12th International Symposium on District Heating and Cooling

For the case of parallel buried pipes former analyticalcalculations by Rizkallah and Achmus usingLeonhardt‘s theory showed a reduction of the verticalstresses between the two pipes [6]. The system usedfor these calculations with the ―shear resistant beam onelastic bedding‖ for two parallel buried pipes is shownin Fig. 2.The <strong>12th</strong> <strong>International</strong> <strong>Symposium</strong> on District Heating and Cooling,September 5 th to September 7 th , 2010, Tallinn, EstoniaFig. 4. Ratio B2/ B dependent on relative overburdenheight and pipe distancesFig. 2. Shear resistant beam for parallel buried pipesThe concentration factors B . B for the area beside andbetween the pipes were found with the followingassumptions:The influenced area for the determination ofthe concentration factor B beside the pipe( B1 ) is defined by a line with an inclination of60° shown in Fig. 3. This angle coincides withthe theoretical slope inclination of a noncohesivesoil with an internal angle of frictionof ' = 30°.Between the pipes ( B2 ) the full interspace istaken as the area of influence.A calculation method for parallel buried pipes instepped trenches was proposed by Hornung and Kittel[7]. With this calculation method the total loading onone pipe is derived from the sum of the partial loadings,which correspond to the trench shape to the right andleft of the pipe. The typical trench condition for districtheating pipes provides a non stepped trench with theflow and return pipes installed on the sameunderground level. The presented study was thereforecarried out without employing the Hornung and Kittelcalculation method.NUMERICAL INVESTIGATIONSNumerical calculations were carried out with the twodimensional finite element program PLAXIS, version8.6. Two standard situations with different outer pipediameters D (DN65, D=140 mm; DN250, D= 400 mm)of two parallel buried district heating pipes wereinvestigated. The distance between the pipes waschosen to be A=10 cm (see Fig. 1). The overburdenheight of the backfill material of the trench wasH/D=3.0. The finite element mesh used for the DN65pipe is shown in Fig. 5 as an example.Fig. 3. Method to determine the concentration factors forparallel buried pipesThe calculations by Rizkallah and Achmus showed onlysmall deviations for the concentration factor B of singlepipes and the concentration factor B1 for parallelburied pipes. However, a significant reduction of thevertical stresses (i.e. B2 < B ) was determined betweenthe pipes. As an example, the ratio of the stress factorsis shown in Fig. 4, dependent on the relativeoverburden height H/D and the relative distance of thepipes A/D.Fig. 5. Finite element mesh for the case DN65, H/D=3The installation process was simulated by a ―stagedconstruction‖ process, considering a retained trenchand the backfilling procedure with several layers. Thecompaction process was accounted for by applying astatic distributed load of p=10 kN/m² on each of thelayers. Ground water was not considered in thisinvestigation.13