Abstract
JOURNAL OF ASIAN ARCHITECTURE AND BUILDING ENGINEERING 2020, VOL. 19, NO. 3, 203–219 https://doi.org/10.1080/13467581.2020.1743294 BUILDING STRUCTURES AND MATERIALS Bending mechanics model and value of transverse joints in precast prestressed utility tunnel a a a a Pengyu Wang , Shuhong Wang , Muhammad Israr Khan and Chengjin Zhu School of Resources and Civil Engineering, Northeastern University, Shenyang City, China ABSTRACT ARTICLE HISTORY Received 11 September 2019 Joints lead to the uneven distribution of structural rigidity of a precast prestressed utility tunnel Accepted 24 February 2020 (PPUT) and changes in internal forces and deformation. From research perspective, bending stiﬀness is important as an important indicator to evaluate the performance of PPUT joints and KEYWORDS an important factor to evaluate the overall mechanical properties of PPUT structures. After Precast prestressed utility considering the actual structural form of a transverse joint section and the characteristics of tunnel; transverse joint; force deformation, a mechanical model that can characterize the joint section from force to high-strength bolts; bending failure and the corresponding analytical expressions were established using the internal force mechanical model balance and deformation coordination conditions. A sensitivity analysis of the factors aﬀecting the bending stiﬀness of joints was carried out using numerical simulation methods. The theoretical calculation results were compared with the numerical simulation results. Finally, according to the obtained trend of bending stiﬀness change, a two-stage bending stiﬀness method is proposed for the transverse joints of PPUT. The results of the study provide a reference for the design and theoretical analysis of PPUT. 1. Introduction technology has the advantages of high eﬃciency, low cost, and environmental protection. In recent years, with the vigorous development of A PPMT can be divided into prefabricated segment urban underground space in China, the maintenance, utility tunnel with only longitudinal joints and prefab- expansion, and renovation of municipal pipelines have ricated municipal tunnel with both longitudinal and led to repeated excavation of urban roads. This causes transverse joints (Figure 3) (Julian Canto, Curiel- urban traﬃc congestion and becomes an important Esparza, and Calvo 2013). The volume and weight of factor for constraining urban infrastructure construc- each section of utility tunnel are relatively large. To tion and sustainable green environmental protection. ensure the convenience of utility tunnel transportation To solve this problem, China has constructed utility and on-site assembly, the width of each section of tunnels in many cities (Canto-Perello and Curiel- utility tunnel is generally controlled between 1.5 Esparza 2013). m and 2 m, thus forming a lot of joints (Wei-chen A utility tunnel is a complex tunnel laid under a city 2002). road by integrating various municipal pipelines such as The joints signiﬁcantly aﬀect the performance of water supply, drainage, communications, electricity, utility tunnel (Yoo and Kim 2003). The presence of and heat, thus achieving “uniﬁed planning and uniﬁed joints leads to the uneven distribution of utility tun- management of various municipal pipelines” (Figure 1) nel’s structural stiﬀness, internal forces, and deforma- and eﬀectively promoting the sharing and comprehen- tion change. Therefore, the joints are important from sive utilization of underground space resources (Hunt, research perspective as a key part of PPMT (Li Yu-Jie Nash, and Rogers 2014; Lbobb, Blanpain, and Buyle- 2012; Zhang Jian-Gang 2013). Bodin 2004). Bending stiﬀness is not only an important index to At present, the construction methods for a utility measure the performance of joint, but also an impor- tunnel mainly include cast-in-place method and pre- tant factor in evaluating the overall mechanical proper- fabrication method (Figure 2) (Chen-Jun, Li, and Shi ties of utility tunnel (WANG Peng-yu, Li, and Jie Ru La 2012). Among them, the precast prestressed municipal 2018; Wang Shu-Hong et al., 2018). Tongji University tunnel (PPMT) is the most widely used construction has conducted full-scale tests on the bending mechan- technology in the prefabrication method (Perello and ical properties of longitudinal joints of PPMT, whereas Curiel-Esparza 2007). PPMT technology has achieved transverse joints have not been studied yet (Xue Wei- remarkable construction achievements in the utility Chen et al., 2009). Theoretical analysis and numerical tunnel project of Shanghai World Expo Park. PPMT CONTACT Shuhong Wang shwangneu@126.com School of Resources and Civil Engineering, Northeastern University, Shenyang City 110819, China © 2020 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group on behalf of the Architectural Institute of Japan, Architectural Institute of Korea and Architectural Society of China. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 204 P. WANG ET AL. Figure 1. Urban utility tunnel. (a)Cast-in-placemethod (b) Prefabricationmethod Figure 2. Urban utility tunnel construction methods. using prestressed tendons, and the transverse joints are connected using high-strength bolts. Joint section reserved seam to ensure assembly accuracy. To satisfy the waterproof requirement at the joints, rubber strips are inﬂated in the reserved grooves. Literature data were used to determine the depth and width of reserved grooves and preloading of high-strength bolts. divide into upper and lower parts 2.2. Basic assumptions The lateral joints are deformed under the action of upper earth pressure and lateral earth pressure as shown in Figure 5. According to the force characteristics and speciﬁc conﬁguration of transverse joints, the following assumptions are made: The relative rotation of transverse joints is the Figure 3. Joint form of precast prestressed utility tunnel. main cause of deformation of side walls of a utility tunnel as shown in Figure 5. Among them, the tensile deformation of high-strength simulation methods were used in this study to evalu- bolts and the compression deformation of con- ate the bending stiﬀness of transverse joints. crete in the compressed area of joint section cause the relative rotation of joint. 2. Transverse joint bending stiﬀness When the joint section is not open, the entire calculation model section is subjected to pressure and satisﬁes the ﬂat section assumption. When the joint section 2.1. Joint construction opens, both the sections of tensioned concrete The construction form and size of a transverse joint are and compression concrete remain ﬂat, conﬁrming shown in Figure 4. The longitudinal joints are connected the ﬂat section assumption. JOURNAL OF ASIAN ARCHITECTURE AND BUILDING ENGINEERING 205 3. Theoretical calculation of bending stiﬀness of transverse joints 3.1. Force of transverse joints First, the transverse joint is subjected to the tightening force of bolt. The bolt tightening force has two func- tions: (i) to ﬁx the joint so that the segment pieces do not move relatively; (ii) to provide the pressure needed for the seal ring to close the joint. Second, after the (a) cross-section (b) side facade foundation pit is backﬁlled, the utility tunnel joint is also subjected to the surrounding earth pressure. The fastening force of high-strength bolt is equiva- lent to a uniform distribution of compressive stress along the cross-section of joint. The upper earth pres- sure is equivalent to pressure load N, and the lateral (c)Transverse joints earth pressure is equivalent to bending moment M, Figure 4. Construction of transverse joints. thus forming a transverse joint force diagram of the utility tunnel, as shown in Figure 6. According to the change of force, the deformation When calculating the bending stiﬀness, the stiﬀ- of transverse joint section of utility tunnel can be ness of waterproof material of joint section is very divided into the following three situations. small; therefore, its eﬀect on the calculation result is negligible. Concrete is only subjected to pressure, and high- 3.2. Opening height of joint section is lower than strength bolts are only subjected to tension. the bolt position Concrete deformation at the outer edge of com- pressed area of joint section can be calculated as When the opening height h < h , the deformation of 1 2 follows: joint section is shown in Figure 7. The opening height h , the height of compressed zone h , and the thick- 1 3 ness of jointhhave the following relationship. δ ¼ εl (1) ef δ h h cos h 2 3 whereε represents the strain of concrete at the ¼ ¼ (10) δ h h 1 1 1 outer edge of compression zone of one-sided joint; l ef represents the range of concrete strain at the outer edge of compression zone of joint. h þ h ¼ h cos (11) 1 3 ● The stress-strain relationship of concrete uses the The compression of concrete at the outer edge of constitutive model proposed by Hognestad (Jiang compression zone of joint section can be expressed Jian-Jing, 2005). as follows: "# 2 θ θ 2ε ε δ ¼ 2h tan ¼ θ h cos h (12) c c 2 3 1 σ ¼ f ; ε ε c c c 0 2 2 ε ε 0 0 (2) Because the corners of joint sections are small, tan θ ¼ ε ε c 0 σ ¼ f 1 0:15 ; ε > ε c c c 0 θ can be approximated. According to the assumption, ε ε max 0 the deformation of outer edge of concrete Figure 5. Sidewall deformation diagram. 