Pipe Stiffness Prediction of Buried GFRP Flexible Pipe

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1 Pipe Stiffness Prediction of Buried GFRP Flexible Pipe Pipe Stiffness Prediction of Buried GFRP Flexible Pipe Joon-Seok Park, Won-Hee Hong, Wan Lee, Jung-Hwan Park, and Soon-Jong Yoon * Department of Civil Engineering, Hongik University, 72-1 Sangsu-dong, Mapo-gu, Seoul , Korea SUMMARY In this paper, we present the result of investigations pertaining to the pipe stiffness (PS) of glass fiber reinforced polymer plastic (GFRP) flexible pipes buried underground. PS formula for the parallel plate loading condition is derived based on the elasticity theory. Vertical and horizontal displacements are also derived. In the study, the mechanical properties and structural behavior of GFRP flexible pipes are investigated experimentally and the results are used in the analysis and design of these flexible pipes. Pipe stiffness of GFRP flexible pipe is investigated by the parallel plate loading test, the finite element analysis, and theoretical analysis. The results of pipe stiffness of the GFRP flexible pipe obtained by the experiment, theory, and the finite element analysis are compared and close agreements are observed. Keywords: Glass fiber reinforced polymer plastic (GFRP), Pipe stiffness, Vertical deflection, Flexible pipe, Parallel plate loading test 1. INTRODUCTION Recently, underground pipes serve in diverse applications such as sewer lines, drain lines, water mains, gas lines, telephone and electrical conduits, culverts, oil lines, etc. It is now possible to use engineering science to design these underground pipes with a degree of precision comparable with that obtained in designing buildings and bridges 1. Almost all of buried pipes can be classified as either flexible or rigid, depending on how they perform when installed. Flexible pipes take advantage of their ability to move, or deflect, under loads without structural damage. Common types of flexible pipes are manufactured from polyethylene (PE), polyvinyl chloride (PVC), steel, glass fiber reinforced thermosetting polymer plastic (GFRP), and aluminum. Both flexible and rigid pipes require a proper backfill to allow the load transfer from the pipe to the soil, although the pipe-backfill interaction differs. * Corresponding author: sjyoon@hongik.ac.kr Smithers Rapra Technology, 2014 When a flexible pipe deflects against the backfill, the load is transferred to and carried by the backfill. When loads are applied to rigid pipes, on the other hand, the load is transferred through the pipe wall into the bedding material 2. GFRP pipes making use of FRP (Fiber Reinforced Plastic) are generally thinner, lighter, and stronger than the existing concrete or steel pipe lines, and it is excellent in stiffness/ strength per unit weight. Therefore, FRP is good for construction when it is buried underground, and can reduce the failure risk of materials due to excessive settlement. In particular, as thick soft grounds exist, there are many large-scale residential development areas with poor soil condition, and high banking sections and bury depths have tendency to be deeper. As a result of it, the applications of GFRP pipes are expected to increase sharply. As for GFRP pipes, since the reinforcing fiber is arranged in the circumferential direction (90 direction) due to the characteristics of manufacturing process, the mechanical property of material can be considered orthotropic in which the circumferential and longitudinal directions of mechanical properties of pipe are different each other. Therefore, the coupling effects, which do not occur in the isotropic materials of member deformations, can occur, and the structural behaviors can be considerably different from that of the existing cast steel and concrete pipes which are assumed to be composed of isotropic materials. Due to the mechanical characteristics of FRP which has different mechanical properties according to the type of reinforcing fiber, stacking angle, and the type of resin, GFRP pipes have merits to design the material properties satisfying required performance, meanwhile, it should be designed and constructed considering the field conditions, because manufacturers use different materials in characteristics. As mentioned earlier, a GFRP pipe derives its soil load carrying capacity from its flexibility. Under soil load, the pipe tends to deflect, thereby developing passive soil support at the sides of the pipe. At the same time, the ring deflection relieves the pipe of the major portion of the vertical soil load Polymers & Polymer Composites, Vol. 22, No. 1,

