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Three-dimensional numerical study of the reactive powder concrete segments in tunnel lining

Three-dimensional numerical study of the reactive powder concrete segments in tunnel lining Curved and Layer. Struct. 2022; 9:286–294 Research Article Hajer Satih Abbas*, Maadh Imad Salman Al-Rubaye, Sarra’a Dhiya’a Jaafer, Bassam farman bassam, and Abdelmajeed Alkasassbeh Three-dimensional numerical study of the reactive powder concrete segments in tunnel lining https://doi.org/10.1515/cls-2022-0022 compared to the conventional in-situ lining appraoch [1–3]. Received Nov 18, 2021; accepted Feb 21, 2022 In general, precast concrete tunnel lining (PCTL) segments are planned for more than 100 years of service life [4] with Abstract: The tunnel lining systems act as lines of defence reinforced concrete (RC). Hence, several cases suffered from against the forces and geotechnical situations. The use of the premature deterioration prior to gaining their service precast concrete tunnel linings (PCTLs) has been escalat- life. It was basically assigned to the corrosion caused by ing due to its effective and economical installation process. chloride infiltration [5–7]. The tunnels usually suffer from the premature deteriora- The Reactive Powder Concrete (RPC) is the ultra-high tion due to corrosion of the reinforcement and thus need strength and ductile concrete prepared by replacing the maintenance. Corrosion leads to the distress in PCTL lead- standard aggregate with quartz powder, silica fume and ing to the cracking and finally the scaling of concrete. This steel fibers [ 8]. The concrete does not comprise coarse ag- study aims to assess the structural durability performance gregates, but involves cement, silica foam, sand, powdered of reactive powder concrete (RPC) as the material of tunnel quartz, superplasticizer, and steel fiber. Avoiding the inclu- lining segments compared to reinforced concrete (RC) and sion of coarse aggregates by the inventors is a significant high performance concrete (HPC). The numerical findings aspect of the microstructure and function of RPC which indicated that the maximum load capacity of PRC-PCTL seg- decreases the heterogeneity in mortar and aggregate mix. ments was greater than that of the corresponding RC and The additives, lack of coarse aggregates, small water-to- HPC segments. Regarding the findings, PRC is a very signif- cement ratio, fine steel fibers, heat treatment, and com- icant option for conventional segments. The high strength pression before and after setting are the RPC’s fundamen- of PRC can decrease the thickness of the PCTL segments, tal features [9–14]. The compressive RPC strength is in the resulting in the decreased material cost. Also, PRC-PCTL 200–800 MPa range, its flexural strength is from 30 to 50 segments can eliminate the laborious and costly produc- MPa, and its Young’s modulus around 50–60 GPa [15–19]. tion of RC segments and mitigate the corrosion damage and Because of RPC’s durability and excellent mechani proper- thus enhance the service life of lining segments. ties, its utilizations are expanded. RPC structural elements Keywords: reactive powder voncrete; corrosion, high com- are resistant against chemical attack, impact loads (with pressive strength; finite-element model; tunnel segment. collision with vehicles and vessels), and sudden kinetic loads based on the earthquakes. Made up of compact and ordered hydrates, RPC is basically characterized by high performance. The microstructure is optimized by accurate 1 Introduction particle gradation to maximize density. RPC heavily relies on the pozzolanic features of the washed silica foam and The use of precast concrete tunnel segments in the projects the optimizing cement concrete to gain the maximum hy- has creased due to its effective and economical utilization drate [20–27]. Thus, PRC can be proven to be a more long- lasting material for precast concrete tunnel lining construc- tion. Besides to enhancing the mechanical and durability *Corresponding Author: Hajer Satih Abbas: Civil Engineering features, the replacement of reinforcement with PRC in tun- department, Al-Esraa university college, Baghdad, Iraq; Email: nel segments can delete the laborious and costly construc- dr.hajer@esraa.edu.iq tion of tunnel segments. Moreover, PRC lining segments’ Maadh Imad Salman Al-Rubaye, Sarra’a Dhiya’a Jaafer, Bassam cross-sectional dimensions can be decreased due to their farman bassam: Civil Engineering department, Al-Esraa university high strength, leading to economical fabrication. Multiple college, Baghdad, Iraq Abdelmajeed Alkasassbeh: Civil engineering department, Faculty research investigated the flexural capacity of conventional of Engineering, Al al-Bayt University, Mafraq 25113, Jordan Open