Finite Element Analysis of Polyethylene Pipe with Elliptical Hole Supported by Saddle Fusion Patch with Fin

Underground pipe installation is one of the crucial components in supporting industrial activities. Damage to the underground pipe is typical and usually done by patching repair. Analysis of the stress distribution on pipe with patch has been done previously. An analysis needs to be done to determine the effectiveness of the patches and the effect of the growth of the damage. The purpose of this paper is to know the effect of the application of fins on the saddle fusion patch with variations in the number of fins, fin angle orientation, and fin height on the stress distribution on the PE 80 pipe. The research was carried out on a polyethylene pipe with elliptical defects that have been repaired with a saddle fusion patch with a fin as a stiffener. The pipe is a medium-density polyethylene pipe (MDPE80), and the patched is high-density polyethylene (HDPE100). The variation in the research is the fin’s height, the fin’s number and orientation of the fin, and the variation of defect dimension as representative of crack growth. The study was carried out using a finite element analysis tool, ANSYS 2020. The simulation results showed that the addition of fins and the difference in given height on the saddle fusion patch could reduce the stress acting on the cracked pipe. The stress drop that occurs in the addition of the number of fins is not only influenced by the number of fins but also influenced by the orientation of the added fins. The results of this study will provide an overview of the optimal patch thickness after being given reinforcement by fins added to the patch. The hole variations carried out aim to simulate so that the damage that occurs does not repeat itself after being given a patch. Information regarding the optimal and efficient patch thickness becomes an input that is used as a consideration in determining effective and economical repair steps.


Introduction
Underground pipe installation using polyethylene material is more widely used instead of the metalbased pipe.Polyethylene-based pipes have more advantages than metal-based pipes in terms of weldability, coil-ability, light weight, flexibility, high ductility, better impact, corrosion, and abrasion resistance [1] [2].On the other hand, like metal-based pipes, PE pipes can also be damaged due to operation, service life, and environmental impact [3].Damage to PE pipe can be in the form of cracks, which eventually form holes on the PE pipe surface.In previous research done by Khademi et al. [4] , It is assumed that the damage to the pipe surface caused by cracks has the shape of an elliptical hole, and patching methods make the repair.The saddle fusion patch method has the most significant effect on maximum stress distribution, reducing the patched area [5].
Stress distribution on the pipe is affected by both internal and external load that works on the pipe.The internal loads come from internal working pressure and thermal load.The external loads come from loads from the ground and traffic loads above the pipe.Increasing the thickness of the patch on pipes with elliptical holes will reduce the stress on the pipe, and the effective thickness is obtained after the pipe stress is reduced to the maximum allowable stress [6].
In this study, the effect of using reinforcing fins on the strength of the pipe was studied.Crack geometry and patch thickness are based on the research of Sulaiman et al. (2021) [7].In this study, an analysis was conducted on the effect of adding a fin on the saddle fusion patch on the stress distribution that works on the PE pipe.Analysis of the addition of fins on the patch with defined variation was carried out with the aim that the patching process is not only able to prevent repeated leaks but also makes the work done more economical.

Modeling The Pipe with A Finned Saddle Fusion Patch
The analysis of an underground pipeline is entirely unlike the analysis of plant piping.The study of the mechanical response of a buried pipeline begins with the estimation of imposed loads.For a pipeline that is buried underground, any pipe motion must overcome soil force, which can be categorized into two parts: friction force generated by sliding and pressure force developing from pushing [8] [9].Therefore, the main problem in underground pipeline analysis is to study soil-pipe interaction, which means the pipe and its surrounding soil act with each other to rule the pipe performance.The external loads applied on an underground polyethylene pipe are divided into two parts.The permanent load from the soil weight is called the dead load.The loads applied on the surface, such as vehicle live loads which might not be permanent are termed surcharge loads [10][11] [12].
The simulation was performed by using the finite element method with ANSYS 2020 R2 as a software tool.The pipe modeling was done by modeling a 4-inch PE 80 pipe with a 500 mm length, and the patching material was PE 100 with a length of 76 mm.The defect was an elliptical hole with a major diameter of crack (2a) is 5mm and a minor crack diameter (2b) is 1 mm.The pipe was buried 125 cm underground, and the soil temperature range was assumed at 13ºC -35°C.The characteristics of the soil layer where the pipe is buried are shown in Table 1.The working loads include internal pressure, P1 = 405.3kPa, and vehicle load, P2 = 544.78kPa.

