important parameter in the design of buried flexible pipes. ... narrow trench, the proportion of the sharing of the soil load between the pipe and the side fill is ...
EFFECTS OF SOIL ARCHING ON THE BEHAVIOUR OF FLEXIBLE PIPES BURIED IN TRENCHES OF VARYING WIDTHS Devapriya. C. Wijeyesekera11 and Suranjith Warnakulasuriya2 ABSTRACT The restraints from the side fill on a buried pipe influence its deformed shape. It is often very difficult to compact well the side fill in narrow trenches. The trench width to pipe diameter ratio must necessarily be an important parameter in the design of buried flexible pipes. A 2m long, 1.5m high soil box with variable width was used to observe the pipe deformations, pipe strains, normal and shear stresses at the soil-pipe interface of a 2mm thick, 150mm diameter glass reinforced plastic pipe. Instrumentation was also provided for direct measurement of the horizontal and vertical soil stresses at the boundaries of the trench. The soil box test data are complemented with numerical analysis results. The observations showed that a distinctive soil-pipe system is developed when the initial layers of fill are placed on a very flexible pipe (Ring stiffness - EpI/D3 < 4 KPa). The rate of increase of soil load/ radial deformation of the pipe with increasing heights of fill decreases with increasing trench width parameter. In a narrow trench, the proportion of the sharing of the soil load between the pipe and the side fill is increased due to the weakening of the soil arch resulting from the limited soil fill at the springing. INTRODUCTION
E3 Bulk fills
C +ve
H Trench Boundary
D -ve
W
Depth of cover (C)
Recent development in flexible pipe manufacture and competition drives pipe manufacturers to develop thinner walled pipes with low cost pipe materials. Hence the more flexible thin walled glass reinforced plastic (GRP) pipes are becoming increasingly popular in the pipeline construction industry. Molin(1981) and Gumble (1983) used numerical modelling techniques to show that in flexible pipe design the effect of horizontal earth loading is a parameter not to be ignored. The performance of the pipe depends not only on the pipe material but also on the interactive soil-pipe system. The stiffness of the side fills restrains the shape of the deformed pipe. Low trench widths to pipe diameter ratios hinder the compaction of the surrounding soil. Pipe deformations determined from Spangler or Barnard methods either represent the instantaneous or end of construction deflections. The design equations proposed by Barnard are used by the American Water Work Association (AWWA manual M11-1964). CIRIA report No. 78 also presented this method as an alternative to the Spangler’s approach.
Wv
Unit area
H
_∆x
E2 Compacted fill
Buried pipes E4 Native soil
E1 Bedding Layer
Pipe deflection ∆D = ∆x
Wh (max) Equivalent Earth column (L)
Figure 1 : Buried pipe - Notations, concepts and pipe trench parameters (study assumes that Ef=E1=E2=E3) Documented field data collated during last 25 years have shown that for very flexible pipes with ring stiffness less than 4 kPa (GRP Pipes), the predicted design deflection differ significantly to the actual deflection. Committee de European Nation (CEN) has recognised the urgency to establish a common European design method for GRP pipes. There is a lack of published information on the significance of the lateral trench boundary and the boundary soil properties on buried pipe design. The paper describes the results from a soil box study as well as that from a numerical modelling analysis with particular study of the limits of the soil boundary (E4/Ef ratio) that could affect the behaviour of buried flexible pipes. 11 2
Devapriya. C. Wijeyesekera, Reader in Civil Engineering, University of East London, Essex RM8 2AS, UK Suranjith. Warnakulasuriya, Research Fellow, University of East London, Essex RM8 2AS, UK.