Access. © 2022 H. Satih Abbas et al., published by De Gruyter. This work is licensed under the Creative Commons Attribution 4.0 License Three-dimensional numerical study of the reactive powder concrete segments in tunnel lining | 287 Table 1: Mechanical properties of RPC vs. HPC RC tunnel segments [28–33]. The corrosion deterioration of conventional RC-PCTL has resulted in developing the reac- SPECIFICATIONS HPC RPC tive powder concrete (PRC) tunnel lining segments. Hence, Compression capacity (MPa) 85~100 200~800 the present research obtains an evaluation of the mechan- Flexural capacity (MPa) 6~8 45-60 ical behaviour of reactive powder concrete (RPC) tunnel Modulus of elasticity (GPa) 35~40 70 lining segments. This study aims to assess the structural Fracture toughness (J/m ) <1000 30000 and durability function of reactive powder concrete (RPC) tunnel lining segments compared to reinforced concrete (RC) and high performance concrete (HPC). Furthermore, Table 2: The durability of RPC vs. HPC finite element analysis using ABAQUS was conducted in Characteristic Value order to verify the experimental behaviour and comparison of the performance of RPC with RC and HPC tunnel lining Wear 2~2.5 times less segments was presented in this study. Absorption of water 6.5~7.5 times less Rate of corrosion 7~8.5 times less Diffusion of chloride ions 20~30 times less 2 RPC in comparison with HPC 3 Numerical verification A comparison between mechanical and durability proper- ties of the RPC and (high performance concrete) HPC shows The finite-element software, ABAQUS [ 36] was applied for the RPC to offer a higher compressive strength and a perme- model verification, contrasting the findings with the exper- ability lower than the HPC. The HPC is a product of novel imental surveys of Abbas [37]. concrete science, which uses additives and scientific tech- niques to control the concrete’s microstructure [34, 35]. Owing to its microstructure, the HPC has achieved its 3.1 Model geometry maximum compressive strength. Nonetheless, at any given strength, coarse aggregates are the weakest links in the Figure 1 illustrates the model geometry, and the meshed concrete structure. The only remaining solution to further model is presented in Figure 2. The model was meshed increase the compression strength of the concrete is to re- using square elements with a length-to-width ratio of 1, as move coarse aggregates, which is the same approach that it has been suggested that they produce the best results has been adopted in developing the RPC. Table 1 compares the mechanical properties of the typical RPC with a regu- lar HPC with an 80 MPa compressive strength. The higher fracture toughn of the RPC is suggestive of its better duc- tility. Aside from the mechanical properties, RPCs have an exceptionally dense microstructure that makes them im- permeable to water and durable. Thanks to its low porosity and permeability, restricted contraction, and high corrosion resistance, the RPC of- fers remarkable durability. Compared to the HPC, the RPC passes no liquid or gas through. The RPC specifications listed under Table 2 enable it to be used in aggressive chem- ical environments and applications where other types of concrete do not last long due to wear and tear. Results in- dicate that RC and HPC concretes are more vulnerable to corrosion problem compared with RPC concrete. Figure 1: 2D model geometry 288 | H. Satih Abbas et al. Figure 5: Numerical boundary conditions in the upper part of the segment A critical parameter in the finite-element techniques is the solution time and complexity, which depend on the shape and number of elements. In light of the above discus- sions, different types of mesh were used in modeling the studied tunnel segment. It was found that similarly accept- able results are obtained by using 50 and 25 mm elements. Therefore, the 50 mm elements were used for the shorter analysis time (Figure 6). Figure 2: Meshed 2D model in the finite-element method. The eight-node linear brick element C3D8R was used for modeling (Figure 2). 3.2 Model boundary conditions As depicted in Figure 3, support conditions were defined for the model by fixing the model in the vertical direction (Figure 4) at the points where the segment is in contact with two bottom frames (reaction). Further, a vertical down- ward velocity was defined for the upper part of the segment (Figure 5) for flexural loading. Figure 6: Load-displacement curve of the model with two mesh sizes 3.3 Result validation The current numerical ABAQUS [36] model (Figure 6) was Figure 3: Experimental boundary conditions in the lower part of the contrasted with the load-displacement curve of the flexu- segment Abbas [37] ral test in the work of Abbas [37] (Figure 7) at the point of loading for validation. The two curves are