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Innovative Infrastructure Solutions
, Volume 5 (3) – Jun 24, 2020

/lp/springer-journals/numerical-investigation-on-rigid-and-flexible-pipelines-embedded-in-GjpBctzxtS

- Publisher
- Springer Journals
- Copyright
- Copyright © The Author(s) 2020
- ISSN
- 2364-4176
- eISSN
- 2364-4184
- DOI
- 10.1007/s41062-020-00320-z
- Publisher site
- See Article on Publisher Site

Self-compacting filling material or controlled low-strength material (CLSM) is a cementitious material which is liquid during filling, and it is used primarily as backfill, e.g., in trenches. Several products are currently used as CLSM such as flowable fill, controlled density fill, flowable mortar and low-strength plastic soil–cement. The low-strength requirement is necessary to allow for future excavation of CLSM. A two-dimensional numerical model was developed using the finite element system ABAQUS. In this model, the material behavior of granular soil and CLSM is described using an elasto-plastic constitutive model with Mohr–Coulomb failure criterion. Rigid and flexible pipes were modeled once embedded in sandy soil and once embedded in self-compacting material. The numerical model allows the modeling of the effect of hardening process on the overall behavior of the pipe–soil system. The main objective of this study is to investigate the behavior of rigid and flexible pipelines embedded in CLSM as a filling material numerically and to show advantages and disadvantages in comparison with the presently widely used filling materials like sand. Keywords Self-compacting material (CLSM) · Finite element method · Mohr–Coulomb material model · Hardening process · Pipelines Introduction water, cement, fly ash or other similar products and fine or coarse aggregates or both. Selection of materials should be Controlled low-strength material (CLSM) is a self-com- based on availability, cost, specific application and the nec- pacted cementitious material used primarily as a backfill essary characteristics of the mixture, including flowability, as an alternative to compacted fill. CLSM should not be strength, excavatability and density. considered as a type of low-strength concrete, but rather The main purpose of the investigations presented here is a self-compacted material with features similar to soil. At the comparison of bending moments of rigid and flexible some sites, the use of self-compacting materials has proven pipes in sand or CLSM, taking the effect of hardening of to be beneficial in providing adequate support to flexible CLSM into account. structures, especially in tight spaces where placement and compaction of more traditional backfill material would be problematic. Challenging situations such as placing bedding Previous investigations on behavior under haunches and backfilling between closely spaced par - of buried pipelines allel structures can be simplified or enhanced by using self- compacting materials. CLSM is a self-compacted, cementitious material, which The most common materials used are either open-graded, was widely known as flowable fill until American Concrete angular aggregates or specially proportioned cementitious Institute Committee 229 documented its name as CLSM mixtures. Conventional CLSM mixtures usually consist of [2]. The CLSM is primarily used as a backfill material in lieu of compacted backfill and has become a popular mate- rial for projects such as void fill, foundation support, bridge * Khalid Abdel-Rahman approaches and conduit bedding [8]. CLSM, with different Khalid@igth.uni-hannover.de additives such as cement and fly ash, has been demonstrated, Institute for Geotechnical Engineering, Leibniz University by many researchers, to be an effective bedding material for of Hannover, Appelstr 9A, 30167 Hannover, Germany Vol.:(0123456789) 1 3 69 Page 2 of 10 Innovative Infrastructure Solutions (2020) 5:69 pipelines due to the self-compacting behavior and strength done taking the hardening process and shrinkage of self- hardening [5, 10]. compacting material into consideration. Although several studies were conducted on the analysis Summarizing, only a limited number of investigations of buried pipes using soil–pipe interaction theories (e.g., [9, exist. In none of these studies, the effect of hardening pro- 12] a limited number of investigations have explored the per- cess of self-compacting materials in the numerical mod- formance of pipes buried in controlled low-strength material eling has been considered. (CLSM) by numerical simulation. McGrath [9] made a study on the pipe–soil interaction during backfilling. Diverse backfilling materials were used at varying compaction levels. Several soil box tests and field Properties of self‑compacting materials tests were conducted on steel, concrete and plastic pipes to compare the results for the different backfilling materials, The properties of CLSM cross the boundaries between trench conditions and bedding materials. Suleiman et al. [12] soils and concrete. CLSM is manufactured from materials investigated the effects of large deflection behavior on bur - similar to those used to produce concrete and is placed ied plastic pipes. This study compared the small deflection from equipment in a fashion similar to that of concrete. analysis theory results by using culvert analysis and design The properties of CLSM are affected by the constituents (CANDE) software with the large deflection analysis theory. of the mixture and the proportions of the ingredients in Zhang et al. [14] developed a kinematic hardening model the mixture. In the following, the main features will be for pipeline–soil interactions under various loading condi- explained briefly. tions, and they conducted experimental tests using calcare- ous sandy soil. The developed hardening model required 13 different material parameters. Tian and Cassidy [13] Hardening process modified the model developed by Zhang et al. [14] and intro- duced three plasticity models that could be used to simulate One of the most important aspects for CLSM is the hard- pipe–soil interactions numerically. Further study should be ening process which describes the dependency of E-mod- conducted to show the efficiency of the developed model ulus and Poisson’s ratio ( ) on time. Figure 1 shows the by Tian and Cassidy [13] on buried steel pipes in different development of E-modulus of CLSM with time. In the first trench conditions. days, the E-modulus is very small almost 10.0 MPA, then Different CLSM materials were investigated experimen- it increases gradually to reach 80.0 MPA after 7 days and tally and numerically by Arsic [3]. He investigated standard finally 80.0 MPA after 28 days (4 weeks), and it remains filling materials and CLSM materials in (1:1) experimen - almost constant. Simultaneously, the Poisson’s ratio ( ) tal model. Then, a numerical model using ABAQUS was decreases from 0.48 (CLSM behaves like a fluid) at the developed to predict the behavior of pipelines embedded starting point of hardening and decreases gradually to in CLSM for different trench dimensions. Based on his reach after 7 days 0.12; then, it increases slightly to its results, the pipeline regulations were adopted and modified final value 0.20 which corresponds to the solid state mate- for CLSM. rials like concrete. The dependency of these parameters Bellaver [4] developed a three-dimensional (3D) nonlin- [E-modulus and Poisson’s ratio ( )] will be implemented ear finite element model of steel pipe coupled with CLSM via a subroutine for the numerical modeling of CLSM. and compacted soil. The finite element model consisted of the pipe and soil interaction during the staged construction of embedment and backfill. The numerical model was used to predict pipe performance under varying backfill and load- ing conditions. Staged construction modeling of steel pipes buried in CLSM was investigated by Dezfooli et al. [7]. The results of field tests were compared with 3D nonlinear numeri- cal model. The comparison of the results indicates that the finite element model is capable of predicting the deflection of the buried steel pipes in different backfilling and trench configurations. Abdel-Rahman et al. [ 1] developed FEM using ABAQUS to simulate the behavior of pipelines embed- ded in self-compaction materials. The computations were Fig. 1 Dependency of E-modulus and Poisson’s ratio ( ) on time [3] 1 3 Innovative Infrastructure Solutions (2020) 5:69 Page 3 of 10 69 typically has a very high water–cement ratio and water con- Shear strength tent that may cause after drying shrinkage. Based on our experimental investigations [6], the shrinkage of CLSM was Since engineering applications of CLSM as a substitute to conventional compacted fill are growing, it is getting more about to 0.1% till 0.3%. Some shrinkage cracks may appear after the hardening important to measure the shear strength parameters for CLSM properties either direct measurement or by develop- process. However, they do not affect the structural integrity of the material for most applications and were not consid- ing correlations between geotechnical testing results. The shear strength properties of CLSM are important and can ered in the presented numerical modeling. be measured using both a direct shear test and a triaxial shear apparatus. Controlled low-strength materials (CLSMs) considered in the numerical investigations have an internal Finite element modeling friction angle ranging from 30.0° to 40.0° degrees and the cohesion ranging from 60.0 up to 90.0 kN/m after the hard- For the investigation of the behavior of pipelines embedded ening process of 28 days [3]. in sand and self-compacting materials, a two-dimensional (2D) numerical model was developed. The finite element Flowability program ABAQUS [11] was used for the numerical analysis. Flowability is very important property which guarantees the construction process of CLSM. It is the property that distin- Numerical model guishes CLSM from other fill materials. It enables the mate- rials to be self-leveling; to flow into and readily fill a void; A two-dimensional (2D-plane strain) finite element model and be self-compacting without the need for conventional was developed. The main aim was to calculate the vertical compacting equipment. This property represents a major and horizontal deformation of the soil and to investigate the advantage of controlled low-strength materials compared deformation response (bending moment) of a pipe with a with the conventional fill materials that must be mechani- diameter of 0.30 m once embedded in sandy soil and once cally placed in layers and compacted using different compac- embedded in self-compacting material. The dimensions of tion equipments. the numerical model used in the analysis are shown in Fig. 2. The elements used to model the soil and CLSM are six- Shrinkage process noded and eight-noded plane strain (CPE6 and CPE8) ele- ments, while beam elements (B22) have been used to simu- The shrinkage of controlled low-strength materials (CLSM) late the pipelines to be able to calculate the bending moment is a very critical aspect. Compared to concrete, CLSM in the pipelines (Fig. 3). In this study, the embedment depth Fig. 2 Dimensions of the numerical model 1 3 69 Page 4 of 10 Innovative Infrastructure Solutions (2020) 5:69 Fig. 3 Finite element mesh (trench is red marked) (h) was set 1.0 m and the trench width (b) was chosen to be trench (Fig. 4). For each part, different soil properties should 0.90 m. be adopted according to the investigated problem. The dimension of the numerical model was varied by The material properties adopted for the subsoil outside different trails, and we came finally to the conclusion that the trench (part E and E ) were varied to investigate their 3 4 the numerical model should be extended horizontally from effect on the behavior of the pipelines embedded in CLSM both sides min. four times the excavation width (3.60 m) and (Table 1). These parameters have a negligible effect on the should also be extended vertically beneath the pipe min. the pipelines. double of the excavation width (1.80 m). The final overall In the case of sandy soil, for the elastic region of dimension of the numerical model was set to 9.30 m*3.20 m. Mohr–Coulomb material model, E-modulus and Poisson’s With these model dimensions, the calculated behavior of ratio are required. For the plastic region, the internal angle the pipe is anticipated to be not affected by the boundary of internal friction (φ′), angle of dilatation (ψ) and cohe- conditions. sion (c) will be implemented (Table 1). The following table To investigate the mesh dependency, different mesh summarizes the main material parameters required for the designs (coarse, medium and fine) were adopted until the different parts. final mesh (no. of elements = 39,574, no. of nodes = 119,347 Regarding controlled low-strength material (CLSM), the and DOFs = 237,122) presented in Fig. 3 was used for the time dependency for both E-modulus and Poisson’s ratio is following investigations. The main purpose was to eliminate implemented as shown in Fig. 1, whereby for simplicity rea- any mesh dependency of the obtained results. sons the other material parameters (internal angle of friction, angle of dilatation and cohesion) required for Mohr–Cou- Constitutive model lomb model are kept constant and are listed in Table 2. In order to investigate the effect of pipe stiffness on the One of the most important issues in geotechnical numerical overall behavior, two different pipe materials will be modeled modeling is the choice of the suitable constitutive