Behaviour of buried small flexible pipes

NOTE

Behaviour of buried small flexible pipes A. GHOBARAH A N D W. K. TSO Department of Civil Engineering and Engineering Mechanics, McMaster Universiry, Hamilton, Ont., Canada L8S 4L7 Received January 13, 1987

Can. J. Civ. Eng. Downloaded from www.nrcresearchpress.com by McMaster University on 02/03/15 For personal use only.

Revised manuscript accepted November 23, 1987 An analytical and experimental investigation was conducted to study the behaviour of buried small diameter flexible plastic drain pipes when subjected to surface wheel loads. Tests were conducted on drain pipes buried under sand and also typical agriculture soil samples from Southern Ontario. In addition to soil types, the effect of soil compaction on the stresses and deformation of the pipe was evaluated. It was found that the modulus of soil reaction is highly dependent on the degree of compaction of the soil adjacent to the pipe. By using compacted sand around the pipe, the modulus of soil reaction can be increased significantly, thereby reducing the deformation of the pipe. Using the appropriate value of the modulus of soil reaction, it is shown that theoretical predictions of pipe deformation correlate well with test measurements. Key words: plastic, flexible, buried, pipe, experimental, deformation. Une ttude exptrimentale et analytique a it6 rtalisee afin d'observer le comportement de tuyaux de drainage de plastique flexible de petit diamttre enterrts, soumis i des charges superficielles. Des essais ont Ctt rCalists sur des tuyaux de drainage recouverts de sable et d'tchantillons de terre arable du sud de l'ontario. En plus des types de sol, l'effet du compactage du sol sur les contraintes et la dtformation du tuyau a Ctt CvaluC. On a constatt que le module de rtaction du sol dCpend fortement du degrC de compactage du sol adjacent au tuyau. En utilisant du sable compact6 autour du tuyau, le module de reaction du sol peut Ctre augment6 de faqon significative, ce qui rtduit la dtformation du tuyau. I1 est dtmontrt, i l'aide d'une valeur de module de rCaction du sol approprite, que les pridictions thtoriques de la dtformation des tuyaux correspondent bien aux mesures obtenues lors des essais. Mots clks : plastique, flexible, tuyau enterrt, Ctude expCrimentale, deformation. [Traduit par la revue] Can. J. Civ. Eng. 15,486-489 (1988)

Introduction Small diameter corrugated plastic drain pipes are being extensively used in agriculture, highways, roads, and construction. Due to the pipe flexibility in the radial direction, a small vertical load will cause relatively large lateral deformations which mobilize the lateral soil support. With adequate lateral passive soil support, the load-carrying capacity of the pipe is increased. Flexible pipe failure is usually characterized by collapse due to excessive deformation which leads to buckling of the ring wall. One of the critical parameters in the analysis and design of buried flexible pipes is the modulus of soil reaction. The value of this parameter depends on the type of soil, degree of compaction, and the pipe diameter. A study of the modulus of soil reaction for buried large diameter flexible pipes was conducted by Howard (1977). The results included a table of the modulus of soil reaction values for several types of soil conditions. These values can then be applied in the Iowa formula (Watkins and Spangler 1958) for predicting the flexible pipe deflection. The published values for the modulus of soil reaction vary broadly over a range between 0.12 and 20 MPa and may be as high as 55 MPa. There is little information available on the modulus variation with pipe diameter. The design procedures for corrugated plastic pipes are summarized by Reeve et al. (1981). The objective of this study is to investigate the structural behaviour of corrugated small diameter (100 mm) plastic drain NOTE: Written discussion of this note is welcomed and will be received by the Editor until September 30, 1988 (address inside front cover).

pipes buried under typical southern Ontario agriculture soil conditions. A test program is carried out to determine the modulus of soil reaction. Theoretical predictions are compared with the result of an experimental program to study the effect of loose and compacted soil conditions on the modulus of soil reaction.

Experimental setup for buried pipe A 9 15 mm deep box was built for the experimental program. The cross-sectional area was designed to be 6 10 X 320 mm. The box dimensions were limited by the available space to fit under the compression head of the hydraulic testing machine. Three sides of the box were made of stiff 19 mm plywood while the fourth side was made of 13 mm transparent plexiglass. The box comers and at mid height were stiffened by-steel angles. Using the very stiff box construction is expected to reduce the effect of flexibility or deformation of the box walls. The influence of the type and condition of the surrounding soil is of prime importance in the performance of plastic flexible pipes. For the experiment, two types of soil materials were used as a bed and fill around the pipe specimen. The first type of material is well-graded sand whose measured angle of internal friction using direct shear test was 39.7" and 54.3" for loose and dense conditions respectively. The second type of material is agriculture soil obtained from various south& Ontario locations in the Niagara Peninsula. Laboratory analysis classified the agriculture soil as silty sand SM with water content of 19.96%. The plastic limit and liquid limits were determined to be 17.12 and 20.48% respectively. The specific gravity of the soil is 2.7 and angle of internal friction from direct shear tests