plotted on the same graph in Figure 8 for a better comparison. Comparing two curves indicate the consistency of this study’s findings with those of Abbas [37]. Figure 4: Numerical boundary conditions in the lower part of the segment Three-dimensional numerical study of the reactive powder concrete segments in tunnel lining | 289 Figure 7: Load-displacement curve from flexural testing Abbas [37] Figure 8: A comparison of the load-displacement curves Table 3: The details of developed models Figure 9: Model geometry Model no. Lining Tunnel Tunnel type overhead-side overhead-top 4.1 Model geometry and meshing (kPa) (kPa) T0 RPC 25 20 Figure 9 illustrates the model geometry, and the meshed T1 UHPC 25 20 model is presented in Figure 10. The model comprises six T2 HPC 25 20 layers of three different materials. The model was meshed T3 RC 25 20 considering the two following points: First, square ele- ments (with a length-to-width ratio of 1) were used for mesh- ing, as they have been recommended for producing the best 4 Optimizing the tunnel segments results in the finite-element method. Second, a finer mesh with RPC was used for the tunnel due to the considerable displace- ment and stress concentration (Figure 11). On the other In this section, the impact of incorporating the RPC in the hand, a smaller element with finer mesh will be closer to tunnel segments are studied with 3D modeling. To this ob- representing distributed loading type, as the nodes will jective, a 3D model of subway tunnel with actual dimension be closer to the locations of the contact. In addition, as a was developed applying ABAQUS [36] Figure 9 indicates general principle of any numerical method, the finer the the segment model with the details about the overhead, discretization the closer it is to the exact solution. tunnel diameter, and lining thickness. Table 3 shows the details of developed models. 290 | H. Satih Abbas et al. Figure 10: Model meshing (a) Figure 11: Finer mesh around the tunnel 4.2 Material and element specifications (b) Table 4 lists the specifications of the materials used to model soil layers. As evident, elastic modulus, Poisson’s Figure 12: Coulomb friction law and vertical behavior between the ratio, cohesion, and internal friction angle are necessary to soil and the concrete (hard contact) ABAQUS (2012) model the soil. The linearly elastic-perfectly plastic model using the Coulomb constitutive law was used to represent 4.3 Model boundary conditions the soil. Further, the concrete was modeled using the linear The support conditions were defined to fix the displace- elastic relationship based on Table 5. In this case, the elastic ment and rotation of the model’s bottom in the horizontal modulus, Poisson’s ratio, and the specimens’ compressive and vertical directions. Further, the sides were fixed in the strength are necessary. Interactions between the soil and horizontal direction. Figure 13 shows the defined boundary the concrete cover were modeled as follows: conditions. The boundaries have been placed far enough from the tunnel to ensure that the boundaries have negligi- Tangential behavior: The tangential behavior between the ble effects in modeling. soil and the concrete followed Coulomb’s friction law in zero-cohesion conditions with a µ = 100 (ϕ = 89.43 ) coef- ficient of friction (Figure 12a). This relationship has been 4.4 Initial conditions of the model recommended by the ABAQUS [36]. Vertical Behavior: The hard contact relation was used to The initial conditions of the problem include in-situ stresses model the vertical behavior, as evident from the g fi ure be- and groundwater conditions. According to Figure 14, the low. This configuration allows for the vertical transfer of model assumes a 19.65 m water table. The model’s pore stress in case of contact between two surfaces. The model water pressure was based on the water level. In the first does not account for tensile stress (Figure 12b). stage, static analysis, in-situ stresses were created in the model. Three-dimensional numerical study of the reactive powder concrete segments in tunnel lining | 291 Table 4: Soil layer specifications Permeability Dry density Poisson’s Elastic modulus Internal friction Cohesion 3 ∘ (m/s) (kN/m ) ratio (MPa) angle ( ) (kPa) ET1 Layer 9e−7 18.4 0.3 75 31 18 ET2 Layer 9e−7 19 0.32 50 28 35 ET3 Layer 9e−7 17 0.35 35 24 31 Table 5: Concrete specifications in the models Model no. Lining type Elastic modulus (GPa) Compressive strength (MPa) Poisson’s ratio T0 RPC 55 200 0.1 T1 UHPC 37 100 0.15 T2 HPC 35 80 0.15 T3 RC 20 25 0.2 Figure 13: Boundary conditions on the sides Figure 15: Comparing the axial force in different models Figure 14: Groundwater conditions in the model 292 | H. Satih Abbas et al. Figure 16: Comparing the shear force in different models Figure 17: Comparing