material in this paper. The first one is a rigid pipe made of concrete and model which represents the stress–strain behavior of the investigated material. An elasto-plastic material law with Mohr–Coulomb failure criterion was used to describe the behavior of the sandy soil and also the behavior of the self- compacting materials. Mohr–Coulomb constitutive model is not a sophisticated material model with the same stiff - ness for loading and reloading paths, but for the planned investigation, Mohr–Coulomb is sufficient enough as one of the important aspects is the hardening process of CLSM, which was implemented in the numerical model, and also, the modeling procedure is monotonic without unloading or reloading stages. According to the pipeline regulations, the pipe trench should be divided into four parts: E above the pipeline, E around the pipeline in the trench, E the soil outside 2 3 the trench and E the soil part beneath the pipe outside the Fig. 4 Pipeline and the different trench parts (E , E , E and E ) 1 2 3 4 1 3 Innovative Infrastructure Solutions (2020) 5:69 Page 5 of 10 69 Table 1 Material properties for 3 2 Zone (kN/m ) E (MPa) (–) C′ (kN/m ) (°) (°) the filling sandy material E 18.0 30.0 0.25 1.0 30.0 1.0 E 18.0 25.0 0.25 1.0 30.0 1.0 E 18.0 50.0 0.25 1.0 35.0 5.0 E 18.0 80.0 0.25 1.0 40.0 10.0 Table 2 Material properties for the filling CLSM executed stepwise. Firstly, the primary stress state under the own weight of the lower soil medium located beneath the pipe- Unit weight 18.0 (kN/m ) line (E ) is generated. In the subsequent steps, different soil Internal friction angle 35.0° layers are activated to simulate the construction steps (Fig. 5). Dilatation angle 5.0° In the following step, both sides of the trench (E ) will Cohesion c 80 (kN/m ) be activated by putting horizontal boundary conditions on the vertical sides to secure the stability of the trench before filling. Consequently, the pipeline is embedded in the middle the second one is a flexible PVC pipe. Table 3 summarizes part (E ) and the contact pairs (CP1 and CP2) will be acti- vated. This step represents the first stage of the trench filling the main material properties [3] adopted for the numerical modeling: around the pipe. Then, the upper part (E ) in the trench will be added with the corresponding contact pair (CP2) between Contact behavior the trench and the surrounding soil. Finally, the vertical sur- charge (p = 30 kN/m ) is applied on the top surface of the To describe the behavior of the embedded pipes accurately, model as traffic load. For the pipelines embedded in self-compacting material two die ff rent contact pairs are adopted in the numerical model. The first contact pair (CP1) describes the contact behavior (CLSM), more steps are required in order to simulate the between the pipe and the surrounding soil in the trench. The second contact pair (CP2) is implemented to simulate the ver- tical sliding between the excavation part (trench) and the sur- rounding soil on both sides of the trench (Fig. 5). This contact pair (CP2) is essential to predict the behavior of the filling material in the trench compared to the surround soil. For both of the contact pairs, an elasto-plastic contact model was used. For this contact model, the maximum frictional shear stress is calculated from the normal stress and the friction coefficient on the sliding surface. For the first contact pair (CP1), the friction coefficient μ = 0.431 (μ = tan (2/3φ)) was adopted, while for the second contact pair (CP2) the friction coefficient μ = 0.70 (μ = tan (φ)) was implemented. For full mobilization of the limit frictional stress, the relative displacement (elas- tic slip) between the pile and the surrounding soil was set to Δu = 2.0 mm. el,slip Numerical modeling procedure The modeling process for the pipes embedded in sandy soil should reflect the construction process in reality, which is very complicated. The modeling process will be simplified and Fig. 5 Steps of the numerical modeling Table 3 Material properties for 3 Material (kN/m ) E (MPa) G (MPa) (–) D (m) Thickness (m) different pipeline materials Concrete 24.0 31,000.0 12,900.0 0.2 0.3 0.04 PVC-U 14.0 2250.0 833.0 0.35 0.3 0.01 1 3 69 Page 6 of 10 Innovative Infrastructure Solutions (2020) 5:69 hardening process taking the dependency of Elastic mod- ulus (E) and Poisson ratio ( ) (Fig. 1) into consideration. Here, two more steps are added to describe the behavior self-compacting material (CLSM) after 7 days and 28 days before applying finally the vertical