2 Joon-Seok Park, Won-Hee Hong, Wan Lee, Jung-Hwan Park, and Soon-Jong Yoon which is supported by the surrounding soil in an arching action over the pipe. The effective strength of the flexible pipe-soil system is significantly high 3. When a GFRP pipe is buried in the soil, the pipe and soil then work as a system in resisting the load (Figure 1). That is, the deflection of the pipe is a function of the load on the pipe, but the load on the pipe is a function of the deflection. The reduction in load imposed on a pipe because of its flexibility is sometimes referred to as arching Design of Buried Flexible Pipe Spangler (1941) 4 proposed, at first, a theory of the magnitude and distribution of various force around a buried flexible pipe as shown in Figure 1. This theory is based on the elastic ring theory and experimental work performed on metal flexible pipes at Iowa Engineering Experimental Station. Spangler s theory considered Marston s load theory and assumed that the load is uniformly distributed over the bedding width of the pipe which is equal to the applied vertical load, and the passive horizontal pressure on the pipe sides is distributed parabolically over 100 and the maximum value of pressure is equal to the modulus of passive resistance side-fill material multiplied by half the horizontal deflection. This stress distribution was used to derive the original Iowa Formula given in Eq. (1) 5. Δx = D c KW c 0.149PS E ' (1) In Eq. (1), Dx is the horizontal deflection of pipe (may be taken also as the vertical deflection with negligibly small error) and K is the bedding constant, dependent upon the support the pipe received from the bottom of the trench, W c is the vertical load per unit of pipe length, PS is the pipe stiffness (as determined by the parallel plate loading test of pipe), D e is the deflection lag factor, E' is the modulus of soil reaction (ASTM D 2412, 2010). W c is generally taken as the prism load from the soil. The E' values (refer to Table 1) recommended by Howard (1977) 6 are extensively used. 1.3 Structural Behavior Flexible pipe stiffness is the measurement of the load carrying capacity of the pipe itself subjected Figure 1. Load transfer mechanism of flexible pipe 3 (a) Flexible pipe (b) Rigid pipe (no deformation) to loading condition. Pipe stiffness is a function of the material type and the geometry of the pipe wall. The pipe stiffness (PS) is defined as the ratio of the applied force (F) in kn per linear m over the measured change of pipe inside diameter (Dy). Pipe stiffness can also be defined as the slope of the loaddeflection diagram. The stiffness factor (SF), which is the value of pipe modulus of elasticity multiplied by moment of inertia, is defined as shown in Eq. (2) 7. The pipe stiffness at 5% vertical ring deflection, i.e., the change in vertical diameter divided by the original pipe diameter, is typically used as the design value of stiffness. This represents the secant pipe stiffness at 5% deflection. ASTM D 2412 (2010) 8 stated that the stiffness of pipes with larger sizes made from relatively low modulus material may be affected by creep due to the time taken to reach the 5% deflection. Both pipe stiffness and stiffness factor are highly dependent on the degree of deflection. The pipe stiffness, PS, for any given deflection may be calculated as follows: PS = F EI = 6.7 ΔY R 3 (2) In Eq. (2), F is the parallel plate load applied to pipe and Dy is the vertical ring deflection of pipe diameter, respectively. Pipe stiffness is a commonly used to compare flexible pipe strengths through the use of a parallel plate loading test as described in ASTM D 2412 (2010) 8 at 5% vertical deflection. 2. PREDICTION OF PIPE STIFFNESS BY EXPERIMENTAL STUDY Table 1. Modulus of soil reaction for pipe embedment 6 Soil Type Standard Proctor Relative Compaction Density 85% 90% 95% 100% CL, ML, CL-ML 3.4 MPa 4.8 MPa 6.8 MPa 9.6 MPa SM, SC 4.1 MPa 6.2 MPa 9.3 MPa 13.6 MPa SP, SW, GP, GW 4.8 MPa 6.8 MPa 10.2 MPa 15.3 MPa 2.1 Mechanical Properties The GFRP pipes used in the test are products manufactured by Hankuk Fiber Co. Ltd. in Korea. The tensile test specimen was taken in the longitudinal direction (i.e., member axis direction) of the GFRP pipe according to the KS M ISO (2002) 9. Specimen 18 Polymers & Polymer Composites, Vol. 22, No. 1, 2014

The specimen was loaded up to failure with a loading speed of 3 mm/min according to the displacement control method.

