Sensitivity Analysis On The Axial Soil Reaction Due To Temperature Induced Pipe Movements

ScienceDirect Available online at www.sciencedirect.com Available online at www.sciencedirect.com ScienceDirect Energy Procedia 00 (2017) 000–000 www.elsevier.com/locate/procedia 1876-6102 © 2017The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. The 15th International Symposium on District Heating and Cooling Assessing the feasibility of using the heat demand-outdoor temperature function for a long-term district heat demand forecast I. Andrića,b,c*, A. Pinaa, P. Ferrãoa, J. Fournierb., B. Lacarrièrec, O. Le Correc aIN+ Center for Innovation, Technology and Policy Research -Instituto Superior Técnico,Av. Rovisco Pais 1, 1049-001 Lisbon, Portugal bVeolia Recherche & Innovation,291 Avenue Dreyfous Daniel, 78520 Limay, France cDépartement Systèmes Énergétiques et Environnement -IMT Atlantique, 4 rue Alfred Kastler, 44300 Nantes, France Abstract District heating networks are commonly addressed in the literature as one of the most effective solutions for decreasing the greenhouse gas emissions from the building sector. These systems require high investments which are returned through the heat sales. Due to the changed climate conditions and building renovation policies, heat demand in the future could decrease, prolonging the investment return period. The main scope of this paper is to assess the feasibility of using the heat demand –outdoor temperature function for heat demand forecast. The district of Alvalade, located in Lisbon (Portugal), was used as a case study. The district is consisted of 665 buildings that vary in both construction period and typology. Three weather scenarios (low, medium, high) and three district renovation scenarios were developed (shallow, intermediate, deep). To estimate the error, obtained heat demand values were compared with results from a dynamic heat demand model, previously developed and validated by the authors. The results showed that when only weather change is considered, the margin of error could be acceptable for some applications (the error in annual demand was lower than 20% for all weather scenarios considered). However, after introducing renovation scenarios, the error value increased up to 59.5% (depending on the weather and renovation scenarios combination considered). The value of slope coefficient increased on average within the range of 3.8% up to 8% per decade, that corresponds to the decrease in the number of heating hours of 22-139h during the heating season (depending on the combination of weather and renovation scenarios considered). On the other hand, function intercept increased for 7.8-12.7% per decade (depending on the coupled scenarios). The values suggested could be used to modify the function parameters for the scenarios considered, and improve the accuracy of heat demand estimations. © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. Keywords: Heat demand; Forecast; Climate change Energy Procedia 116 (2017) 365–373 1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. 10.1016/j.egypro.2017.05.083 10.1016/j.egypro.2017.05.083 Available online at www.sciencedirect.com ScienceDirect Energy Procedia 00 (2017) 000–000 www.elsevier.com/locate/procedia 1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. The 15th International Symposium on District Heating and Cooling Sensitivity Analysis On The Axial Soil Reaction Due To Temperature Induced Pipe Movements Ingo Weidlicha* aHafenCity Universität Hamburg, Überseeallee 16, 20457 Hamburg, Germany Abstract Seen from an international perspective preinsulated bonded pipe systems dominate in heat distribution. These pipe systems are usually buried in sand and soil-pipe interaction hinders thermal strains, which make economic solutions for bow-and T-sections possible. For static design pipe-soil interaction must be known as accurate as possible. However, several parameters are influencing the quantity of the expected soil reaction. Main influencing factors are dependent on the used bedding material and geometry. Furthermore current research results made additional soil-phenomena evident, which are hardening effects and stress redistribution during operation. A new calculation approach for the axial soil reaction was developed