the bending moment in different models The maximum shear in the models corresponds to the case 4.5 Results analysis with the RPC and is about 30% higher than other kinds of 4.5.1 Axial force on the tunnel lining concrete. Almost the same shear force is exerted on the tun- nel lining in the other cases, and similarly to the argument The axial force on the tunnel lining for multiple segments is made about the axial force, the higher shear capacity aids plotted in Figure 15. The values in the g fi ure are in kN. Based make lighter tunnel segments. on Figure 15, substituting the RC with the RPC enhances the maximum axial force which the tunnel lining can with- stand. The findings indicate that the maximum axial force 4.5.3 Bending moment on the tunnel lining corresponds to RPC and the minimum axial force to the RC concrete. Hence, RPC withstands 48, 38, and 20% higher The bending moment on the tunnel lining for different seg- axial force than RC, HPC, and UHPC, respectively. Thus, ments is plotted in Figure 17. The values in the g fi ure are in considering the RPC’s excellent performance, a smaller seg- kN·m. The findings indicate that the maximum axial force ment thickness can be regarded in the design than with corresponds to the RPC and the minimum axial force to other kinds of concrete. the regular concrete. A same argument to that created for the shear stress on the tunnel lining holds for the bending moment, as the higher control over the displacements and 4.5.2 Shear force on the tunnel lining the deformation around the tunnel increases the maximum bending moment in the case of the reinforced concrete. The shear force on the tunnel lining for multiple segments Moreover, RPC withstands 46, 48, and 26% higher axial is plotted in Figure 16. The amounts in the g fi ure are in kN. Three-dimensional numerical study of the reactive powder concrete segments in tunnel lining | 293 ware ABAQUS. The numerical models were approved via experimental results. Results show that reinforced concrete- PCTL segments are more vulnerable to corrosion problem compared with RPC-PCTL. The numerical findings indi- cated that the compressive strength of PRC segments was greater than that of the RC and HPC segments. Regarding the findings, PRC is a very significant option for conven- tional RC-PCTL segments. Very high strength of PRC can permit decreasing the thickness of PCTL segments, result- ing in the decreased material cost and more sustainable fabrication. Besides, PRC-PCTL segments can delete the laborious and costly manufacturing of RC segments which mitigates the corrosion damage, resulting in the improved service life of tunnel segments. The ndin fi gs indicate that the maximum axial force corresponds to the RPC and the minimum axial force to the conventional RC. The same ar- gument to which created for the shear stress on the tunnel lining holds for the bending moment, as the higher con- trol over the displacements and the deformation around the tunnel increases the maximum bending moment in the case of the reinforced concrete. Moreover, the RPC with- stands 48, 38, and 20% higher axial force than RC, HPC, and UHPC, respectively. Hence, considering the RPC’s ex- cellent performance, a smaller segment thickness can be regarded in the design than with other kinds of concrete. Figure 18: Horizontal displacement on the tunnel lining in different Funding information: The authors state no funding in- models volved. Author contributions: All authors have accepted responsi- force than regular concrete, HPC, and UHPC, respectively. bility for the entire content of this manuscript and approved Thus, given the RPC’s excellent performance, a smaller seg- its submission. ment thickness can be regarded in the design than with other kinds of concrete. Conflict of interest: The authors state no conflict of inter- est. 4.5.4 Displacement on the tunnel lining The displacement on the tunnel lining in multiple cases is References plotted in Figure 18. Considering the displacement symme- try on the tunnel lining, the g fi ure plots the displacement [1] Elliott K. Precast Concrete Structures. 1st Ed. Boston, USA: for only half of the tunnel segment. The values in the g fi - Butterworth-Heinemann; 2002. ures are in mm. It is clear from Figure 18 that horizontal [2] Wang S, Jiang X, Bai Y. The influence of hand hole on the ultimate strength and crack pattern of shield tunnel segment joints by displacement of tunnel lining is decreased by reinforcing scaled model test. Front Struct Civ Eng. 2019 Oct;13(5):1200–13. the tunnel segment with RPC. [3] Ma B, Zou D, Xu L. Manufacturing technique and performance of functionally graded concrete segment in shield tunnel. Front Archit Civ Eng China. 2009 Mar;3(1):101–4. 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Structural and durability performance of precast seg- [21] Salman BF, Al-Rumaithi A, Al-Sherrawi MH. Properties of Reactive mental tunnel linings [dissertation]. London (ON): The University Powder Concrete with Different Types of Cement. IJCIET. 2018 of Western Ontario; 2014. Oct;9(10):1313–21. [22] Poorhosein R, Nematzadeh M. Mechanical behavior of hybrid steel-PVA fibers reinforced reactive powder concrete. Comput Concr. 2018;21(2):167–79. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Curved and Layered Structures de Gruyter