3 Pipe Stiffness Prediction of Buried GFRP Flexible Pipe designation and dimension of the tensile test specimen are shown in Table 2. For the tensile strength test, the specimen was installed and loaded using the universal testing machine (UTM) with 1,000kN capacity. The specimen was loaded up to failure with a loading speed of 3 mm/min according to the displacement control method. The strain is measured with foil strain gage and the load and strain data collected using data acquisition system (TDS-302). As the results of tensile strength test, all specimens suffered from brittle breaking within the gage length. Major values of test results were briefly summarized in Table 3. Modulus of elasticity in Table 3 was determined from the strain in the range of 500-2,500 μm according to the method suggested by the KS M 3082 (2007) The Parallel Plate Loading Test The GFRP pipes used in the test are produced by Hankuk Fiber Co. Ltd. The parallel plate loading test specimen was taken in the transverse direction of the pipe according to the KS M ISO 9969 (Thermoplastic pipes-determination of ring stiffness) 11. Specimen designation and dimension of the parallel plate loading test specimen are shown in Table 4. Table 2. Specimen designation and dimension (longitudinal direction) Specimen Dimension Designation Width (cm) Thickness (cm) Cross-Sectional Area (cm 2 ) GFRP GFRP GFRP GFRP Table 3. Tensile strength test result Specimen Designation Modulus of Elasticity (GPa) Tensile Strength (MPa) GFRP GFRP GFRP GFRP Average Table 4. Specimen designation and dimension (transverse direction) Specimen Designation Dimension GFRP-1 GFRP-2 GFRP-3 Length (mm) Diameter (mm) Thickness (mm) Figure 2. Parallel plate loading test specimen and testing The parallel plate loading test set-up and testing of GFRP pipes are shown in Figure 2. The load at 5% ring deflection and the pipe stiffness are 10.78kN and 718.4kN/m 2, respectively. 3. PREDICTION OF PIPE STIFFNESS BY THEORETICAL STUDY The ring stiffness of flexible pipe specimen is usually measured in the laboratory according to the parallel plate loading test method 8. When the laboratory test equipment is not available, a theoretical solution based on the elastic curved bar theory is often used to estimate the ring stiffness of the flexible pipe. If we consider a curved bar (refer to Figure 3) slightly bent in the plane of its initial curvature, and let us assume that this plane is the plane of symmetry of the bar. Representing by R the initial radius of curvature of the center line of the bar and by ρ the radius of curvature after deformation at any point of the center line, defined by the angle q, we may express the relation between the change in curvature and the magnitude of the bending moment M in the case of a thin bar by Eq. (3). EI 1 ρ 1 = M R (3) Polymers & Polymer Composites, Vol. 22, No. 1,

4 Joon-Seok Park, Won-Hee Hong, Wan Lee, Jung-Hwan Park, and Soon-Jong Yoon Figure 3. Bending of a thin curved bar 12 In which dq+d dq denotes the angle between the normal cross sections m 1, n 1 of the deformed bar and ds+dds denotes the length of the element m 1, n 1. The governing second-order ordinary differential equation of thin curved bar is given by Eq. (7). d 2 w ds 2 + w = MR2 EI (7) In Eq. (7), For an infinitely large radius R this equation coincides with that for a straight bar (Park, 2011) 12. As an example of the application of Eq. (7), we may consider a ring of radius R compressed by two forces P acting along a diameter which is the same situation in the parallel plate loading test of the pipe (Figure 4). Denoting the bending moment at A and B by M o, we may find that the moment at any cross-section m is given by Eqs. (8) and (9). In Eq. (3), EI is the flexural rigidity of the bar in the plane of its initial curvature. The minus sign on the righthand side of the equation follows from the sign of the bending moment, which is taken to be positive when it produces a decrease in the initial curvature of the bar. The change in the curvature of the bar during bending will be found from a consideration of the deformation of a small element m, n of the ring included between two radii with the angle dq between them 12,13. The initial length of the element and its initial curvature are expressed by: ds = Rdθ (4) dθ ds = 1 R (5) The radial displacement w of a point m during bending, assumed to be a small quantity, is taken positive when it is directed toward the center. There will be also some displacement of the point m in a tangential direction, but this will be disregarded, and we shall assume that the curvature of the element m, n after deformation is the same as the curvature of the element m 1, n 1 included between the same radii m, n. This latter curvature is given in Eq. (6). M = M 0 + PR 2 ( 1 cosθ) ) d 2 w ds + w = M 0R 2 PR 3 2 EI 2EI ( 1 cos θ) ) The general solution of Eq. (9), by adding the homogeneous and particular solutions together, is: w = A 1 sin θ + A 2 cosθ M0 R 2 EI (8) (9) PR 3 2EI + PR 3 4EI θsin θ (10) The bending moment M o can be found from Castigliano s theorem. The strain energy U for a thin ring is obtained by using the same formula as for a straight bar; hence, for the ring in Figure 4. U = 0 2π M 2 Rdθ 2EI = 2R EI 0 π/2 M 2 dθ (11) The final expression for the radial deflection is found by substituting relations Eq. (8) into Eq. (11) From this expression the radial deflection at any point can be found. For example, at q = 0 and q = p/2 we obtain the elongation of diameter AB and the contraction of diameter CD, respectively, are: Figure 4. Ring of radius compressed by two forces action 12 1 dθ + Δdθ = ρ ds + Δds (6) 20 Polymers & Polymer Composites, Vol. 22, No. 1, 2014