surcharge on the top on the model (p = 30 kN/m ). This modeling procedure is different compared to the trench excavation, but this concept simplifies the numerical modeling and gives very reasonable results for comparison reasons between conventional filling materials and self- compacting materials (CLSM). Numerical modeling results Fig. 7 Bending moment around rigid pipeline embedded in sand (p = 30.0 kN/m ) The numerical modeling deals with the behavior of rigid and flexible pipes embedded in granular material and in self- 0.26 kNm/m at 90°. In the lower half of the pipe from 90° up compacting material “CLSM” taking the effect of harden- ing process into consideration. The vertical soil deformation 180°, we have a similar bending moment distribution but the maximum value reaches finally 0.32 kNm/m at the bottom. and embedded pipe behavior including the vertical stress, horizontal stress and bending moments will be presented This distribution indicates that the pipe was compressed in the vertical direction and extended in the horizontal direc- and evaluated. tion which is a typical behavior for pipeline embedded in the sandy soil. Concrete pipe embedded in sand Concrete pipe embedded in CLSM Figure 6 shows the vertical soil deformation (U2) in the last step after applying the surcharge (p = 30.0 kN/m ). In case of self-compacting material, a similar distribution of The maximum settlement reaches almost 2.40 mm at the ground surface, whereby in the trench due to the concrete vertical displacement in the numerical model was obtained (Fig. 8). The maximum settlement at the ground surface pipe the settlement is about 1.80 mm. Also, there is a rela- tive displacement along CP2 between the soil domain and reaches 2.20 mm, and in the trench, the vertical deformation of 1.1 mm was obtained which is lower than the sandy soil. the trench. In order to investigate the deformation response of the This is due to the hardening process of the CLSM, which leads to higher stiffness modulus compared to the sand. pipeline, the bending moment around the pipeline embedded in sand after applying the surcharge loading (p = 30.0 kN/ The bending moment in the pipeline is based on the change in the vertical and horizontal contact stress acting m ) is presented in Fig. 7. The x-axis shows the angle meas- ure from the crown (zero at the pipe top, 90° at the hori- on the pipeline due to the hardening process of CLSM. This is explained firstly in detail. zontal pipeline axis and 180° at the bottom of the pipeline). The bending moment in the pipe at the crown is Figures 9 and 10 show the distribution of contact stress (normal and shear stress) between the pipeline and the 0.22 kNm/m, decreases gradually to zero by almost 45.0° measured from the crown and then increases up to surrounding soil “CLSM” projected vertically to give the Fig. 6 Vertical displacement distribution in the soil domain 1 3 Innovative Infrastructure Solutions (2020) 5:69 Page 7 of 10 69 Fig. 8 Vertical displacement distribution in the soil domain Fig. 11 Bending moment around rigid pipeline embedded in CLSM Fig. 9 Vertical stress around rigid pipeline embedded in CLSM hardening process due the change in the material properties (increase in the soil stiffness and decrease in the Poisson’s ratio). By applying the traffic load of 30.0 kN/m , the verti- cal stress reaches a maximum value of 61.0 kN/m at the top. Figure 10 shows the horizontal stress component pro- jected along the diameter of the pipeline (D = 0.30 m). At the crown and the bottom of the pipe, the horizontal stress component is equal to zero as the main stress component is the vertical stress (Fig. 9). Then, the horizontal stress increases gradually to reach its maximum value at almost an angle of 45.0° measured from the vertical axis. As before, in the first 2 weeks there is redistribution of the horizontal stress acting on the pipe and it decreases at 90.0° from 8.0 to 4.5 kN/m . Then, by applying the traffic loading, the horizontal stress compo- nent reaches 21.0 kN/m at almost 45.0° and then reduces Fig. 10 Horizontal stress around rigid pipeline embedded in CLSM to 8.50 kN/m at 90.0°. These two previous figures will help us to derive the vertical stress component (Fig. 9) and horizontally to give bending moment around the pipeline. The bending moment the horizontal stress component acting on the pipe (Fig. 10). distribution is shown in Fig. 11. The vertical stress distribution as shown in Fig. 9 has its In the first days up to 14 days, the bending moment is maximum value on the