in 2015 based on existing test results and numerical simulations. A sensitivity analyses were carried out to estimate the significance of relevant parameters and the existing calculation approaches. This paper identifies the significant parameters and suggests parameter sets for lowest and highest axial soil reaction. Two main boundary situations are taken into account a) first movement b) during operation. ©2017The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. Keywords: buried pipe design, pipe soil interaction, friction force 1. Introduction Seen from an international perspective pipe laying according to state of the art in heat distribution is primarily based on preinsulated bonded pipe systems. These pipe systems are usually buried in sand. The interaction of soil * Corresponding author. Tel.: 49-40-42827-5700 E-mail address: ingo[email protected] Available online at www.sciencedirect.com ScienceDirect Energy Procedia 00 (2017) 000–000 www.elsevier.com/locate/procedia 1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. The 15th International Symposium on District Heating and Cooling Sensitivity Analysis On The Axial Soil Reaction Due To Temperature Induced Pipe Movements Ingo Weidlicha* aHafenCity Universität Hamburg, Überseeallee 16, 20457 Hamburg, Germany Abstract Seen from an international perspective preinsulated bonded pipe systems dominate in heat distribution. These pipe systems are usually buried in sand and soil-pipe interaction hinders thermal strains, which make economic solutions for bow-and T-sections possible. For static design pipe-soil interaction must be known as accurate as possible. However, several parameters are influencing the quantity of the expected soil reaction. Main influencing factors are dependent on the used bedding material and geometry. Furthermore current research results made additional soil-phenomena evident, which are hardening effects and stress redistribution during operation. A new calculation approach for the axial soil reaction was developed in 2015 based on existing test results and numerical simulations. A sensitivity analyses were carried out to estimate the significance of relevant parameters and the existing calculation approaches. This paper identifies the significant parameters and suggests parameter sets for lowest and highest axial soil reaction. Two main boundary situations are taken into account a) first movement b) during operation. ©2017The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. Keywords: buried pipe design, pipe soil interaction, friction force 1. Introduction Seen from an international perspective pipe laying according to state of the art in heat distribution is primarily based on preinsulated bonded pipe systems. These pipe systems are usually buried in sand. The interaction of soil * Corresponding author. Tel.: 49-40-42827-5700 E-mail address: [email protected] © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. 366 Ingo Weidlich / Energy Procedia 116 (2017) 365–373 2Ingo Weidlich /Energy Procedia 00 (2017) 000–000 and pipe hinders thermal strains, making economic solutions for bowand T-sections possible. Regarding the static design, pipe-soil interactions must be known as accurate as possible. Nomenclature k0earth pressure coefficient at rest = 1-sinϕ' Geffective weight of the pipe filled with water σveffective soil stress at pipe axis for granular soils: σvγB*Hw+γBW*(Z-Hw)for Hw< Z σvγs*Z for Hw≥Z Zdepth of the pipe axis Hwdepth of ground water table γBunit weight of the soil γBw buoyant weight of the soil γSweight of the saturated soil Daouter diameter µ coefficient of friction δ contact friction angle ϕ'internal soil friction angle κlfactor for the relationship between initial stress state and subsequent stress state σr,avg average contact pressure on the pipe perimeter Fr,u ultimate friction force ∆Ttemperature increment κlfactor for the relationship between initial stress state and secondary stress state Hdepth of overburden to the top of the pipe Drrelative density of soil bedding αTthermal expansion coefficient Asarea of steel medium pipe EYoung’s Modulus FRultimate friction force l0length of the gliding section However, several parameters are influencing the quantity of the expected soil reaction [1]. Main influencing