Pipe Stiffness Prediction of Buried GFRP Flexible Pipe AB = PR 3 4 4EI π 1 CD = PR 3 π 8 4EI π (12a) (12b) Eq. (7), should be used in investigating bending of long circular tube.

5 Pipe Stiffness Prediction of Buried GFRP Flexible Pipe AB = PR 3 4 4EI π 1 CD = PR 3 π 8 4EI π (12a) (12b) Eq. (7), should be used in investigating bending of long circular tube. In this case M denotes the bending moment per unit length of circular tube 11. Therefore, ring stiffness of circular tube or pipe is given by Eq. (13). Δy = 2w θ π/2 = PR 3 π 8 = 0.149P R 3 4EI π EI P = Pipe stiffness ( PS) = 6.72 EI 1 / Δy R Δx = 2w θ 0 = PR 3 4 2EI π 1 = 0.137P R 3 EI P Δx ( ) EI = 7.32 so, 3 ( Δy > Δx and Δy Δx but Δy Δx) R (13a) (13b) 4. PREDICTION OF PIPE STIFFNESS BY ANALYTICAL STUDY Pipe stiffness of GFRP pipe is investigated by the finite element analysis, ANSYS Ver ANSYS Ver. 11 is a general purpose finite element analysis program used to solve various structural problems. It has a large library of element types, permit small and large deflection analyses, and eight types of nonlinearities. ANSYS also allows the user to program using the ANSYS special programming language which is called ANSYS Parametric Design Language (APDL). This language allows the user to build the finite element model, repeat the commands, use macro, if-then-else branching, do loops, and vector and matrix operations. Figure 5. Finite element model of GFRP pipe The file can be used to create model, do the calculations, solve and generate the results for each load step. Problems with different load increments can also be solved, and the model parameters such as number of elements, can be updated for each load step. In the finite element analysis (FEA) modeling, mechanical properties of material and loading conditions are considered in the finite element simulation. In addition, both end supports are assumed to be simple as a boundary condition and pipe bottom supports is assumed to be fixed as a boundary condition. The mechanical properties of the GFRP pipe material used in the modeling for the finite element analysis are considered to be isotropic material based the tensile test results. For the finite element analysis, the test specimen is modeled based on the dimension and material properties of GFRP pipe. AutoCad 2008 program is used for the accurate modeling of the pipe and then the data used in the modeling is transferred to the finite element analysis program, ANSYS Ver. 11. The modeling for the finite element analysis of entire length of GFRP pipe is shown in Figure 5, and the actual dimension of pipe was used in the 3D solid element modeling. One of the typical deformed shapes of the GFRP pipes obtained by the finite element analysis is shown in Figure COMPARISON OF RESULTs In this study, we presents the pipe stiffness measured by the parallel plate loading test. In addition, the prediction by theoretical analysis and the finite element analysis are conducted and the results are also presented. The results on the pipe stiffness of the flexible pipes are compared and close agreements are observed. It was found that the approach discussed in this paper could Polymers & Polymer Composites, Vol. 22, No. 1,