Although Allgood(1968) and Gumble(1983) have considered the soil/pipe interaction in categorising the buried pipe, no consideration was given to the effect of the trench geometry. Most pipeline construction involves trench excavation, where the pipe is laid and then backfilled (figure 1). Consider the case of a trench excavated in loose ground (where E4 is very low), and the trench is backfilled with a stronger backfill material (Ef >> E4). The level of lateral support from the backfill to the pipe will depend on the trench geometry and can be less than that predicted. The installation procedure also plays an important role in the soil/pipe interaction. During the process of backfilling, the sides of the pipe are backfilled first. The lateral thrust from the soil reduces the horizontal pipe diameter to a pre-designed value. The allowable inward deflection of the horizontal diameter is pre-calculated, based on the burial height. With the completion of backfill, (soil load), the pipe will expand horizontally to reach the nominal pipe diameter (see figure 1). It is currently not feasible to allow for the installation process in a rigorous pipe stiffness classification. However, it is useful to consider the trench geometry and existing ground condition in stiffness classification. DETAILS OF SOIL BOX & INSTRUMENTATION Table 1 Soil Properties of Sharp River Figure 2 illustrates the details of the electronic instrumentation and the soil box, which was fabricated with 5mm thick steel plates, stiffened using 50mm x 50mm angle iron bracing. The movable wall facility permitted trench width of 350, 450, 600, 750 and 800mm to be investigated. Four sliding doors at the two ends of the soil box helped to position the pipe centrally. Plumb blocks mounted at the ends of the soil box were on a system of vertical and horizontal rails to facilitate the positioning of aluminium mandrel which carried the displacement transducers. A 150mm diameter, 2mm thick, 2 m long GRP pipe was used in the test. (Elastic modulus of GRP pipe = 10MPa, Poisson's ratio = 0.35, Density of GRP pipe = 1400 kg/m3.). The backfill was Sharp River sand whose geotechnical properties are given in table 1.
Description
Value
effective particle size D60 effective particle size D30 effective particle size D10 Uniformity coefficient Cu Coefficient of curvature Cc Soil classification Specific Gravity Soil density (kg/m3) Relative density (Dr ) Angle of Internal friction (φ) Angle of Dilation (ϕ) Friction angle between sand and the Soil box wall Friction angle between sand and the GRP pipe Elasticity modulus of soil Poissons ratio Bulk modulus Shear modulus
0.59 0.32 0.20 3.01 2.27 SWG 2.6 Uncompacted Compacted 1540 1790 0.59 0.69 38o 46.5o 0.54o -
9o 14.6o
-
17.7o
-
16 (MPa) 0.28 3.13 (MPa) 6.06 (MPa)
Soil Pressure plate transducers
GRP pipe Contact stress transducers
View from top
Axle
View from left
Displacement transducers View from right
Strain gauges (x4)
2000 mm 450mm-900 mm
1200 mm
Movable door of the soil box
Figure 2 : Details of buried instrumented pipe in soil box. Sliding doors
SOIL BOX TEST OBSERVATIONS
2
-1
-2
-3
-4
-5
0
100mm 1
Initial reading Layer-1(C/D Init ial reading = -1) Layer-2(C/D -0.5) Layer-1(C/D = = -1) Layer-2(C/D = = -0.5) Layer-3(C/D 0.649) Layer-3(C/D = = 0.649) Layer-4(C/D 1.295) Layer-4(C/D = 1.295) Layer-5(C/D = 1.948) Layer-5(C/D = 1.948) Layer-6(C/D 2.597) Layer-6(C/D = = 2.597) Layer-7(C/D =3.247) Layer-7(C/D =3.247) Layer-8(C/D = = 3.896) Layer-8(C/D 3.896) Layer-9(C/D = = 4.545) Layer-9(C/D 4.545) Layer-10(C/D =5.195) Layer-10(C/D =5.195)
-1
-2
-3
-4
-5 0
20
20
40
40
60
80
100
120
140
160
Layer –12 Layer –11 Layer –10 Layer –9 Layer –8 Layer –7 Layer –6 Layer –5 Layer –4 Layer –3
100mm 100mm 100mm
0
100mm 100mm 100mm 100mm 100mm 177mm 77mm 180 150mm 180
+ve Layer –2
-ve Layer –1
60 80 100 120 140 160 Angular position from (Degree) Angular pospipe ition crown from pipe crown (Degre e)