vertical (symmetry axis) of the pipe small (ca. 0.05 kNm/m) and almost constant around the and the minimum value at the end of pipe (x = radius of the pipe line. With the hardening process and the application of pipe = 0.15 m). In the first 2 weeks, there is a redistribu - the surcharge (p = 30.0 kN/m ), the pipe will be deformed tion of the vertical stress and it decreases slightly with the (Fig. 8) and consequently the bending moment increases 1 3 69 Page 8 of 10 Innovative Infrastructure Solutions (2020) 5:69 up to a maximum value of 0.21 kNm/m at the crown, in the middle and at the bottom. These values are smaller than in the case of sandy soil. This can be explained as the CLSM has a higher stiffness than the sand and therefore a less pipe deformation, which leads to a smaller bending moment in the pipeline. Flexible pipe embedded in sand For comparison reasons, a flexible pipe (PVC-U) was also modeled. Figure 12 shows the vertical soil deformation (U2) in the last step. The maximum settlement reaches almost 2.40 mm at the ground surface, whereby in the trench due to the flexible pipe the settlement is about 2.0 mm. These Fig. 13 Bending moment around flexible pipeline embedded in sand values are little bit higher than the previous case (rigid pipe) (p = 30.0 kN/m ) as the flexile pipe has a smaller stiffness than the rigid one. The bending moment around flexible pipeline embedded pipe has as a smaller stiffness than the rigid one, this leads in sand after applying the surcharge loading (p = 30.0 kN/ m ) is presented in Fig. 13. As the flexible pipe was com- to higher settlement compared to the rigid pipe (Fig. 8). Figures 15 and 16 show the distribution of contact pressed in the vertical direction and extended in the hori- zontal direction, a similar bending moment distribution to stress between the pipe and the surrounding soil “CLSM” projected vertically to give the vertical stress component the rigid pipeline will be obtained. The bending moment in the pipe at the crown is 0.21 kNm/m and decreases gradu- and horizontally to give the horizontal stress component acting along the flexible pipeline. ally to zero by almost 45.0° measured from the crown and then increases up to 0.22 kNm/m at 90°. In the lower half Similar as before, the vertical stress distribution (Fig. 15) has its maximum value on the vertical (symmetry of the pipe from 90° up 180°, we have a similar bending moment distribution but the maximum value reaches finally axis) of the pipe and the minimum value at the end of pipe (x = radius of the pipe = 0.15 m). In the first 2 weeks, there 0.29 kNm/m at the bottom. The higher values are located at the crown, at the hori- is a slight decrease in the vertical stress and the maximum value reached is 18.0 kN/m . Under the traffic loading, the zontal axis of the pipe line and at the bottom of the pipe line. These values are smaller than the previous case (rigid maximum value at the piper vertical axis is 48.0 kN/m . These values are smaller than the previous rigid pipeline. pipeline), as the stiffness of flexible pipe is lower than the stiffness of the rigid pipe (Table 3). Figure 16 shows the horizontal stress component drawn along the diameter of the pipeline (D = 0.30 m). Dur ing Flexible pipe embedded in CLSM the hardening process, the horizontal stress component deceases by about 11% in the first 8 days. By apply- In case of self-compacting material, a similar distribu- ing the vertical surcharge, the horizontal stress compo- nent increases gradually to reach its maximum value of tion of vertical displacement in the numerical model was 2 2 obtained (Fig. 14). The maximum settlement at the ground 18.0 kN/m at 45.0° and then reduces to 11.0 kN/m at 90.0°. These values are smaller compared to the other val- surface reaches 2.20 mm, and in the trench, a vertical deformation almost 1.50 mm was obtained. As the flexible ues obtained by rigid pipe. Fig. 12 Vertical displacement distribution in the soil domain 1 3 Innovative Infrastructure Solutions (2020) 5:69 Page 9 of 10 69 Fig. 14 Vertical displacement distribution in the soil domain Fig. 17 Bending moment distribution for flexible pipeline embedded in CLSM Fig. 15 Vertical stress around flexible pipeline embedded in CLSM moment increases up to 0.17 kNm/m, which is lower than the previous case (rigid pipe) and also lower than the embed- ded case in sandy soil. Finally, these results show that the hardening of self-compacting materials (CLSMs) affect pos- itively the behavior of rigid as well as the flexible