Experimental Study on Long-Term Ring Deflection of Glass Fiber-Reinforced Polymer Mortar Pipe

Long-term pressurizing of buried glass fiber-reinforced polymer (GFRP) pipe will result in the reduction of stiffness in the pipes. It leads to excessive deflections in long-term design limits. In situ tests were performed for 664 days to measure deflections of buried GFRP pipe with a large diameter of 2,400mm. Based on the field test results, finite element analysis was conducted to determine the pipe deflections with respect to the soil conditions and buried depth as variables. Regression analysis has been conducted to determine the long-term deflection of the GFRP pipe after 50 years of construction..e long-term deflection of the GFRP pipe was less than 5 percent suggested by the existing specifications including ASTM D5365 and AWWA M45. .e comparison indicates the current specifications significantly conservative to predict long-term deflection of the buried GFRP pipe.


Introduction
Glass fiber-reinforced polymer (GFRP) pipe exhibits excellent resilience due to the stiffness and strength of the material compared to other types of pipes.GFRP pipes are compatible with other flexible pipes.Also, GFRP pipes are used in the construction industries due to the advantages of mechanical characteristics such as light weight, high specific strength and stiffness, and high corrosion resistance.
Furthermore, the mechanical properties of GFRP pipe, which depend on the arrangement and amount of reinforcing fibers, satisfy various conditions.GFRP pipes are classified as ductile pipes because, unlike rigid pipe, they interact with the ground and resist external loads.e structural behavior of underground pipes must be considered with regard to the possible effects of the foundation, the soil surrounding the pipe, and the characteristics of the backfill.
Most studies that have investigated the durability of the pipe material have examined the long-term properties of the pipe itself.For example, Farshad and Necola [1] conducted an experimental study of the short-term and long-term behavior of GFRP pipes in underwater environments.eir study's experimental results show that the stiffness of GFRP pipes does not decrease; regression analysis predicted the GFRP pipe strength to be about 7.5 kN after 50 years.
Farshad [2] predicted the long-term behavior of multilayer pipes according to internal water pressure.Farshad estimated the long-term strength of the composite pipe by combining secondary and linear regression analysis.e analysis, design, evaluation, residual analysis, and long-term estimation of the pipe were performed via "automated design and analysis of pipes" (ADAP) software.As a result, Farshad [2] derived a new long-term estimation method to predict the long-term life of pipes composed of various layers.
Faria et al. [3] investigated the creep and relaxation behavior of glass-reinforced thermosetting polymer plastic pipes using the same reliability as conventional methods by developing a method to replace the long-term characteristics of the pipe.
Faria and Guedes [4] compared measurement errors for four types of GFRP pipes using the standard method by regression analysis of the data to reduce the prediction time long-term behavior tests of the GFRP pipe.ey found the measurement error to be 10 percent less than the measurement error derived from the standard method in shortterm testing.
Sargand et al. [5] investigated the behavior of thermoplastic pipes for five years when installation under at least 6.1 m to 12.2 m was applied to thermoplastic pipes, high-density polyethylene (HDPE) pipe, and polyvinyl chloride (PVC) pipe.
eir results confirmed that both seasonal temperature differences and soil moisture conditions affect the earth pressure.Based on Sargand et al.'s [5] theoretical analysis, both the changes in soil conditions changes and effects of earth pressure were found to be significant.
Kim et al. [6] predicted the turbulent deflection of glass fiber-reinforced thermosetting polymer plastic pipe embedded in nuclear cooling water.Ten thousand hours of experimental data are required to predict pipe bending strain.
Yoon and Oh [7] predicted the 50-year long-term failure of GRP pipes from failure pressure and time to failure which was tested up to 10,000 hours through the sustained internal pressure test.
Na et al. [8] tested the long-term ring-bending strain (Sb) of the GFRP pipe using the standard method to predict the life of the pipe after 50 years.A comparison of the standard method and an optimized statistical method via GFRP pipe tests showed that the error was less than 8 percent. is work confirmed that the bending strain of the pipe after 50 years can be predicted using the proposed statistical method without performing tests that take 10,000 hours.
Lee et al. [9] measured the short-term behavior of a 2,400 mm large diameter reinforced thermosetting resin pipe for 387 days in a buried pipe field test and predicted long-term behavior for 40 to 60 years.
Most studies have focused on the durability of flexible pipe.Also, long-term behavior of the flexible pipe was predicted by short-term experimental test results.In order to predict the exact long-term ring deflection of buried pipe underground, the structure should be buried for a long time.However, limitations of such work include high costs and a large budget, and finding an appropriate test site.
In this study, a large diameter reinforced polymer mortar pipe (RPMP) reinforced with resin and mortar was embedded between the resin and fiberglass sections, and the long-term ring deflection of the GFRP pipe was measured for 664 days.
e safety of a buried underground GFRP pipe can be determined through the finite element analysis and predicted pipe ring deflections using the Iowa formula proposed by the American Water Works Association (AWWA M45).To predict long-term ring deflection, the long-term behavior of the GFRP pipe was predicted statistically using initial measurement data (pipe ring deflection data) proposed in American Society for Testing and Materials (ASTM D5365) [10].

