60 cm.
This could suggest that while deeper burial effectively shields pipelines from live loads or damages from external activities, it might also create conditions conducive to SCG.16,17 Factors such as increased soil pressure or variations in soil properties with depth could potentially contribute to this increased PoF.
However, despite this trend, the data also shows a broad variation in results across different depths, indicating that although deeper burial generally correlates with a faster onset of failure probabilities, this is not a uniform rule. This variability underscores the potential for strategic management of other variables to improve resilience against SCG. Even if depth adjustments are not feasible due to design constraints, optimizing other factors could mitigate the adverse effects of a deeper burial or maximize the benefits of shallower installations.
In essence, while depth of cover is a significant factor, its impact on the PoF due to SCG can be effectively managed by carefully considering the interaction with other pipeline design variables.
Compaction level. The examination of compaction levels, represented by Proctor values, uncovers their marked impact on the timing at which pipelines reach medium (PoF > 10−3) and high (PoF > 10−2) thresholds in pipelines. As illustrated in the line graph in FIG. 6, pipes buried with a high proctor compaction level tend to enter these higher PoF thresholds later than those with slight compaction. On average, a high proctor compaction delays the entry into the medium and high PoF phases by 15 yrs compared to a slight compaction level.
Moreover, the data also reveals a wide variation in results across different compaction levels, suggesting that while compaction significantly influences the timing at which pipelines reach higher PoF, its impact can be modulated by other design choices. This indicates that even if it is infeasible to alter the compaction level due to specific design constraints, selecting the appropriate combination of other variables can still enhance the resistance of the pipeline to SCG.
As shown in TABLE 3 (Part 1), higher compaction levels increase the elastic modulus (Ebʹ) of the backfill or foundation material, as well as the density of the backfill. Observing this behavior, the growth in Ebʹ is beneficial for reducing the PoF in SCG. Although the density also increases, which could impose a greater dead load on the pipeline, the effect of the increased Ebʹ is more substantial, suggesting that to enhance SCG reliability, a generalized increase in Ebʹ is advantageous.
Soil class. In the assessment of soil classes defined by the particle size distribution, the analysis indicates that the average PoF for different soil classes does not show marked differences in the time frames for reaching medium and high failure probabilities.
The line graph in FIG. 7 shows that the PoF trends for Classes I, II and III soils closely align, suggesting that particle size distribution (PSD), within the scope of these classifications, has a limited impact on the progression towards SCG.
The accompanying box-and-whisker plots further substantiate this observation, displaying a narrow and overlapping distribution of PoF across the three soil classes. This convergence implies a uniform PoF profile regarding SCG across various soil classes.
While the interaction of soil properties with pipeline integrity is indeed important (highlighted by the marked influence of compaction level, depth of cover and bedding angle), the data suggests that PSD, specifically within the range of Classes I to III, might not critically impact SCG susceptibility.
Trench width to pipe diameter ratio (Bd/D). Upon examining the Bd/D, the analysis reveals a significant correlation between the trench width relative to the pipe diameter and the time at which pipelines exceed critical SCG failure probability thresholds.
The graphical representation in FIG. 8 illustrates that pipelines laid in trenches where the width is only 1.5 times the diameter show a slower progression toward the medium and high SCG failure probabilities, as opposed to those in trenches with a width five times that of the pipe diameter.
The line graph delineates a pronounced delay for pipes with a Bd/D ratio of 1.5, reaching the medium PoF threshold of approximately 15, which is later than pipes in trenches with a Bd/D ratio of five. This pattern extends to the high PoF level transition, where a Bd/D ratio of 1.5 correlates with exceeding the high PoF threshold of 25, compared to a Bd/D ratio of five.
The accompanying box-and-whisker and half-violin plots not only corroborate the average trends observed in the line graph, but also reveal a significant spread in the data. This variability underscores that while larger Bd/D ratios generally correlate with an earlier onset of SCG failure probabilities, the trend is not uniform across all instances. It suggests that there can be considerable divergence from the average, indicating that other variables may influence the timeline to exceed critical failure probability thresholds.
Natural ground to backfill elasticity modulus ratio (Enʹ/Ebʹ). The investigation into the Enʹ/Ebʹ ratio, which compares the modulus of elasticity of the natural ground to that of the backfill material, reveals significant insights into its influence on the timing at which HDPE pipelines reach medium PoF (> 10−3) and high PoF (> 10−2) thresholds due to SCG. It is observed that pipelines in environments where the natural ground’s Ebʹ surpasses that of the backfill material (indicating a higher Enʹ/Ebʹ ratio) tend to enter these higher failure probability thresholds later (FIG. 9).