6 Joon-Seok Park, Won-Hee Hong, Wan Lee, Jung-Hwan Park, and Soon-Jong Yoon Table 5. Result of the parallel plate loading test, theoretical and FE result Vertical Ring Deflection Dy (%) Experimental Result PS (kn/m 2 ) Theoretical Result PS (kn/m 2 ) FEA Result PS (kn/m 2 ) Difference (%) ( - )/ x100 ( - )/ x100 GFRP pipe Figure 6. Deformed shape of GFRP pipe that the design and construction could be accomplished economically and efficiently. ACKNOWLEDGEMENT This work was supported by 2012 Hongik University Research Fund and Korea Science and Engineering Foundation (KOSEF) grant (No. R ) funded by the Korean government (MEST). be used to predict the pipe stiffness of the GFRP pipes for the purpose of preliminary design of GFRP pipes. Detailed results with % difference are given in Table 5. In Table 5, The results on the pipe stiffness of the GFRP pipes are compared and close agreements (maximum difference 8.1%), which is generally accepted in the structural engineering, are observed. It was found that the approach discussed in this paper could be used to predict the pipe stiffness of GFRP pipe. 6. CONCLUSIONS In this paper, we present the results of investigations pertain to the pipe stiffness, PS, of GFRP pipes buried underground. The pipe stiffness is generally measured by experiment using the parallel plate loading test. In this paper, mechanical properties of the GFRP pipes produced by Hankuk Fiber Co. Ltd. are tested and the results are reported. In addition, PS is determined by the parallel plate loading tests, theoretical analysis, and the finite element analysis. The difference between experimental result, theoretical result, and FEA result is less than 10%. So, the theoretical analysis and the finite element analysis can be used to predict the pipe stiffness instead of conducting the parallel plate loading test. The pipe stiffness of flexible pipe specimen is usually measured in the laboratory according to the parallel plate loading test method. When the laboratory test equipment is not available, a theoretical solution based on the elastic curved bar theory is often used, as an alternative approach, to estimate the pipe stiffness of the flexible pipe. In the elastic curved bar theory, vertical and horizontal displacements are also derived. Vertical deflection is always larger than the horizontal deflection because some of energy due to overburden load is stored in the pipe but the difference is negligibly small. In this paper, short-term structural behavior of GFRP pipe is discussed. Durability issues such as creep, degradation, long-term deflection, etc. should also be investigated so REFERENCES 1. Park J.-S., Kim S.-H., Kim E.- H., and Yoon S.-J., Journal of the Korean Society for Advanced Composite Structures, 2) (2011) Suleiman M.T., The Structural Performance of Flexible Pipes, MS. Thesis, School of Civil Engineering, Iowa State University, Iowa, USA (2002). 3. Moser A.P., Buried Pipe Design, McGraw-Hill, New York, USA (2011). 4. Smith G. and Watkins R., Iowa Formula: It s Use and Misuse When Designing Flexible Pipe, Proceeding of Pipelines International Conference, American Society of Civil Engineers, ASCE, (2004) Spangler M.G. and Handy R.L., Soil Engineering, Harper and Row, New York, USA (1982). 6. Akinay E. and Kilic H., Use of Emperical Approaches and Numerical Analyses in Design of Buried Flexible Pipes, Scientific Research and Essays, Vol. (24) (2010) Watkins R.K. and Anderson L.R., Structural Mechanics of Buried Pipes, CRC Press, New York, USA (2000). 22 Polymers & Polymer Composites, Vol. 22, No. 1, 2014

7 Pipe Stiffness Prediction of Buried GFRP Flexible Pipe 8. ASTM D 2412, Standard Test Method for Determination of External Loading Characteristics of Plastic Pipe by Parallel-Plate Loading, American Society for Testing and Materials (ASTM), Philadelphia, USA (2010). 9. KS M ISO , Thermoplastics Pipes-Determination of Tensile Properties-Part 2: Pipes Made of Unplasticized Poly (Vinyl Chloride) (PVC-U), Chlorinated Poly (Vinyl Chloride) (PVC-C) and High-Impact Poly (Vinyl Chloride) (PVC-HI), Korean Agency for Technology and Standards (KS)., Seoul, Korea (2002). 10. KS M 3082, Test Methods for Shear Properties of Fiber Reinforced Plastics by the V-Notched Specimen, Korean Agency for Technology and Standards (KS), Seoul, Korea (2007). 11. KS M ISO 9969, Thermoplastics Pipes-Determination of Ring Stiffness, Korean Agency for Technology and Standards (KS), Seoul, Korea (2008). 12. Park J.-S., A Study on the Ring Deflection Limitation of Buried Flexible Pipes, Ph.D. Thesis, Hongik University, Seoul, Korea (2011). 13. ANSYS Release 11.0 Documentation for ANSYS, Pennsylvania, USA (2008). Polymers & Polymer Composites, Vol. 22, No. 1,

8 Joon-Seok Park, Won-Hee Hong, Wan Lee, Jung-Hwan Park, and Soon-Jong Yoon 24 Polymers & Polymer Composites, Vol. 22, No. 1, 2014

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