Table 1.
Properties of each soil level around and above the pipe [2] Type of the soil Modulus of Eelasticity (MPa) Density (kg/m 3 ) Asphalt 173.0 2 200 GW soil with 90% Proctor density 6.9 1 700 SM soil with 90% Proctor density 6.9 1 900 GW soil with 95% Proctor density 15.0 2 000 GW soil with 85% Proctor density 4.8 1 600 Optimum patch thickness was studied by Sulaiman et al. l, 2021 [7].Based on the simulation results of patch thickness variations, it is known that the stress distribution tends to stay, and the maximum von Mises stress decreases when the patch thickness is increased.The optimum patch is achieved when the maximum stress distribution on cracked PE 80 decreases below the maximum allowable stress of PE 80 at 6.4 MPa, as shown in Figure 1.From the study, it was obtained that the optimum patch thickness is The addition of fins on the patch is purposed to reduce the maximum stress that works on the damaged PE 80 pipe.The purpose of the variation in the added fin is to see changes in the stress drop that occur in the PE 80 pipe.The variations made are variations in the number of fins added and the orientation of the fins.The fin will be variated from 1 up to 3 fins, and the orientation is 75º, 30º, and 345º, as shown in Figure 2. The fin's thickness and height are constant at 45 mm, which is the same as the optimum patch obtained in the previous study by Sulaiman.

Figure 2. Fins Variation on Saddle Fusion Patch
The installation of a patch on the pipe will close the elliptical hole and increase the thickness of the pipe so that the pipe strength increases and the stress on the pipe decreases.The occurrence of a decrease in stress in the pipe is due to the parameters that affect the stress that occurs in the pipe, which is a function of the load and the thickness of the pipe.The addition of pipe thickness will reduce the stress in the pipe quadratic, as described in Equation 1 [7].Simulation is started by validating the carried-out modeling of the patched cracked pipe.Model validation is carried out by using the results of research conducted by Sulaiman, 2021, which is variations in the thickness of the patching material on the damaged pipe section to obtain the optimum patch thickness.The results of the simulation can be seen in Table 2, and the graph can be seen in Figure 3.The optimum thickness of the patch is obtained when the maximum von Mises stress reduces to PE 80 maximum allowable stress, 6.4 MPa.The maximum deviation between the previous result and this study is 1.5%.Since the result is below 5%, thus the model is passed for validation.In order to obtain an accurate simulation and a smooth stress distribution, high-quality meshing is used in this study, where the smallest mesh size is 0.03mm, and there is an inflation layer connecting the edges of the ellipse and the elliptical hole [5] as shown in Figure 5.

Results and Discussion
From the modeling simulation, it is known that the maximum stress is located at the edges of the crack.Adding the patch means adding thickness to the cracked area.The patched area shows a decrease in maximum stress.Orientation and the number of fins added on the patch are affecting the maximum stress works on the cracked area.From the simulation, one fin is added at Orientation 75º, and the maximum stress is increased.The increasing stress is possibly caused by the presence of external loads, which come from soil loads and vehicle loads, acting on the fins and providing additional load on the cracked pipe area so that the stress on the cracked pipe increases.The maximum stress is reduced after adding more fins to the saddle patch.The stress distribution on the crack area before and after being given additional fin can be seen in Table 4, Figure 6, and Figure 7.  From the simulation above, adding three fins to the patch can reduce the working stress up to 5.558 MPa from 6.4 MPa or 13%.The next variation in this simulation is the variation in the height of the fins.The purpose is to see the effect of the fin's height to maximize Von Mises's stress on the crack area.Fin height variations are 45 mm, 90 mm, and 135 mm.The result of the variation in the fin's height can be seen in Table 5, Figure 7, and Figure 8.The appearance of cracks at both ends of the elliptical hole due to ineffective patching can cause the elliptical hole to become longer.This also causes the ratio of long diameter and short diameter (a/b) to be larger, where this parameter is directly proportional to the magnitude of the maximum stress acting on both ends of the elliptical hole, as described in Equation 2. The larger the a/b diameter ratio, the greater the maximum stress at both ends of the ellipse.The simulation results obtained show agreement with the research conducted by Khademi- Zahedi & Shishesaz (2018), where a decrease in the ratio of short diameter to long diameter (w/a) or an increase in the ratio of long diameter to short diameter (a/w) will increase the maximum Von Mises stress that occurs in the pipe [4], [9]. where

Conclusion
In the study above, it is known that the addition of fins on the saddle fusion patch can reduce the stress acting on the cracked pipe.The stress drop that occurs in the addition of the number of fins is not only influenced by the number of fins but also influenced by the orientation of the added fins.
The difference in height on the fins used can also affect the magnitude of the stress acting on the finned saddle fusion.In the height variation, it was found that a height of 90 mm, or twice the thickness of the patch, gave the maximum stress reduction compared to other height variations.

Figure 7 .
Figure 7. Stress Distribution on Crack Area (a) Patch without Fin (b) Patch with 1 Fin (c) Patch with 2 Fins (d) Patch with 3 Fins

Figure 10 .Figure 11 .
Figure 10.Von Mises Stress Distribution on Various Crack Sizes

Table 2 .
Patched PE pipe model validation

Table 3 .
Crack growth model validation

Table 6 .
Maximum Von Mises Stress on Variation Length of Crack