206 P. WANG ET AL. Figure 6. Bending mechanical model of joint surface. h θ h θ M ¼ nT h cos þ F y cos (16) 2 1 1 2 2 2 2 ð θ h cos F ¼ σ ðyÞbdy (17) 1 1 ð θ h cos σ ðyÞydy y ¼ (18) 1 ð θ h cos σ ðyÞdy In the formula, E is the strain of concrete at the outer edge of compression zone on one side of joint section. E is the strain of concrete when the compression area of joint section is at the y height position. F is the resistance generated by concrete in the compression zone. y is the centroid position of concrete in the compression zone of joint section; b represents the Figure 7. Geometric deformation of joint surface. widthofeachsection of utilitytunnel; E represents the elastic modulus of precast concrete. δ is the max- imum amount of opening of joint section; δ is the compression zone on one side of the joint section can maximum amount of compression of joint section; h be expressed as follows: is the distance from the high-strength bolt to the inside δ ¼ ε l (13) 2 2 ef of side wall of utility tunnel. Finally, the bending stiﬀness of joint at this stage According to the ﬂat section assumption, the following can be obtained using equation (19). relationship can be obtained: ε M 2 y ¼ (14) K ¼ (19) h h θ h cos h 1 y 1 According to the force balance of the joint section (Figure 8), the following relationship can be obtained: 3.3. Opening height of joint section is higher than the bolt position N ¼ 0 nT þ N ¼ F (15) When the opening height h < h < h, the deformation X 2 1 M ¼ 0 of joint section is shown in Figure 9. According to the JOURNAL OF ASIAN ARCHITECTURE AND BUILDING ENGINEERING 207 Figure 8. Strains after the seam opening. θ θ ﬂat section assumption, the following relationship can 2h tan h h cos 1 1 2 2 2 ¼ E A b b be obtained: h l 1 b h h cos Δl 1 2 ¼ (20) θ θ δ h 1 1 ¼ E A h h cos (22) b b 1 2 l 2 ε ε 2 3 where E is the elastic modulus of high-strength bolt; ¼ (21) θ θ h cos h h h cos A is the cross-sectional area of high-strength bolt;l is 1 1 2 b b 2 2 the length of high-strength bolt. where E is the strain of high-strength bolt when the According to the force balance of joint section opening height of joint section is h . According to Eq. (Figure 10), the following relationship can be obtained: 20, the force of high-strength bolt can be obtained as follows: N ¼ 0F ¼ nTðÞ þ T þ N (23) 1 b δ h h cos 1 1 2 T ¼ E A b b b M ¼ 0 h l 1 b Figure 9. Geometric deformation of joint surface. 208 P. WANG ET AL. h θ h θ E ¼E (25) 2 cu M ¼ nTðÞ þ T h cos þ F y cos 2 1 1 2 2 2 2 E is the ultimate compressive strain of concrete. cu (24) The load continues to increase until the high- Finally, the bending stiﬀness of joint at this stage can strength bolt yields. At this time, a part of the concrete be obtained using Formula (19). of joint section has already stopped working, and the joint is unstable. The force of joint section is shown in Figure 12. 3.4. Crushing of joint section concrete and T ¼ f A (27) yielding of bolts b b b When the outer edge of compression zone concrete of where f is the yield stress of high-strength bolt; Δh is joint section reaches the ultimate compressive strain, the height of concrete that stopped working. the joint section is collapsed. At this point, the force of According to the above formula, the values of θ and joint section is shown in Figure 11, and the following h can be obtained. Finally, the bending stiﬀness of relationship can be obtained: joint at this stage can be obtained using Formula (19). Figure 10. Strains after the bolts bearing force. Figure 11. Strains at concrete beginning crushing. JOURNAL OF ASIAN ARCHITECTURE AND BUILDING ENGINEERING 209 Figure 12. Strains obtained after the bolt bearing force. E ¼E (28) yields. The high-strength bolt has yield strength of Δh cu 480 MPa and an ultimate strength of 600 MPa. The ð θ ðhΔhÞ cos constitutive relationship of the steel uses the ideal F ¼ σ ðyÞbdy (29) 1 1 elastoplastic two-fold line model. The steel is linear elastic before yielding, and the strength does not change after yielding. The yield stress of steel is ð θ ðhΔhÞ cos 436 MPa, and the modulus of elasticity is 198 GPa. σ ðyÞydy y ¼ (30) 1 θ ðhΔhÞ cos σ ðyÞdy 4.2. Deﬁning constraints A 3D numerical model of the transverse joint of utility tunnel is shown in Figure 14. The model is made of two standard segments joined by bolts. The initial strain 4. Numerical