factors are the bedding material utilized and its parameters (e.g. average effective unit weight, compactness or coefficient of lateral earth pressure) and the geometry of the pipe and trench (e.g. depth of the pipe (crown) below the surface or external pipe diameter). Furthermore, current research results evidently showed the influence of additional phenomena, such as hardening effects and stress redistribution during operation [2]. A new calculation approach for the axial soil reaction was developed in 2015 based on existing test results and numerical simulations [3]. Soil reactions relevant for the design of district heating pipelines are divided into two groups: Axial soil reaction and lateral soil reaction. Since the magnitude of the expected lateral soil reaction is a current research topic [4] the axial soil reaction, which is the skin friction among the perimeter of the pipe, was suggested to be described sufficiently by standard calculation approaches in the last decades. However, major deviations between calculated reactions and measurement of the bearing behaviour of district heating pipes in situ have been reported by engineers quite frequently. Against this background, a new approach for calculating the skin friction was developed taking into account contemporary research results. 2. State of the art The European state of the art for the calculation of pipe skin friction of district heating pipes is defined in EN13941 Ingo Weidlich / Energy Procedia 116 (2017) 365–373 367 Ingo Weidlich /Energy Procedia 00 (2017) 000–000 3 [5]. According to this approach, the skin friction FRis assumed to be proportional to the radial contact pressure around the pipe and may be calculated using equation (1).              −+ + = 2 0 2 ***** 2 1 a BavR D GD k F πγπσµ (1) The term in brackets describes the resulting earth pressure acting on the pipe. However, several other methodologies are available for the calculation of the resulting earth pressure on pipes (e.g Marston [6], Spangler [7], Leonhardt [8]). µis the coefficient of friction according to COULOMB,generally ranging between µ=0.3to 0.4 for normal conditions, cf. according to EN 13941 [5]. Alternatively,equation 2 may be used for the calculation of µ.       == 3 '*2 tantan ϕ δµ (2) Since the internal friction angle ranges between ϕ‘=32° to 40° for sands, equation (2) leads to µ=0.39…0.5. Considering fast movements,µ=0.6 isgiven in [5], which is 1.5-times higher than the value occurring due to normal movement. 3. Initial stress condition Regarding constant geometric boundaries, the initial stress condition after installation depends on the properties of the bedding material. In order to avoid settlements of the surface, a high degree of compactness is usually wanted for the trench backfill. The compactness achieved within the trench influences the unit weight of the soil and the earth pressure coefficient [1]. Thus, an increased coefficient of earth pressure probably occurs and has to be taken into account when calculating the maximum friction force in the sense of a worst case scenario. 4. Stress conditions during operation During initial operation of the pipeline, two main effects have to be taken into account for the description of axial soil reaction: 1. Due to temperature dependent radial expansion ∆rethe normal soil stress increases along the perimeter of the pipe and 2. Temperature driven axial expansion leads to axial pipe movements resulting in a hardening effect due to dilatant soil reaction. Both effects are illustrated in Figure 1. 368 Ingo Weidlich / Energy Procedia 116 (2017) 365–373 4Ingo Weidlich /Energy Procedia 00 (2017) 000–000 Fig. 1. Two major effects during initial operation. The radial pipe-soil interaction was investigated in a two-dimensional numerical model by ACHMUS in 1995 [9]. Axial hardening effects due to dilatancy are known from buried structural components such as piles and anchors. These effects were considered to understand skin friction of district heating pipelines by the author in 2007 [10]. Achmus calculated 1995 typical parameter combinations for sand with different relative densities. As a measure of temperature dependence, the factor κl, was defined: )0( , , )0( , , )100( )100( ur ur avgr avgr lF KTF KT =∆ = =∆ = σ σ κ (3) The results indicated that this factor significantly depends on the relative density of the sand, as well as the overburden height H. Achmus derived equation (4) for the calculation of κlfrom the results (valid for ∆T=100K). For lower ∆T, κlmay be interpolated. rl DmH *22.1][*1.018.1 +−= κ (4) Systematic fundamental investigations on the interacting effects of radial expansion and hardening due to dilatancy are missing. However, few isolated single results exist but an overall evaluation has not been carried out yet. An example for current results is the investigation of HUBER et al. from 2014 [2], which are shown in extracts in Figure 2. Ingo Weidlich / Energy Procedia 116 (2017) 365–373 369 Ingo Weidlich /Energy Procedia 00 (2017) 000–000 5 Fig. 2. Results from HUBER et al. [2]. HUBER et al. observed an increased friction force, represented by κl,Huber=1.5 for a temperature increment of ∆T=50K. Medium dense boundary conditions of the bedding were reported, which is related to Dr≈0.5. After interpolation, equation (4) delivers κl,Achmus=1.36 for ∆T=50K. Thus, experimental 3d-results approximately showed values 10% above the results of the 2d-approach. Values of this magnitude for axial hardening were observed before without temperature load in [11]. Merging the two-dimensional numerical investigations of ACHMUS with the axial hardening effect due to dilatancy, a more realistic approach for the calculation of friction force during initial loading is assumed, see equation (5). rAchmusl R KTR l DmH F F *34.1][*11.030.11.1* , 0, 100, mod, +−=== =∆ κκ (5) Considering repeated thermal loading, the soil contact pressure will decrease due to stress redistribution in the surrounding soil. In present practice, the initial friction force is assumed to drop by 50% simulating the residual state upon cyclic loading according to EN13941 [5]. The actual phenomena of friction degradation were investigated by the author, whereas additional equations describing stresses occurring during operation are given e.g. in [10]. 5. Sensitivity analysis A sensitivity analysis was carried out considering two boundary parameter sets resulting in low and high friction, s. Table 1. A high temperature increment ∆T was used for operation temperatures up to 120°C according to EN13941 [5]. 370 Ingo Weidlich / Energy Procedia 116 (2017) 365–373 6Ingo Weidlich /Energy Procedia 00 (2017) 000–000 Table 1. Parameter set. Parameter Low friction High friction Overburden height H=0.8 m H=0.8 m Nominal Diameter/Outer Diameter DN100/200 DN100/200 Temperature Increment ∆T=100K ∆T=100K Unit weight of soil γ=16kN/m³ γ=20kN/m³ Earth pressure coefficient K=0.5=1-sin(ϕ’=30°) K=1.0 Coefficient of friction µ=0.36=tan(2*(ϕ’=30)/3) µ=0.54=tan(2*(ϕ’=43)/3) Relative density Loose Dense, D r =0.7 Equations (1) (1) and (5) Furthermore, equation (1) was used according to EN13941 representing the lower boundary. In addition, κl,mod was applied for describing the upper boundary. A common single beam static model was used for the sensitivity analysis, which is shown in Figure 3. Fig. 3. Single beam model for DH-pipe. According to equations (6) and (7), the length of the gliding section l0and the maximum displacement umax may be derived for this model. R sT F EAT l *** 0 ∆ = α (6) s R EA lF u2 2 0 max = (7) The results of the calculations are given in table 2. The ratio of high and low friction is 5.41. This difference demonstrates the importance of choosing accurate parameters for the bedding conditions in the field in order to calculate the friction forces occurring correctly. Ingo Weidlich / Energy Procedia 116 (2017) 365–373 371 Ingo Weidlich /Energy Procedia 00 (2017) 000–000 7 Table 2. Results. Results Low friction High friction Ratio High vs. Low Skin friction F R 2.33 kN/m 12.6 kN/m 5.41 Gliding length l 0 137.26 m 25.35 m 0.18 Maximum displacement u max 84.6 mm 15.6 mm 0.18 Basing on the examinations on a future development of the supply flow temperatures for district heating conducted by LUND et al. in 2014 [12], the sensitivity analysis was enhanced for a future scenario according to the temperature development shown in Fig. 4. Fig. 4. Future supply temperature according to [12]. For a fictitious average ambient temperature Ta=20°C, the relevant temperature increment ranges here between ∆T1880=180K and ∆T2050=30K. The results for umax and l0under low friction condition according to Table 1 are given for decreasing ∆T in Fig. 5. 