Angular position from pipe crown (De gree)
Figure 3 : Pipe deformations observed with 800-mm trench wide soil box Similar pattern of results was observed with other trench width too, but the magnitude of the gain in strain diminished with increasing trench widths. The deformed shape of the pipe suggests a single wave buckling as postulated by Cheney(1976). Figure 5 shows that the deformation per unit increase in cover depth decreases with increasing width of the trench. A silo effect causes the mid length of the pipe to sag resulting in larger inward deformation of the pipe near the haunch in the quarter length section. This is an unavoidable phenomenon in soil box testing as well as in field situation of trenches with end restraints. 5000
W/D = 2.33 W/D = 3 W/D = 4 W/D = 5.33
0 -5000 -10000 -15000 -20000 -25000 -30000 -35000 -40000
H/D ratio 2
8
H/D = 0 H/D = 1.80 H/D = 3.10 H/D = 4.40 H/D = 5.69 H/D = 6.99
7 6 5
H/D =1.15 H/D =2.45 H/D = 3.75 H/D = 5.05 H/D =6.34 H/D = 7.64
4 3 2 1
W/D ratio
0
-45000
0
percentage reduction in vertical diameter (%)
0
Radial pipeRadial deformation (mm) pipe deformations (mm) Radial pipe deformation (mm)
1
Strain at crown (micro strains)
Radial pipe deformations (mm)
The change in pipe diameter was monitored at 10 0 intervals for each stage of filling. The pipe deformations at different cover depth to diameter ratio (C/D) for 800mm wide box are presented in figure 3. Notably at negative cover depths, the effect of the lateral pressure on the pipe from the side fill was to uplift the pipe as the sand is poured and compacted to reach the layer-1 and 2 (C/D of -1 and -0.5). The crown moved outward while the springing moved inwards. With further burial, the pipe deformed giving net reduction in both horizontal and vertical diameter. There was consistent reduction over all angular positions apart from the observation at the vicinity of the haunch of the pipe. This results from the inevitable zone of weakly compacted fill that occurs in the vicinity of pipe haunch. This effect is the cause for the decreasing compressive strain observed with the 2 strain gauge at the pipe's crown, springing and invert (figure 4).
4
6
Figure 4 Observations of strains in the pipe at different stages of burial
8
1
2
3
4
5
6
Figure 5 Deformation per unit increase in cover depth decreases with increasing width of trench
NUMERICAL MODELLING 3D , a three dimensional explicit finite Numerical modelling of the soil test was carried out using FLAC difference programme. A 3D-plane strain model was used to model conceptually the soil box test. An interactive common fish programme was developed using FLAC3D software to model all the soil box tests for
SOIL - PIPE SYSTEM
5
Radial pipe deformation (mm)
different trench widths simultaneously. Though the magnitude of pipe deformation from soil box test and numerical modelling predictions are not identical a similar trend of variation with changing trench width is confirmed (Figure-6). If the effect of settlement is deducted from pipe deformation, then the numerical modelling results reasonably agree with soil box results, for instance deformation of pipe crown observed from numerical modelling is 3.5mm while that from soil box study shows 4mm. The contour plot of minor principal stress (maximum compressive stress) showed in Figure-7 indicates that the development of soil arching is more defined in the wide trench. One can visualise readily the soil particle movements during the formation of the soil arching.
FLAC3D, W=350 mm FLAC3D, W=400 mm FLAC3D, W=600 mm FLAC3D, W=800 mm Soil box test, W=350 mm Soil box test, W=400 mm Soil box test, W=600 mm Soil box test, W=800 mm
4 3 2 1 0 -1
0
30 60 90 120 150 Angular position from pipe crown ( θ 0 )
180
Figure 6 Comparison of soil box pipe deformation data with that from numerical modelling.