simulation of transverse joints applied to the high-strength bolts was used to simu- 4.1. Constitutive relationship of materials late the anchoring force of high-strength bolts during an actual construction. To prevent the local damage of ABAQUS software was used for numerical simulation. concrete, steel gaskets with a thickness of 6 mm were When a numerical model for transverse joints is estab- set as the support. The steel gasket and segment are lished, it is assumed that the prefabricated utility tun- bound by Tie unit. The constraint of steel gasket are nel is an isotropic homogeneous material, and the U1 ¼ 0, U2 ¼ 0, and U3 ¼ 0, that is adding the hinge diﬀerence in material can be ignored. Precast concrete constraint as the boundary condition. Constraint was is simulated by a solid element, and the constitutive deﬁned in the integration module, and embedded was relationship is based on the Hognestad constitutive selected for establishing the constraint between the model. The rising ascending section of the model is steel and concrete. The contact between two trans- a quadratic parabola, and the falling descending sec- verse joints of precast segments was deﬁned as the tion of the model is an oblique straight line. The peak surface-to-surface contact, deﬁned as a hard contact in stress corresponds to a strain of 0.002; the ultimate the normal and deﬁned as the friction in the tangential compressive strain is 0.0038; the compressive strength (Chen-Jun, Li, and Shi 2012). The penalty function algo- is 28 MPa; the tensile strength is 2.6 MPa; the Poisson’s rithm was selected, and a friction coeﬃcient of 0.2 was ratio is 0.2 (Figure 13). taken. The same deﬁnition form was used between the The high-strength bolts were simulated using the high-strength bolt and hole wall; hard contact was in Beam unit, a good model for simulating an elongated the normal and tangential directions. A penalty func- structure. The constitutive relationship uses the tion was used to deﬁne friction with a friction coeﬃ- bilinear isotropic strengthening model, reﬂecting the cient of 0.3 (Choi, Choi, and Choi 2013). characteristic that the stress can still grow after the bolt 210 P. WANG ET AL. Figure 13. Precast concrete constitutive relationship. Figure 14. Transverse joint 3D model. 4.3. Loading method increased. Therefore, in the design of utility tunnel, it is necessary to consider the thickness of joint. According to the force characteristics of joint section in actual engineering, the upper earth pressure load N was simulated by applying a horizontal load F , X 4.4.2. Bolt location and the bending moment M generated by the lateral The position of bolt of transverse joint section of earth pressure was simulated by applying a vertical a prefabricated prestressed utility tunnel is shown load. The numerical model under load is shown in in Figure 16. Generally, the bolts are located close Figure 15. to the inner side of joint section. The horizontal load N is taken as 100 kN and 200 kN. The initial tightening force F of high-strength bolt is 40 kN, 4.4. Analysis of factors aﬀecting bending stiﬀness and the thickness t of joint is 0.3 m. When the bolt is 0.05 m, 0.1 m, and 0.15 m away from the inner 4.4.1. Joint thickness side of joint section, the curve of M θ of the joint The horizontal load N is 200 kN; the high-strength bolt is shown in Figure 17. is 0.1 h from the inner side of side wall plate; the initial Figure 18 shows that when the position of bolt is tightening force F of the bolt is 40 kN. When the above closer to the inner side of joint section, the bolt is more parameters are unchanged, the joint thickness is eﬀective in promoting the stability of joint section, 0.25 m, 0.30 m, 0.35 m, and 0.4 m; the curve of M θ because when the bolt moves inward, the bolt’s ability of joint section is shown in Figure 16. to restrain the joint opening is improved, and the time Figure 16 shows that when the thickness of trans- for the joint to reach a stable state is shortened, thus verse joint is increased from 0.25 m to 0.45 m, the improving the bending stiﬀness of joint. bending stiﬀness of joint section is doubled. Therefore, At the same time, it was also found that when the the thickness of transverse joint signiﬁcantly aﬀects the horizontal load N increases, the eﬀect of bolt position bending stiﬀness of joint. Mainly because of the increase on the bending stiﬀness of joint is gradually reduced, in joint thickness, the height of joint compression zone because an increase in the horizontal load increases is increased, so that the transverse joint