372 Ingo Weidlich / Energy Procedia 116 (2017) 365–373 8Ingo Weidlich /Energy Procedia 00 (2017) 000–000 Fig. 5. Significance of decreasing supply temperature. This simple parametric study for the single beam system shows a significant reduction of maximum displacement and gliding length as well as the related strains and stresses. For a future temperature increment of ∆T=30K only a displacement of 7.1 mm remains which is less than 10% of the displacement for ∆T=100K. 6. Conclusions After a review of scientific results from numerical and experimental investigations, higher values for the friction force during initial temperature loading are expected for dense bedding conditions. Since two soil-mechanical phenomena have been examined independently in the past, a new empirical calculation approach is suggested. A sensitivity analysis is done, applying two boundary parameter sets, showed major discrepancies in friction forces assessing the magnitude of the characteristic designs. However, the presented merged calculation approach for initial skin friction is based only on limited data. Before practical implementation the approach shall be evaluated by field measurements and additional experimental investigations. Finally it must be noted for the suggested future scenarioswith decreasing supply temperatures in district heating networks static engineering and soil-pipe interaction issues may play a minor role in the future. References [1] I. Weidlich, D. Wijewickreme, „Factors influencing soil friction forces on buried pipes used for district heating“ 13th International Symposium on district heating and cooling, Copenhagen September 2012, (2012). [2] M. Huber, D. Wijewickreme, “Thermal Influence on axial pullout resistance of buried district heating pipes”, The 14th International Symposium on District Heating and Cooling, Stockholm, (2014). [3] I. Weidlich, „Zur Reibungskraft bei Inbetriebnahme einer Fernwärmeleitung“, (On the friction force during taking into operation a district heating pipeline), EuroHeat&Power, 44.Jg., Heft 12, Publisher: EW Medien und Kongresse GmbH, Frankfurt am Main, pages: 32-36, (2015). [4] M. Achmus, M. Grehl, “Cyclic lateral soil resistance on district heating pipes”, The 14th International Symposium on District Heating and Cooling, Stockholm, (2014). [5] EN 13941:2010, „Design and installation of preinsulated bonded pipe systems for district heating“, CEN/TC 107, Deutsches Institut für Normung e.V. Normenausschuss Heizund Raumlufttechnik (NHRS), Beuth Verlag, Berlin, (2010). [6] M. Spangler, Stresses in pressure pipe-lines and protective casting pipes. Journal of Structural Engineering (82), pp. 1-33 (1956). Ingo Weidlich / Energy Procedia 116 (2017) 365–373 373 Ingo Weidlich /Energy Procedia 00 (2017) 000–000 9 [7] M.G. Spangler and R.L. Handy, „Soil Engineering“. Harper and Row, Publishers, New York, (1982). [8] G. Leonhardt, „Belastung von starren Rohrleitungen unter Dämmen“ Promotionsschrift, Mitteilungsheft 4, Institut für Grundbau, Bodenmechanik und Energiewasserbau, Universität Hannover, (1973). [9] M. Achmus, Zur Berechnung der Beanspruchungen und Verschiebungen erdverlegter, Fernwärmeleitungen. (On the caclulation of loads and displacements of buried district heating pipelines) Promotionsschrift, Mitteilungsheft 41, Institut für Grundbau, Bodenmechanik und Energiewasserbau, Universität Hannover, (1995). [10] I. Weidlich, Untersuchung zur Reibung an zyklisch axial verschobenen erdverlegten Rohren. (Investigation on the interface friction of cyclic axial displaced buried pipelines) Promotionsschrift 64, Institut für Grundbau, Bodenmechanik und Energiewasserbau, Leibniz Universität Hannover (2008). [11] D. Wijewickreme, H., Karimian and D. Honegger,, “Response of Buried Steel Pipelines Subject to Relative Axial Soil Movement”, Canadian Geotechnical Journal, Vol. 46, No. 7, pp. 735-752, (2009). [12] Lund H., Werner S., Wilthire R., Svendsen S., Thorsen J.E., Hvelplund F., Mathiesen B.V., “4th Generation District Heating (4GDH) Integrating smart thermal grids into future sustainable energy systems”, Energy 68, 1-11, Elsevier. (2014).