Three-dimensional numerical study of the reactive powder concrete segments in tunnel lining

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de Gruyter
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© 2022 Hajer Satih Abbas et al., published by De Gruyter
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2353-7396
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10.1515/cls-2022-0022
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Abstract

Curved and Layer. Struct. 2022; 9:286–294 Research Article Hajer Satih Abbas*, Maadh Imad Salman Al-Rubaye, Sarra’a Dhiya’a Jaafer, Bassam farman bassam, and Abdelmajeed Alkasassbeh Three-dimensional numerical study of the reactive powder concrete segments in tunnel lining https://doi.org/10.1515/cls-2022-0022 compared to the conventional in-situ lining appraoch [1–3]. Received Nov 18, 2021; accepted Feb 21, 2022 In general, precast concrete tunnel lining (PCTL) segments are planned for more than 100 years of service life [4] with Abstract: The tunnel lining systems act as lines of defence reinforced concrete (RC). Hence, several cases suffered from against the forces and geotechnical situations. The use of the premature deterioration prior to gaining their service precast concrete tunnel linings (PCTLs) has been escalat- life. It was basically assigned to the corrosion caused by ing due to its effective and economical installation process. chloride infiltration [5–7]. The tunnels usually suffer from the premature deteriora- The Reactive Powder Concrete (RPC) is the ultra-high tion due to corrosion of the reinforcement and thus need strength and ductile concrete prepared by replacing the maintenance. Corrosion leads to the distress in PCTL lead- standard aggregate with quartz powder, silica fume and ing to the cracking and finally the scaling of concrete. This steel fibers [ 8]. The concrete does not comprise coarse ag- study aims to assess the structural durability performance gregates, but involves cement, silica foam, sand, powdered of reactive powder concrete (RPC) as the material of tunnel quartz, superplasticizer, and steel fiber. Avoiding the inclu- lining segments compared to reinforced concrete (RC) and sion of coarse aggregates by the inventors is a significant high performance concrete (HPC). The numerical findings aspect of the microstructure and function of RPC which indicated that the maximum load capacity of PRC-PCTL seg- decreases the heterogeneity in mortar and aggregate mix. ments was greater than that of the corresponding RC and The additives, lack of coarse aggregates, small water-to- HPC segments. Regarding the findings, PRC is a very signif- cement ratio, fine steel fibers, heat treatment, and com- icant option for conventional segments. The high strength pression before and after setting are the RPC’s fundamen- of PRC can decrease the thickness of the PCTL segments, tal features [9–14]. The compressive RPC strength is in the resulting in the decreased material cost. Also, PRC-PCTL 200–800 MPa range, its flexural strength is from 30 to 50 segments can eliminate the laborious and costly produc- MPa, and its Young’s modulus around 50–60 GPa [15–19]. tion of RC segments and mitigate the corrosion damage and Because of RPC’s durability and excellent mechani proper- thus enhance the service life of lining segments. ties, its utilizations are expanded. RPC structural elements Keywords: reactive powder voncrete; corrosion, high com- are resistant against chemical attack, impact loads (with pressive strength; finite-element model; tunnel segment. collision with vehicles and vessels), and sudden kinetic loads based on the earthquakes. Made up of compact and ordered hydrates, RPC is basically characterized by high performance. The microstructure is optimized by accurate 1 Introduction particle gradation to maximize density. RPC heavily relies on the pozzolanic features of the washed silica foam and The use of precast concrete tunnel segments in the projects the optimizing cement concrete to gain the maximum hy- has creased due to its effective and economical utilization drate [20–27]. Thus, PRC can be proven to be a more long- lasting material for precast concrete tunnel lining construc- tion. Besides to enhancing the mechanical and durability *Corresponding Author: Hajer Satih Abbas: Civil Engineering features, the replacement of reinforcement with PRC in tun- department, Al-Esraa university college, Baghdad, Iraq; Email: nel segments can delete the laborious and costly construc- dr.hajer@esraa.edu.iq tion of tunnel segments. Moreover, PRC lining segments’ Maadh Imad Salman Al-Rubaye, Sarra’a Dhiya’a Jaafer, Bassam cross-sectional dimensions can be decreased due to their farman bassam: Civil Engineering department, Al-Esraa university high strength, leading to economical fabrication. Multiple college, Baghdad, Iraq Abdelmajeed Alkasassbeh: Civil engineering department, Faculty research investigated the flexural capacity of conventional of Engineering, Al al-Bayt University, Mafraq 25113, Jordan Open Access. © 2022 H. Satih Abbas et al., published by De Gruyter. This work is licensed under the Creative Commons Attribution 4.0 License Three-dimensional numerical study of the reactive powder concrete segments in tunnel lining | 287 Table 1: Mechanical properties of RPC vs. HPC RC tunnel segments [28–33]. The corrosion deterioration of conventional RC-PCTL has resulted in developing the reac- SPECIFICATIONS HPC RPC tive powder concrete (PRC) tunnel lining segments. Hence, Compression capacity (MPa) 85~100 200~800 the present research obtains an evaluation of the mechan- Flexural capacity (MPa) 6~8 45-60 ical behaviour of reactive powder concrete (RPC) tunnel Modulus of elasticity (GPa) 35~40 70 lining segments. This study aims to assess the structural Fracture toughness (J/m ) <1000 30000 and durability function of reactive powder concrete (RPC) tunnel lining segments compared to reinforced concrete (RC) and high performance concrete (HPC). Furthermore, Table 2: The durability of RPC vs. HPC finite element analysis using ABAQUS was conducted in Characteristic Value order to verify the experimental behaviour and comparison of the performance of RPC with RC and HPC tunnel lining Wear 2~2.5 times less segments was presented in this study. Absorption of water 6.5~7.5 times less Rate of corrosion 7~8.5 times less Diffusion of chloride ions 20~30 times less 2 RPC in comparison with HPC 3 Numerical verification A comparison between mechanical and durability proper- ties of the RPC and (high performance concrete) HPC shows The finite-element software, ABAQUS [ 36] was applied for the RPC to offer a higher compressive strength and a perme- model verification, contrasting the findings with the exper- ability lower than the HPC. The HPC is a product of novel imental surveys of Abbas [37]. concrete science, which uses additives and scientific tech- niques to control the concrete’s microstructure [34, 35]. Owing to its microstructure, the HPC has achieved its 3.1 Model geometry maximum compressive strength. Nonetheless, at any given strength, coarse aggregates are the weakest links in the Figure 1 illustrates the model geometry, and the meshed concrete structure. The only remaining solution to further model is presented in Figure 2. The model was meshed increase the compression strength of the concrete is to re- using square elements with a length-to-width ratio of 1, as move coarse aggregates, which is the same approach that it has been suggested that they produce the best results has been adopted in developing the RPC. Table 1 compares the mechanical properties of the typical RPC with a regu- lar HPC with an 80 MPa compressive strength. The higher fracture toughn of the RPC is suggestive of its better duc- tility. Aside from the mechanical properties, RPCs have an exceptionally dense microstructure that makes them im- permeable to water and durable. Thanks to its low porosity and permeability, restricted contraction, and high corrosion resistance, the RPC of- fers remarkable durability. Compared to the HPC, the RPC passes no liquid or gas through. The RPC specifications listed under Table 2 enable it to be used in aggressive chem- ical environments and applications where other types of concrete do not last long due to wear and tear. Results in- dicate that RC and HPC concretes are more vulnerable to corrosion problem compared with RPC concrete. Figure 1: 2D model geometry 288 | H. Satih Abbas et al. Figure 5: Numerical boundary conditions in the upper part of the segment A critical parameter in the finite-element techniques is the solution time and complexity, which depend on the shape and number of elements. In light of the above discus- sions, different types of mesh were used in modeling the studied tunnel segment. It was found that similarly accept- able results are obtained by using 50 and 25 mm elements. Therefore, the 50 mm elements were used for the shorter analysis time (Figure 6). Figure 2: Meshed 2D model in the finite-element method. The eight-node linear brick element C3D8R was used for modeling (Figure 2). 