Fabrication of GFRP Pipe.
e fabrication of the GFRP pipe involves a continuous filament winding process in which several mandrels are moved to wind up reinforcing fibers at multiple locations.e axial tensile strength of the pipe is increased by arranging the reinforcing fiber in the axial direction.
e GFRP pipe used in this study was fabricated from RPMP that was reinforced with resin and mortar between sections that were composed of resin and glass fiber.Table 1 presents the mechanical properties of the GFRP pipe used in this study.

Structural Behavior of Buried Flexible Pipe.
e structural behavior of the pipe that is embedded underground differs according to the type of external pressure.When the external load is a static load, the vertical earth pressure that is acting on the buried pipe is determined by the load on the upper part of the pipe and the area to be loaded.
In this case, the pipe buried in the ground deforms to induce earth pressure in the horizontal direction, and the vertical earth pressure generated from the load becomes greater than the horizontal earth pressure generated by the pipe deflection.
erefore, as shown in Figure 1, under normal loading conditions, the pipe is deformed by Δ v in the vertical direction and deformed by Δ h in the horizontal direction.
When a preload is applied to the upper part of the pipe without consideration of the effect of the surrounding soil on the pipe deflection, the amount of pipe deflection for each direction is calculated using the following equations [11]: where Δ v is the vertical deflection (mm), Δ h is the horizontal deflection (mm), r is the mean radius of the pipe (mm), E is the modulus of elasticity for hoop direction (MPa), I is the moment of inertia of the pipe (mm 4 /mm), and w is the line load applied on top of the soil (kN/m).
Although equations ( 1) and ( 2) will differ somewhat depending on the materials that constitute the pipe, a small deflection theory is adopted.e predictions are relatively accurate within about 3 percent of pipe strain, but the accuracy is diminished slightly due to material and geometric nonlinearities above 3 percent of the pipe strain [11].
In addition, pipe stiffness (PS) must be determined in order to predict the deflection of buried pipes.e PS can be determined using equations (3a) or (3b).
e PS is determined from the original stiffness test and is the value obtained by dividing the force (F) per unit length that corresponds to the 5 percent pipe strain caused by vertical displacement.e PS can be computed by the ring flexural modulus (E).e moment of inertia (I) of the pipe can be obtained from equation (3b): where E is the ring exural modulus (GPa), I is the moment of inertia of unit length (mm 4 /mm −(t) 3 /12), r is the mean pipe radius (mm (OD − t)/2), F is the force, and Δ v is the vertical de ection (%).e Iowa formula proposed in ASTM D2412 [17] was applied in this study to predict the de ection of the exible buried pipe.e Iowa formula is shown in equation ( 4) and includes load and boundary conditions, such as the sti ness of the exible pipe, the soil reaction force coe cient of the rebound soil, and foundation conditions for exible underground pipes.
e behavior of the exible pipe is clearly expressed in the buried underground: where D L is the de ection lag factor to compensate for the time consolidation rate of the soil, dimensionless, W c is the vertical soil load on the pipe (N/m 2 ), W L is the live load on the pipe (N/m 2 ), K X is the bending coe cient, dimensionless, PS is the pipe sti ness (kPa), E ′ is the composite soil constrained modulus (MPa), and Δ h is the horizontal de ection (mm).Equation ( 4) in the Iowa formula limits the de ection of the pipe to within 5 percent by applying a safety factor of 4 when pipe de ection occurs at about 20 percent.e reason for this limitation is to consider the safety of the pipe even for long-term ring de ection.
e e ects of pipe joint leakage also are considered [18].