487


NOTE

TOP DEFLECTIONIDIAM RATIO

FIG. 1. Idealized pipe and loading system: (a) vertical loads; (b) horizontal loads.

were found to be 39.5" and 46" for loose and compacted conditions respectively. The pipe deformations were measured using two linear variable displacement transducers (LVDT). Five pressure transducers were used to measure the pressure distribution on the pipe wall. The pipe was laid on top of a 200 mm layer of compacted soil or sand. The rest of the box was filled with the soil or sand material. To simulate a dense soil condition, the soil or sand material was filled and compacted in 100 mm layers by means of a vibrator. Loose condition of the soil was simulated by free falling of soil or sand into the box enclosure. Loading was applied at the surface of the box at a rate of 6.25 mm/min. Deflection and pressure readings were taken at 250 N load increment. Pipe failure by buckling was not reached during the tests. For each soil and compaction condition, tests were repeated several times using new pipe samples and new soil in an attempt to establish the reproducibility of the test setup and measurements.

Load distribution The flexible pipe behaviour is characterized by lateral passive support which is a function of the deflection curve. For analysis purposes, the distribution of all the components of vertical and horizontal loads acting on the buried pipe is assumed as shown in Fig. 1. The region over which the applied vertical load acts is defined by the angle a , and the vertical reaction load is assumed to act over a region defined by a , . The region of application of the lateral load is defined by the angles PI and PZ, measured from the vertical axis. The vertical load components w, and wb, acting on the top

FIG. 2. Load-deflection relationship for loose soil: A , test #I; 0, test #2; +, test #3; -, theoretical ( E ' = 0.138 MPa).

and bottom surfaces of the pipe respectively, are assumed to be uniformly distributed and are represented by the following expressions: [2]

wb=constant

for-a, < 8 < a ,

The relationship between the vertical loads is determined based on equilibrium consideration: [3]

Wb

=

sin (Y wt sin a ,

The lateral soil pressure w,(e) is assumed to vary parabolically for the range < 8 < PZ where Ax = the maximum horizontal component of the pipe deformation u; e = E ' l r = the modulus of passive resistance in units of MPa/mm; E' = modulus of soil reaction; and r = the radius of the pipe. The constants a, b, and c can be determined from the conditions of zero load at 8 = PI and P2 and maximum load at 8 = (PI + P2)/2.

Pipe deformation Given the load distribution in the vertical and horizontal directions, the pipe deformation can then be estimated. Due to the pipe and load symmetry, the radial deflection is expressed in the form of a cosine series. 3:

[51 6,

=

C a,, cos , ~ e

n= 1

CAN. I. CIV. ENG. VOL. 15, 1988


488

0

2.5

5

7.5

10

12.5%

TOP DEFLECTION/DIAM RATIO FIG.3. Load-deflection relationship for dense soil: A , test # 1; 0, test #2; +, test #3; -, theoretical (E' = 0.483 MPa).

The positive direction of 6, is taken towards the centre of the ring. The coefficients a, are determined by virtual displacement principle. When the system is given a virtual displacement, the work done by the applied load is equal to the change of the strain energy of the ring. Since the value of soil reaction depends on the deformation of the pipe, an iterative procedure is a convenient method of solution to the problem. First, initial values for the angles a,a,, pi, and p2 need to be estimated. The solution for the pipe deformation is numerically evaluated using an iterative technique, which converges to the required deflection curve. The maximum vertical deflection at the top of the pipe is denoted by Ay. The maximum horizontal deflection Ax is taken to be the value of 6, at 0 = 90" and 270". The value of the resulting deflection is considered to be sufficiently close to its maximum value for the purposes of this analysis. The values of pipe stiffness El used in the analysis were determined experimentally using the parallel plate loading method as described in the American Society for Testing and Materials, ASTM standard D2412-77 (1977).

Test results and discussions Four different groups of tests were conducted in which the cases of loose and dense agriculture soil and loose and dense sand were used. The vertical load applied by the compression machine is increased to a value of 8.8 kN. The load is distributed at the soil surface by 325 X 300 X 13 mm steel plate. The range of applied loads was chosen to cover the practical values of field load conditions.

TOP DEFLECTIONIDIAM RATIO FIG. 4. Load-deflection relationship for loose sand: 0, test # 1; theoretical (E' = 1.241 MPa).