3.2 Model boundary conditions As depicted in Figure 3, support conditions were defined for the model by fixing the model in the vertical direction (Figure 4) at the points where the segment is in contact with two bottom frames (reaction). Further, a vertical down- ward velocity was defined for the upper part of the segment (Figure 5) for flexural loading. Figure 6: Load-displacement curve of the model with two mesh sizes 3.3 Result validation The current numerical ABAQUS [36] model (Figure 6) was Figure 3: Experimental boundary conditions in the lower part of the contrasted with the load-displacement curve of the flexu- segment Abbas [37] ral test in the work of Abbas [37] (Figure 7) at the point of loading for validation. The two curves are plotted on the same graph in Figure 8 for a better comparison. Comparing two curves indicate the consistency of this study’s findings with those of Abbas [37]. Figure 4: Numerical boundary conditions in the lower part of the segment Three-dimensional numerical study of the reactive powder concrete segments in tunnel lining | 289 Figure 7: Load-displacement curve from flexural testing Abbas [37] Figure 8: A comparison of the load-displacement curves Table 3: The details of developed models Figure 9: Model geometry Model no. Lining Tunnel Tunnel type overhead-side overhead-top 4.1 Model geometry and meshing (kPa) (kPa) T0 RPC 25 20 Figure 9 illustrates the model geometry, and the meshed T1 UHPC 25 20 model is presented in Figure 10. The model comprises six T2 HPC 25 20 layers of three different materials. The model was meshed T3 RC 25 20 considering the two following points: First, square ele- ments (with a length-to-width ratio of 1) were used for mesh- ing, as they have been recommended for producing the best 4 Optimizing the tunnel segments results in the finite-element method. Second, a finer mesh with RPC was used for the tunnel due to the considerable displace- ment and stress concentration (Figure 11). On the other In this section, the impact of incorporating the RPC in the hand, a smaller element with finer mesh will be closer to tunnel segments are studied with 3D modeling. To this ob- representing distributed loading type, as the nodes will jective, a 3D model of subway tunnel with actual dimension be closer to the locations of the contact. In addition, as a was developed applying ABAQUS [36] Figure 9 indicates general principle of any numerical method, the finer the the segment model with the details about the overhead, discretization the closer it is to the exact solution. tunnel diameter, and lining thickness. Table 3 shows the details of developed models. 290 | H. Satih Abbas et al. Figure 10: Model meshing (a) Figure 11: Finer mesh around the tunnel 4.2 Material and element specifications (b) Table 4 lists the specifications of the materials used to model soil layers. As evident, elastic modulus, Poisson’s Figure 12: Coulomb friction law and vertical behavior between the ratio, cohesion, and internal friction angle are necessary to soil and the concrete (hard contact) ABAQUS (2012) model the soil. The linearly elastic-perfectly plastic model using the Coulomb constitutive law was used to represent 4.3 Model boundary conditions the soil. Further, the concrete was modeled using the linear The support conditions were defined to fix the displace- elastic relationship based on Table 5. In this case, the elastic ment and rotation of the model’s bottom in the horizontal modulus, Poisson’s ratio, and the specimens’ compressive and vertical directions. Further, the sides were fixed in the strength are necessary. Interactions between the soil and horizontal direction. Figure 13 shows the defined boundary the concrete cover were modeled as follows: conditions. The boundaries have been placed far enough from the tunnel to ensure that the boundaries have negligi- Tangential behavior: The tangential behavior between the ble effects in modeling. soil and the concrete followed Coulomb’s friction law in zero-cohesion conditions with a µ = 100 (ϕ = 89.43 ) coef- ficient of friction (Figure 12a). This relationship has been 4.4 Initial conditions of the model recommended by the ABAQUS [36]. Vertical Behavior: The hard contact relation was used to The initial conditions of the problem include in-situ stresses model the vertical behavior, as evident from the g fi ure be- and groundwater conditions. According to Figure 14, the low. This configuration allows for the vertical transfer of model assumes a 19.65 m water table. The model’s pore stress in case of contact between two surfaces. The model water pressure was based on the water level. In the first does not account for tensile stress (Figure 12b). stage, static analysis, in-situ stresses were created in the model. Three-dimensional numerical study of the reactive powder