Experimental Program
3.1.Full-Scale Field Experiments.In order to investigate the structural behavior of the GFRP pipe, the GFRP pipe composed of RPMP was buried and the soil was compacted at the underground location of the pipe.Field test was carried out at four sites of the buried GFRP pipe, as shown in Figure 2. Figure 3 shows the location of measurement for vertical and horizontal de ections of the GFRP pipe using a laser distance meter which was installed at each site.

Numerical Analysis.
In order to analyze the structural behavior of the buried GFRP pipe and compare it with the eld measurements, the nite-di erence analysis (FDA) was carried out with respect to buried depth as variables.e MIDAS/GTS program [19] was used for two-dimensional numerical analysis.
e Mohr-Coulomb failure criterion was adopted for the soil conditions which use an elastoplastic modeling associated with a homogenous material.Linear elastic modeling was used for the beam elements for the GFRP pipe.Both end supports and bottom supports are assumed as a xed boundary condition.e characteristics of the pipe bedding material (PBM) are summarized in Table 2 which is obtained by eld test results.Table 3 presents three cases of the compaction conditions for the GFRP pipe used for the numerical analysis in this study.
Analytical modeling takes place when 5 m, 10 m, and 16 m are lled in the upper part of the GFRP pipe, as shown in Figure 4(a).Figure 4(b) shows the grid mesh for the FDA.
Figure 5 presents displacement contour with FDA results for each case at a buried depth of 16 meter.
e stress distribution surrounding the buried GFRP pipe is in uenced by the characteristic of PBM.Table 4 provides a summary of the results of the FDA and experimental results.Based on the measurements, the vertical de ection and horizontal deection were found to be the same as for the analytical results when the compaction condition of the ground around the GFRP pipe in Case 1 was well matched in the nite element        e accuracy of the FDA was validated by test results, and it proved to be capable of simulating ring deflection with respect to buried condition.
e horizontal ring deflections and vertical ring deflections in Case 1 calculated by the finite-difference analysis agreed with the experimental results.According to the comparison results, it can be seen that the compaction density of soil around the buried pipe affected on the deflection of the pipe embedded underground.

Field Test Results and Prediction of Pipe Deflection.
Figure 6 shows the measured vertical and horizontal displacements at 1 m, 3 m, and 5 m from the entrance of the pipe.e measured pipe deflection was within 1.5 percent.Most of the total deflection occurred within the first 30 days after construction.As soil is placed over a buried GFRP pipe, the ring tends to deflect primarily into an ellipse with a    6 Advances in Materials Science and Engineering decrease in vertical ring de ection and an almost equally increase in horizontal direction.
Figure 7 shows the comparisons between the vertical and horizontal pipe de ections and the pipe de ections in the AWWA M45 design method.e vertical pipe de ection for the case of the buried depth of 16 m is about 20 percent smaller than the pipe de ection predicted by AWWA M45.In that case, the horizontal pipe de ection was estimated to be about 10 percent smaller than the de ection predicted by AWWA M45. e vertical pipe de ection was also about 53 percent larger than the horizontal pipe de ection.However, the di erence in the maximum pipe de ection that was actually measured is about 8 mm, which is almost negligible considering the measurement error of the design parameters,  Advances in Materials Science and Engineering such as the ground characteristics, given the 2,400 mm inner diameter of the pipe.In short, the AWWA M45 design method yields a conservative design, including the e ects on long-term behavior.
e formula used in AWWA M45 for pipe de ection calculations was derived from the Iowa formula, which in turn was derived from an experimental study of small corrugated steel pipes.In the case of such small pipes, local excessive stress can be concentrated, and strict pipe deection management is required.However, in the case of the pipe with a diameter of 2,400 mm, the curvature occurring in a pipe section is very small, and thus, the possibility of local excessive stress is negligible.
In addition, de ection occurs in the vertical direction due to the vertical load that is in turn due to the vertical de ection buried pipe, and this vertical de ection (Δ v ) is transferred to the horizontal de ection that is due to the characteristics of the circular section that is bound by the surrounding soil.erefore, the vertical de ection is larger than the horizontal de ection (Δ v > Δ h ) when the vertical load is not transmitted within all the horizontal de ections, but some of the energy accumulates in the pipe.
e Iowa formula is proposed to predict the horizontal de ection in this experimental study.However, in AWWA M45, the safety design (designed to produce less pipe deection) is assumed to be the same (Δ v ≈ Δ h ) for both vertical and horizontal strains.