+ , test #2; -,

Using loose soil as fill around and on top of the test pipe, the applied load is plotted in Fig. 2 against the top deflection/ diameter ratio. The test measurements identified by test #1, #2, and #3 refer to repeated tests using new pipe samples and new soil to establish the consistency of the testing methodology. In addition to the experimental measured data points, the solid line represents the theoretical prediction of the pipe deformation based on the analytical solution. In the analysis, the value of the modulus of soil reaction used is 0.138 MPa. This value of the modulus of soil reaction is determined experimentally using the expression: E'

=

measured horizontal pressure 0.4565 x measured top deflection

A pressure transducer located at 0 = 270" is considered to measure the maximum horizontal lateral soil pressure on the pipe. A value for E' can be calculated for each set of pressure transducer and deflection readings. For each test setup, one value of the modulus E' was calculated as the average of all the values corresponding to all sets of instrument readings taken during the test. From the behaviour of the pipe represented by Fig. 2, the top deflectionldiameter ratio for the pipe, under the range of practical field loads, does not exceed about 12.5%. The load-deflection relationship for a pipe surrounded by compacted agriculture soil is shown in Fig. 3. The modulus of soil reaction used in the theoretical predictions is taken to be 0.483 MPa. This value was again obtained as the average of many values


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489

diameter of 12.5%) to a shallow pipe (600 mm below ground surface). The modulus of soil reaction can be increased to about 0.48 MPa when the agriculture soil around the pipe is compacted. In this case, the top deflection is reduced to about half its value for loose soil for the same vertical load on the pipe. Further reduction in the pipe deflection values can be achieved by surrounding the pipe with well-graded loose sand whose modulus of soil reaction is 1.241 MPa. The pipe top deflectionldiameter can be reduced to a low of 2% when the pipe is surrounded by well-graded dense and compacted sand whose modulus of soil reaction is 6.9 MPa. In this case, small lateral deflections of the pipe under vertical loads are sufficient to mobilize considerable lateral soil support to the flexible pipe. Test results were shown to be reproducible and to correlate well with theoretical predictions.

Acknowledgements The authors wish to acknowledge the support of the Natural Sciences and Engineering Research Council of Canada. This work was carried out under an NSERC grant to McMaster University.

TOP DEFLECTIONIDIAM RATIO

FIG. 5. Load-deflection relationship for dense sand: A, test # 1; 0, test #2; +, test #3; -, theoretical (E' = 6.9 MPa). corresponding to experimental measurements. In comparing the pipe deflection under a given load between Figs. 2 and 3, it becomes evident that the pipe deflection can be substantially reduced by compacting the agriculture soil around the pipe. For the case of loose and compacted well-graded sand fill around the plastic pipe, the load-top deflectionldiameter relationships are shown in Fig. 4 and Fig. 5 respectively. For the case of sand, the pipe deformations are even smaller than for the agriculture soils case.

Conclusions From the analysis of the deformation of buried flexible plastic pipes and the testing program, the following conclusions can be arrived at: The most important parameters that affect the pipe deformation are the soil type, degree of compaction around the pipe, and the pipe stiffness. The modulus of soil reaction for loose agricultural soil in southern Ontario is determined to be 0.14 MPa. Field load conditions can cause substantial deformation (top deflection1

AMERICAN SOCIETY FOR TESTING AND MATERIALS, ASTM STANDARD D2412-77. 1977. Standard test method for external loading properties of plastic pipe by parallel-plate loading, 1982 Annual Book of ASTM standards, Vol. 34. HOWARD,A. K. 1977. Modulus of soil reaction values of buried flexible pipe. ASCE Journal of Geotechnical Engineering Division, 103(GTI):33-43. REEVE,R. C., SLICKER, R. E., and LANG,T. J. 1981. Corrugated plastic tubing. Proceedings of the International Conference on Underground Plastic Pipe, New Orleans, LA, pp. 227-242. WATKINS,R. K., and SPANGLER, M. G. 1958. Some characteristics of the modulus of passive resistance of soil: a study in similitude. Highway Research Board Proceedings, 37: 576-583.

List of symbols constants coefficients in the deflection expression modulus of passive resistance (MPa/mm) modulus of soil reaction (MPa) pipe stiffness pipe radius vertical uniform distributed load on the top of the pipe vertical uniform distributed load on the bottom of the pipe lateral parabolic load distribution horizontal component of pipe deformation maximum horizontal deformation of pipe maximum vertical deformation at top of pipe angles of vertical load distribution angles of horizontal load distribution radial deflection variable representing angle at centre of pipe