concrete segments in tunnel lining | 291 Table 4: Soil layer specifications Permeability Dry density Poisson’s Elastic modulus Internal friction Cohesion 3 ∘ (m/s) (kN/m ) ratio (MPa) angle ( ) (kPa) ET1 Layer 9e−7 18.4 0.3 75 31 18 ET2 Layer 9e−7 19 0.32 50 28 35 ET3 Layer 9e−7 17 0.35 35 24 31 Table 5: Concrete specifications in the models Model no. Lining type Elastic modulus (GPa) Compressive strength (MPa) Poisson’s ratio T0 RPC 55 200 0.1 T1 UHPC 37 100 0.15 T2 HPC 35 80 0.15 T3 RC 20 25 0.2 Figure 13: Boundary conditions on the sides Figure 15: Comparing the axial force in different models Figure 14: Groundwater conditions in the model 292 | H. Satih Abbas et al. Figure 16: Comparing the shear force in different models Figure 17: Comparing the bending moment in different models The maximum shear in the models corresponds to the case 4.5 Results analysis with the RPC and is about 30% higher than other kinds of 4.5.1 Axial force on the tunnel lining concrete. Almost the same shear force is exerted on the tun- nel lining in the other cases, and similarly to the argument The axial force on the tunnel lining for multiple segments is made about the axial force, the higher shear capacity aids plotted in Figure 15. The values in the g fi ure are in kN. Based make lighter tunnel segments. on Figure 15, substituting the RC with the RPC enhances the maximum axial force which the tunnel lining can with- stand. The findings indicate that the maximum axial force 4.5.3 Bending moment on the tunnel lining corresponds to RPC and the minimum axial force to the RC concrete. Hence, RPC withstands 48, 38, and 20% higher The bending moment on the tunnel lining for different seg- axial force than RC, HPC, and UHPC, respectively. Thus, ments is plotted in Figure 17. The values in the g fi ure are in considering the RPC’s excellent performance, a smaller seg- kN·m. The findings indicate that the maximum axial force ment thickness can be regarded in the design than with corresponds to the RPC and the minimum axial force to other kinds of concrete. the regular concrete. A same argument to that created for the shear stress on the tunnel lining holds for the bending moment, as the higher control over the displacements and 4.5.2 Shear force on the tunnel lining the deformation around the tunnel increases the maximum bending moment in the case of the reinforced concrete. The shear force on the tunnel lining for multiple segments Moreover, RPC withstands 46, 48, and 26% higher axial is plotted in Figure 16. The amounts in the g fi ure are in kN. Three-dimensional numerical study of the reactive powder concrete segments in tunnel lining | 293 ware ABAQUS. The numerical models were approved via experimental results. Results show that reinforced concrete- PCTL segments are more vulnerable to corrosion problem compared with RPC-PCTL. The numerical findings indi- cated that the compressive strength of PRC segments was greater than that of the RC and HPC segments. Regarding the findings, PRC is a very significant option for conven- tional RC-PCTL segments. Very high strength of PRC can permit decreasing the thickness of PCTL segments, result- ing in the decreased material cost and more sustainable fabrication. Besides, PRC-PCTL segments can delete the laborious and costly manufacturing of RC segments which mitigates the corrosion damage, resulting in the improved service life of tunnel segments. The ndin fi gs indicate that the maximum axial force corresponds to the RPC and the minimum axial force to the conventional RC. The same ar- gument to which created for the shear stress on the tunnel lining holds for the bending moment, as the higher con- trol over the displacements and the deformation around the tunnel increases the maximum bending moment in the case of the reinforced concrete. Moreover, the RPC with- stands 48, 38, and 20% higher axial force than RC, HPC, and UHPC, respectively. Hence, considering the RPC’s ex- cellent performance, a smaller segment thickness can be regarded in the design than with other kinds of concrete. Figure 18: Horizontal displacement on the tunnel lining in different Funding information: The authors state no funding in- models volved. Author contributions: All authors have accepted responsi- force than regular concrete, HPC, and UHPC, respectively. bility for the entire content of this manuscript and approved Thus, given the RPC’s excellent performance, a smaller seg- its submission. ment thickness can be regarded in the design than with other kinds of concrete. 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Journal

Curved and Layered Structuresde Gruyter

Published: Jan 1, 2022

Keywords: reactive powder voncrete; corrosion; high compressive strength; finite-element model; tunnel segment

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