Figures 8 show the contour plots of total displacement at the end of each layer of filling for both narrow and wide trench. As these plots show the state of the soil/pipe system at the end of each stage of backfill, the development and its cumulative performance can be easily recognised through these plots. The development of soil arching is initiated from the first layer of fill above the pipe, though there is a difference in the magnitude for different trench widths. This difference in soil load is higher, at 350mm trench than that for 800mm trench. The higher concentration of soil load at the shoulder in 350mm wide trench than that in 800mm trench, is caused by the distribution of soil load according to the width of the side fill. This difference in the compressive stress causes higher displacement (settlement) in soil at the side of the pipe for narrow trench than in wider trench. With the settlement of the soil at the side of the pipe, the crown of the pipe is further subjected to an increased soil load, which causes more displacement at the pipe crown. The peak compressive normal stress developed at the springing redistributes again in the soil mass below the pipe springing working around the pipe. The flexibility of the pipe and the high compressive soil load developed at the level of the pipe springing causes the pipe wall to displace inward and hence reduces the stiffness of the soil mass and the compressive stress adjacent to the pipe springing
Trench width (W) = 800 mm
C/D = -0.5
C/D = 0.65
C/D = 1.30
C/D = 1.95
C/D = 2.60
C/D = 2.60 Trench width (W) = 350 mm C/D = 1.95 C/D = 1.30 C/D = 0.65
C/D = -0.5
Figure 7 : Contour plot of vertical and horizontal stress in the soil
SOIL ARCHING Figure 9 shows the normal stress acting on the tangential plane to the pipe at crown, springing and at the invert for the pipe in a shallow trench of widths 350 and 800 mm respectively. These plots compare the stress distribution on the pipe encloses with pipes of varying flexibility. Both figures show similar pattern of results but differ in magnitude of the stress. Therefore, the load distribution patterns will also be similar. Soil load acting from each direction on the pipe increases with the decreasing flexibility (increasing ring stiffness) of the
pipe. Vertical soil load on the load plane of the pipe increase and the position of resultant vertical soil load is concentrated closer to the pipe crown with decreasing flexibility of the pipe. This means that with decreasing flexibility the soil load acting at the crown of the pipe is increased, while soil load transferred to side fill due to soil arching is reduced. The flexibility of the pipe is significant in the progressive development of soil arching. Similar to the load at pipe crown, the vertical soil resistance at the invert increases with the increasing flexibility and position of the Trench width resultant soil resistance comes closer to the pipe invert. This (W) = 350 shows the sensitivity of the pipe flexibility on the soil load mm acting on the pipe and the load distribution pattern on the pipe. Design methods adopted by U.K. Denmark and Sweden do not consider trench width effect on soil loading, where for all the trench width condition they have predicted same value of soil loading and have linear relationship height of soil cover. However soil load, predicted from the design methods adopted by France, Austria and Germany have shown variation with the change of trench width. Further more they have shown a non-linearly decreasing trend of soil load with increasing soil cover. Warnakulasuriya (1999) shows that there is nearly five fold (for 350mm wide trench) differences in overburden soil load predicted from the above design methods, and the high values predicted from U.K., Denmark, Sweden designs methods. The low stiffness of the trench boundary does not reduce the lateral support near the pipe for the higher trench width. For this reason, the pipe that fails when buried in the narrow trench and the trench boundary condition of E 4/Ef=0.001 does not fail when buried in the
Cover depth (C ) = 200 mm
C/D = 0.65
C/D = 1.30 C/D =
C/D =
Vertical stress at the level of pipe crown (Pa)
Figure 8 : Total displacement plots
300 200 100 800 mm
0
1000
2000
wide trench
3000
0
C/D = 2.60
C/D = 0.5
E=1e6 30 MPa E=1e7 300 MPa E=1e8 3000 MPa E=1e9 30000 MPa 300000 MPa E=1e10
Cover depth (C ) = 200 mm 0
Vertical stress at the level of pipe invert (Pa)
0 100 200 300 400 500
E=1e9 30000 MPa 300000 MPa E=1e10
C/D = 1.95
0
Vertical stress at bottom (Pa)
(Pa)
1000
2000
3000 0
E=1e6 30 MPa E=1e7 300 MPa E=1e8 3000 MPa
Horizontal stress on the vertical plane at springing (Pa)
Vertical stress at the level of pipe crown (Pa) 4000
350 mm wide trench
Vertical stress at the level of pipe invert
Horizontal stress on the vertical plane at springing (Pa)
0
C/D = 1.30
Trench width (W) = 800 mm
800mm wide trench. With increased trench width the soil load acting on the pipe is unaffected from a yielding trench boundary condition (figure 10).