For instance, pipelines with an Enʹ/Ebʹ ratio of two enter the medium PoF threshold approximately 5 yrs later than those with a ratio of 0.5. This trend continues into the high PoF threshold, maintaining the same temporal difference. This phenomenon is visually represented by the parallelism observed in the PoF lines for the two Enʹ/Ebʹ ratios of 0.5 and 2.
The examination of the Enʹ/Ebʹ ratio in relation to SCG failure probabilities reveals a substantial variation in the timing to reach critical failure thresholds, as evidenced by the significant dispersion observed in the violin and box-and-whisker diagrams. This spread suggests that, while the Enʹ/Ebʹ ratio is influential, its impact on SCG PoF can be significantly modulated by the control and optimization of other study variables.
Such variability in the data indicates that even in cases where the Enʹ/Ebʹ ratio cannot be readily altered—due to the impracticality of changing inherent soil properties or economic constraints—strategic management of variables such as compaction level, bedding angle and pipe diameter may offer avenues to mitigate SCG failure probabilities effectively.
Additionally, these results show that a greater Enʹ/Ebʹ ratio is beneficial regarding SCG reliability, as a higher modulus of elasticity of the natural ground ensures that the combined Ebʹ, which considers both the backfill and the natural ground’s moduli, is increased. Ultimately, to enhance SCG reliability, the goal is to increase this Eʹ value.
Analysis of variable importance in pipeline PoF level assessment. In FIG. 10, the values of relative importance for different variables in the random forest analysis are presented, highlighting their contributions to pipeline susceptibility to SCG. The bedding angle emerges as the most influential factor, scoring an importance of 0.35, which highlights the critical role of installation practices in determining pipeline durability. This factor is particularly significant, as it shows a pronounced increase in the probability of SCG failure for pipelines with bedding angles < 90°, and its importance is more than double that of the next variable.
Following closely is diameter, with an importance score of 0.15. This variable plays a significant but not exclusive role in SCG failure probabilities, with larger diameters tending to accelerate the entry into medium and high PoF. Although there is a clear trend, the wide variability in the data suggests that other factors may also modulate these probabilities.
The depth of cover is similarly impactful with an importance score of 0.14. Deeper burials often hasten the entry into higher SCG failure probabilities, pointing to complex interactions with other variables, such as bedding angle, that may influence failure thresholds more quickly.
The Bd/D ratio has a slightly lower importance at 0.13, illustrating that narrower trench widths relative to pipe diameter can delay entry into higher SCG failure probabilities, potentially serving as a protective measure. The variability observed in the data underscores the potential for adjusting other variables to mitigate the challenges imposed by the Bd/D ratio.
Compaction level, indicated by proctor values with an importance score of 0.12, significantly affects the timing of entering higher SCG failure probabilities. Higher compaction levels typically extend the time to reach these critical thresholds, a trend that is consistent across the data. Importantly, higher compaction increases the Ebʹ of the backfill material, which contributes to an overall increase in the combined Eʹ, enhancing the pipeline’s resistance to SCG.
The Enʹ/Eʹ ratio has a lower score of 0.08, yet it still impacts the timing of SCG failure probabilities. Pipes in environments where the natural ground’s modulus of elasticity significantly exceeds that of the backfill tend to delay the entry into higher failure probabilities. This is because a higher Enʹ/Ebʹ ratio contributes to an increased Eʹ, the subgrade reaction modulus, which considers both the Ebʹ of the natural ground and the backfill. The interplay between the En and Eb moduli thus significantly modifies Eʹ, reinforcing the pipeline’s structural integrity against SCG.
Lastly, soil class has the lowest relative importance at 0.02. While it has a minor direct impact on SCG failure probabilities according to the random forest analysis, the similar timings across soil classes suggest that soil PSD within Classes I to III may not be as pivotal to SCG failure probabilities as other factors.
The alignment of the random forest importance scores with the data underscores the need for a comprehensive approach in pipeline management, integrating all variables to effectively mitigate SCG failure probabilities.
Given the significant importance of the bedding angle derived from random forest analysis and the observed data trends, the authors conducted a thorough analysis of how variations in bedding angles affect the timing of entering medium and high SCG failure probabilities. FIGS. 11a and 11b visually encapsulate the impact of different bedding angles effect on the timing of pipelines entering failure phases.
FIG. 11a includes all combinations and highlights that configurations with bedding angles < 90° frequently enter medium and high failure states much earlier—within 18 yrs and 30 yrs, respectively. In contrast, FIG. 11b focuses solely on combinations that adhere to bedding angles greater than 90°, demonstrating that these configurations largely avoid entering high PoF phases until after the standard 50-yr lifespan of HDPE pipes.