restraint cap- the restraining ability of joint section rotation, thereby ability is enhanced. The joint opening capacity and reducing the eﬀect of bolt position. space are reduced, and the joint bending stiﬀness is JOURNAL OF ASIAN ARCHITECTURE AND BUILDING ENGINEERING 211 Figure 15. Schematic diagram of numerical model loading for transverse joint. Figure 16. Relationship of M-θ curve of segment joint with diﬀerent thicknesses. variation of M θ was analysed when the preload 4.4.3. Bolt preload force F was 20 kN, 40 kN, 60 kN, 80 kN, and 100 kN. In the numerical simulation, the initial tightening force Figure 19 shows that the bolt fastening force slightly was obtained by applying the initial strain to the bolts. aﬀects the bending stiﬀness of transverse joint. When The bolt section stress is σ ¼ F=S, and the correspond- the initial tightening force of bolt is increased, the joint ing strain is ε ¼ σ=E, so that the initial preload is F ¼ section angle is slightly reduced, and the bending stiﬀ- εES (Sun Wen-Hao and Lan 2008). Among them and ness is improved to some extent. Because the bolt indicate the elastic modulus and cross-sectional area of tightening force forms a partial eccentric pressure on the bolt (Jiang Hong-Sheng 2004), respectively. The Figure 17. Diagram of bolt radial layout position. 212 P. WANG ET AL. (a)horizontal load N=100kN (b) horizontal load N = 200 kN Figure 18. Relationship M-θ curve of utility tunnel joints with diﬀerent radial positions of bolts. the joint section during the deformation of joint section, obtained by numerical simulation and theoretical cal- the pressing action of pressure on the joint section culation, as shown in Figure 20. causes the joint to remain in a closed state, Figure 20 shows that when the bending moment of Therefore, the bolt tightening force is larger, and transverse joint section increases, the maximum open- the corner angle is smaller when the joint section ing amount of section shows a nonlinear growth trend, reaches a steady state. With the increase in axial which ﬁrst increases slowly and then increases rapidly. force, the restraining ability of joint rotation is gradu- When the bending moment is the same, the larger the ally increased, weakening the eﬀect of bolt fastening horizontal load N, the smaller the maximum opening force on joints. Overall, the bolt tightening force has amount of joint section. less eﬀect on the bending stiﬀness of transverse joint. The maximum opening amount of joint section should satisfy the waterproof design requirement (less than 3 mm). Therefore, according to the variation 5. Comparison of two calculation models curve of Figure 20, it can be concluded that the max- When the bending stiﬀness of joint is calculated using imum bending moment that the joint section can with- the theoretical model of bending stiﬀness of trans- stand must be less than 300, thus providing a reference verse joint of utility tunnel, the horizontal loads N are for the waterproof design of utility tunnel. taken as 100 kN and 200 kN. Left is taken as 0.5 times, When the bending moment is small, the theoretical 1.0 times, and 1.5 times of the joint thickness, and the calculation results are consistent with the numerical bolt tightening force is taken as 40 kN. Other calcula- simulation results. At this stage, the constitutive model tion parameters are shown in Table 1. of concrete is more consistent with the actual elastic state of concrete. When the bending moment exceeds 250 kN/m, the theoretical calculation result is larger 5.1. Maximum opening comparison than the numerical simulation result. At this time, the concrete in the compression area of joint section A curve of maximum opening amount of transverse shows a nonelastic state. joint section as a function of bending moment was JOURNAL OF ASIAN ARCHITECTURE AND BUILDING ENGINEERING 213 (a) horizontal load N = 100 kN (b) horizontal load N = 200 kN Figure 19. Relationship M-θ curve of utility tunnel joints with diﬀerent bolt pretensions. Table 1. Calculation parameters. h hA f E l E 2 b b b b c 2 2 5 2 4 2 100 mm 300 mm 706 mm 903 N/mm 2.01 N/mm 500 mm 3.52 N/mm Compared with the left taken as 1 H and 1.5 H, the The trend of curves obtained using the two calcula- theoretical calculation result is closer to the numerical tion methods is consistent: The opening height of joint simulation result when the left is taken as 0.5 H. section increases with the increase in bending moment. When the bending moment is small, the opening height of joint section increases linearly; 5.2. Bolt force comparison when the