E ect of Pipe Sti ness in Ring De ection.
e parameters that determine the de ection of the underground GFRP pipe are the sti ness of the pipe, the sti ness of the ground, and the condition of the foundation.However, as time elapses, it is di cult to change the state of the foundation in the middle of these variables.Also, if the sti ness of the soil around the pipe is rmly consolidated, then any increase in the pipe de ection is mainly due to the mechanical properties.
In a previous study [9], the durability of the GFRP pipe did not change signi cantly under a low temperature range.However, the durability of the GFRP pipe may be decreased due to the various variables found in underground conditions that are used to predict pipe de ection in AWWA M45. Figure 8 shows the pipe de ection with respect to the various ring sti ness of the GFRP pipe.
e pipe de ection was computed by equation ( 4). e de ection of the GFRP pipe can be predicted by changing the PS from 288 kN/m 2 to zero, assuming that the GFRP pipe buried at 16 m has signi cantly reduced sti ness due to external environmental factors.When the PS is 288 kN/m 2 , the pipe de ection is 2.515 mm, and when the PS is zero, the pipe de ection is 2.603 mm.erefore, the e ect of PS on pipe de ection is minor, having less than about 3.5 percent ring de ection.While the e ect of PS and the soil foundation combined is about 96.5 percent, the fact indicates that the soil foundation is the dominant variable for pipe de ection.Advances in Materials Science and Engineering

Prediction of Long-Term Pipe De ection.
Although no speci c method for predicting long-term pipe de ection has been developed yet, ASTM D5365 proposes a method to estimate long-term data for pipe de ection using statistical methods via the initial measurement data for pipe de ection.Equation ( 5) can be used to compute long-term de ection in accordance with ASTM D5365.e parameters a and b for pipe strain are de ned as equations ( 6) and (7), respectively: ring deflection (%) 10 a−b×log 10 t , ( where a and b are the parameters relating to ring de ection and t is the elapsed time (in hour): where Y is the arithmetic mean of all the ring strain values, X is the arithmetic mean of all the time to failure in hours of observation, and c is the slope of the load versus strain curve.e pipe de ection was predicted according to the time course proposed in ASTM D5365. is study predicted long-term pipe de ection up to 50 years after the GFRP pipe is buried.e computed results are summarized in Table 5.
Table 5 con rms that all of the pipe de ection that occurred after 50 years is within 5 percent.e allowable pipe de ection of 5 percent is considered to yield a very high safety factor of 4 from the structural point of view.us, judging from the fact that the standard of repair for pipe maintenance is limited to 7.5 percent in several of the relevant design standards, the buried GFRP pipe has sucient structural safety and long-term durability.

Conclusion
In this study, pipe ring de ections were measured in the eld for the buried GFRP pipe.In addition, the FDA was carried out including various parameters, such as the soil compaction density of the bedding, back ll materials, and different depths.Both the analytical and experimental results were compared and discussed.
e pipe de ection measured by the eld tests indicates that the vertical load increased with an increase in the soil depth at the initial stages of construction.e increase in the pipe de ection tended to decrease with the soil depth of 16 m.e increase in pipe de ection after the completion of the embankment appears to have been caused by the fact that the back ll stabilized over time and that some load was added to the buried pipe due to the minor settlement of the soil around the pipe.
Field tests of the buried GFRP pipes were carried out for 664 days.e measured de ection of the GFRP pipes was less than 1.5 percent during these eld tests.is measured de ection of 1.5 percent was less than the 5 percent pipe de ection suggested by AWWA M45.Also, the safety of the buried GFRP pipe was veri ed by eld tests.

Data Availability
e data sets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

Figure 3 :
Figure 3: Measurements of GFRP pipe de ections.(a) Locations of measurement.(b) Laser distance meter and taking measurements.

Figure 6 :
Figure 6: Measured de ections for the underground GFRP pipe.

Figure 7 :
Figure 7: Comparison of ring de ection of the GFRP pipe with respect to buried depth.

Figure 8 :
Figure 8: Ring de ection of GFRP pipe versus pipe sti ness.

Table 1 :
Mechanical properties of the GFRP pipe.

Table 4 :
Comparisons of numerical analysis results and experimental results.

Table 5 :
Predicted results of long-term ring de ection of pipe.