This stark contrast in outcomes between the two figures underscores the critical influence of bedding angle selection on pipeline durability and validates the recommendation to use bedding angles > 90° to optimize pipeline longevity and reliability.
While suggesting that specific burial conditions such as precise bedding and embedment may not be crucial for HDPE pipes capable of basic installation, the importance of bedding angle in influencing the lifespan of pipelines should not be underestimated.
Although the manual permits simpler installations where the pipe can be laid directly on the trench bottom under stable conditions, the authors’ findings indicate that angles < 90° could significantly reduce the operational life of HDPE pipes, potentially leading to medium or high PoF levels before reaching the expected 50-yr lifespan. While other variables beyond bedding angle directly impact the reliability of HDPE pipelines in resisting SCG, their variation does not directly influence the standard 50-yr lifespan of the pipelines.
To extend the operational life of these pipelines beyond this baseline, it is crucial to consider the broader set of variables identified in the study. This approach ensures that even beyond the typical expectancy, the pipelines maintain high levels of integrity and functionality.
TAKEAWAYS
This study has elucidated the significant influence of geometric burial design and soil characteristics on the SCG phenomenon in HDPE pipelines. By employing a reliability-based assessment approach that integrates Monte Carlo simulations and machine-learning techniques, the authors have identified key factors that contribute to the PoF due to SCG and provided insights into optimizing geometrical burial design for enhanced longevity.
Bedding angle. Among the variables analyzed, the bedding angle is paramount. Pipelines with bedding angles < 90° enter zones of medium and high PoF much more quickly. The findings emphasize that maintaining bedding angles ≥ 90° is crucial for minimizing the PoF.
This recommendation is substantiated by the fact that bedding angles > 90°effectively mitigate SCG, aligning with the expected 50-yr service life of HDPE pipelines. This highlights the importance of precise installation practices, particularly in trench bedding, to ensure pipeline reliability.
Diameter and depth of cover. While the diameter and depth of cover of HDPE pipelines do influence their progression towards higher failure probabilities, their impact is notably less critical than that of the bedding angle.
Larger diameters and greater depths of cover do accelerate the move towards higher failure probabilities of SCG, but this effect can be significantly mitigated by optimizing other design parameters. For instance, adjusting trench width and compaction levels can effectively manage the adverse effects associated with larger diameters and deeper burial.
Therefore, while important, the influence of diameter and depth of cover is considerably lower than that of the bedding angle in determining pipeline reliability.
Compaction level and soil class. The level of soil compaction, indicated by proctor values, slightly affects the probability of failure. Higher compaction levels increase the Ebʹ of the backfill, which in turn enhances pipeline resistance to SCG.
Although the soil class, based on particle size distribution, shows a relatively low impact across different classifications, the compaction level within each class is crucial to optimize pipeline performance. Therefore, ensuring high compaction levels is recommended to improve the structural integrity of the pipeline.
The Bd/D ratio influences the load distribution around the pipeline, with narrower trench widths relative to pipe diameter proving beneficial for SCG resistance.
Additionally, the En/Eb ratio, which compares the elasticity moduli of natural ground and backfill, impacts the combined modulus of elasticity (E′), with higher ratios contributing to better performance against SCG. Strategic management of these ratios is essential for enhancing pipeline reliability.
Machine-learning insights. The use of random forest analysis has provided a nuanced understanding of the relative importance of different variables. The bedding angle emerged as the most significant factor, with an importance score markedly higher than all other variables. This underscores its critical role in determining pipeline PoF.
The other variables, such as diameter, depth of cover, Bd/D and compaction level, have similar but significantly lower importance scores compared to the bedding angle. This analysis highlights the necessity of a holistic approach in pipeline design, considering all influential factors to mitigate SCG risks effectively, while emphasizing the paramount importance of optimizing the bedding angle.
Literature Cited
15 Chevron Phillips Chemical, “Performance pipe,” online: https://www.cpchem.com/what-we-do /solutions/performance-pipe
16 Warman, D.J., Hart, J.D. and R.B., Francini, Canada Energy Pipeline Assessment Report, “Development of a pipeline surface loading screening process and assessment of surface load dispersing methods,” 2009
17 Zha, S.X., Lan, H.Q. and H. Huang, “Review on lifetime predictions of polyethylene pipes: limitations and trends,” 2022. Online: https://doi.org/ 10.1016/j.ijpvp.2022.104663
Editor’s note: This article was originally published in the Journal of Pipeline Science and Engineering, Volume 5, Issue 2, June 2025, 100247.