pipelines. Conclusions For the investigations presented, a FEM was developed to simulate the behavior of pipelines embedded in sandy soil and in self-compaction materials. The computations were executed taking the hardening process of self-compaction material into consideration. It is evident for the investigated Fig. 16 Horizontal stress around flexible pipeline embedded in case that the bending moments are smaller and the overall CLSM behavior is therefore better than by the use of the standard filling material. Also the hardening process of the CLSM Finally, the bending moment distribution is shown in has a minor effect on the vertical stress and horizontal stress Fig. 17. Similar to the rigid pipe, up to 14 days, the horizon- components. Another advantage is the reduced quality of tal and the vertical stress are similar, which means that the compaction below and beneath the pipe in usual fill materi- bending moment is relatively small and constant all around als. In subsequent investigations, further parametric studies the pipe. With the hardening process and the application will be carried out for different trench widths and embed- of the vertical surcharge stress (30.0 kN/m ), the bending ment depths. 1 3 69 Page 10 of 10 Innovative Infrastructure Solutions (2020) 5:69 Acknowledgements Open Access funding provided by Projekt DEAL. 5. Boschert J, Butler J (2013) CLSM as pipe bedding: computing predicted load using the modified Marston equation. ASCE Pipe- lines 2013:1201–1212 Open Access This article is licensed under a Creative Commons Attri- 6. Buhr F (2015) Untersuchung zur Schwind-bzw. Schrumpfneigung bution 4.0 International License, which permits use, sharing, adapta- von Flüssigböden im Zuge der Erhärtung. Bachelor thesis, IGtH, tion, distribution and reproduction in any medium or format, as long Hannover (unpublished) (in German) as you give appropriate credit to the original author(s) and the source, 7. Dezfooli M, Abolmaali A, Park Y, Bellaver F (2015) Staged con- provide a link to the Creative Commons licence, and indicate if changes struction modeling of steel pipes buried in CLSM using 3D non- were made. The images or other third party material in this article are linear finite-element analysis. Int J Geomech 15(6):1–13 included in the article’s Creative Commons licence, unless indicated 8. Folliard KJ, Trejo D, Sabol SA, Leshchinsky D (2008) Develop- otherwise in a credit line to the material. If material is not included in ment of a recommended practice for use of controlled low-strength the article’s Creative Commons licence and your intended use is not material in highway construction, NCHRP 597 report, pp 5–39 permitted by statutory regulation or exceeds the permitted use, you will 9. McGrath TJ (1998) Pipe–soil interactions during backfill place- need to obtain permission directly from the copyright holder. To view a ment. Ph.D. dissertation, University of Massachusetts, Amherst, copy of this licence, visit http://creativ ecommons .or g/licenses/b y/4.0/. MA 10. Rajah S, McCabe M, Plattsmier J (2012) Classification and speci- fication of bedding and backfill for buried pipelines. In: ASCE References pipelines 2012: innovations in design, construction and mainte- nance, pp 940–951 11. Simulia (2018) User’s manual, version 6.18. Simulia, Providence, 1. Abdel-Rahman K, Achmus M, Gerlach T (2017) Behavior of pipe- RI, USA lines embedded in self-compactions materials under traffic loads. 12. Suleiman MT, Lohnes RA, Wipf TJ, Klaiber FW (2002) Analysis In: International conference GeoMEast, Sharm El-Sheikh, Egypt, of deeply buried flexible pipes. Transp Res Rec 1849:124–133 July 15–19, 2017 13. Tian Y, Cassidy MJ (2008) Modeling of pipe–soil interaction and 2. American Concrete Institute (1994) Committee 229, Controlled its application in numerical simulation. Int J Geomech (ASCE) low-strength materials (CLSM). ACI 229R-94 report 4(8):213–229 3. Arsic Igor (2009) Über die Bettung von Rohrleitungen in Flüssig- 14. Zhang J, Stewart DP, Randolph MF (2002) Kinematic hardening böden. Institute for Soil Mechanics and Geotechnical Engineering, model for pipeline–soil interaction under various loading condi- University of Bochum, Germany (in German) tions. Int J Geomech (ASCE) 4(2):419–446 4. Bellaver F (2013) Large diameter steel pipe field test using con- trolled low-strength material and staged construction modeling using 3-D nonlinear finite element analysis. M.Sc. thesis, Univer - sity of Texas at Arlington, Arlington, TX 1 3

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