300 200 100 0
C/D = 0.65
C/D = -0.5
0 100 200 300 400 500
Figure 9 : Normal stress acting on the tangential plane at pipe crown, springing and at the invert
E4/Ef = 0.001
E4/Ef = 0.01
E4/Ef = 0.1
E4/Ef = 100
E4/Ef = 1000
Pipe fails
E4/Ef = 1
Figure 10
E4/Ef = 10
Contour plot maximum compressive stress for various flexibility trench boundary conditions for the pipe buried in 350mm wide trench for (C/D=1.295)
CONCLUSIONS The following conclusions are supported by the observations from the soil box test as well as the analysis from the numerical modelling. • When the first layer of fill above the (C/D = 0.649) is placed on a very flexible pipe a distinctive soil/pipe system is formed with the development of a soil arch, for any trench width. • Trench width parameter is shown to have significant effect on the behaviour of buried flexible pipes. The magnitude of such effects on soil load and the radial deflection could have even doubling effect depending on the trench width. The rate of increase of soil load /strain at crown with increasing fill height is seen to decrease with increasing trench width parameter (W/D). Performance of buried flexible pipe depends on the yielding properties of boundary soil. A yielding trench boundary reduces the resultant lateral soil support and can cause the pipe to fail at a lower soil load through excessive buckling. Wide trench fills can minimise the influence of boundary soil on the pipe behaviour. • The trench width controls the degree of soil arching which plays a major role in the behaviour of buried flexible pipe. As the trench with decreases, for example in the narrowest study trench (W/D =350/150 =2.33), the proportionate sharing of the soil load between the pipe and the side fill is increased due to the weakening of soil arch resulting from the limited soil fill at the springing. Thus a very flexible pipe buried with similar boundary conditions will be subjected to even higher soil loads and consequently higher displacement than those buried in a wider trench. The distribution of soil load due to soil arching causes the shoulder of the pipe to carry a higher soil load and the pipe is supported more at the haunch than at the pipe invert. In very flexible buried pipes a higher vertical stress in the soil is developed at the level of the pipes springing, where soil in this zone act as vertical earth column supporting the soil arch. In the case of a narrow trench this zone is in close proximity to the trench boundary but in wider trench this zone separates from trench boundary act as a separate pillar for the soil arch. The effect of soil arching is reduced with increasingly stiffer pipes. REFERENCES Allgood, J.R., Ciani, J.B.and Lew, T. (1968). "Influence of soil modulus on the behaviour of cylinders buried in sand", Tech. Report R-582, Naval Civ. Engng. Lab., Port Hueneme, Calif. AWWA manual M11 (1964) Cheney. J.A.,(1976). "Buckling of thin walled cylindrical shells in soil", Dept of Environmet, TRRL Suppl. Report 204. CIRIA Report No. 78 Gumble, J.E., (1983). "Analysis and design of buried flexible pipes", PhD Thesis, University of Surrey, UK. Molin, J. (1981). "Flexible pipe buried in clay", Proc. Int. Conf. Underground Plastic Pipe, ASCE, New Orleans, USA, pp 37-55. Warnakulasuriya. H. S.(1999)."Soil structure interaction of buried pipes", PhD Thesis, University of East London, UK