bending moment is more than 200 kN·m, Through numerical simulation and theoretical calculation, the opening height increases slowly, because the a curve of the force of high-strength bolt with the open- opening height exceeds the position of high-strength ing height of joint was obtained, as shown in Figure 21. bolt at this time, and the joint section is subjected to The trend of curves obtained using the two calcula- the pulling force of bolt. tion methods is consistent: When the opening height When the bending moment is the same, the open- of joint section is lower than the bolt position, the bolt ing height of joint section decreases with the increase is almost unstressed. When the opening height is in horizontal load N, indicating that the horizontal load higher than the bolt position, the force of bolt shows has a restraining eﬀect on the opening of joint section. an approximately linear increasing trend with the increase in opening height, indicating that the high- strength bolt is in the state of linear elasticity. 5.4. Comparison of bending stiﬀness Through numerical simulation and theoretical calcula- 5.3. Open height comparison tion, a curve of bending stiﬀness of transverse joint was obtained, as shown in Figure 23. Through numerical simulation and theoretical calcula- When the bending moment is small, the bending tion, a curve of opening height of joint with bending stiﬀness tends to increase linearly. As the bending moment was obtained, as shown in Figure 22. 214 P. WANG ET AL. Figure 20. Comparison of joint maximum opening amount. Figure 21. Comparison of bolt stresses. Figure 22. Comparison of opening height. moment increases, the pressure on the concrete out- deformation gradually decreases. The pressure on the side the joint section increases; the concrete is further concrete inside the joint section is continuously compressed; the compression stiﬀness increases; the reduced; the compression stiﬀness is continuously JOURNAL OF ASIAN ARCHITECTURE AND BUILDING ENGINEERING 215 Figure 23. Comparison of M-θ. reduced and gradually enters the relaxation compres- The numerical model is a spatial three-dimensional sion stage, leading to an increase in the pressure dif- model that considers the longitudinal space of the ference between the inner and outer sides. gallery, thereby improving the ﬂexural performance The recovery rate of compression deformation is of joint. The theoretical calculation model is a planar greater than the rate of decrease of deformation incre- two-dimensional model, ignoring the eﬀect of joint ment of the pressure increase part, resulting in space eﬀect on the mechanical properties; there are a continuous increase in the rotation angle at the diﬀerences in the stress distribution patterns of joint joint, gradual separation of joint cross-section, and sections of theoretical and numerical models. the formation of compression zone and open zone. In the theoretical calculation model, the deforma- Then, the bolts are subjected to tensile forces and tion of the outermost concrete in the compression the concrete is under pressure. Both of them jointly zone of joint section is approximated, inevitably diﬀer- resisted the external load, and the ﬁnal joint section ent from the state of numerical model. gradually became stable. In general, although the theoretical and numerical With the increase in bending moment, the concrete models of transverse joints all have their own assump- in the compression zone and compressed section of tions and equivalent processes leading to diﬀerences the joint section is crushed, the bolts yield, and the in the calculation results, both the models reﬂect the joint stiﬀness decreases, thus resulting in a rapid changes in the bending stiﬀness of joints. increase in the joint angle. A comprehensive comparison and analysis of calcu- 6. Experimental study on the stress lation results of the two models showed that when the performance of transverse joints inﬂuencing depth of the concrete compressive strain in the compression area of joint section is 1.0 H and 6.1. Test piece design 1.5 H in the theoretical calculation model, the theore- The mechanical properties of transverse joints of bolted tical calculation results show a large deviation from the prefabricated utility tunnel were evaluated by 1: 1 full numerical simulation results. When Left ¼ 0:5H, the scale model test. The test piece in the model was spliced comparison results of the two models are consistent. using two prefabricated segments by fastening 10.9 stage Therefore, Left is recommended to be (take) 0.5 H in M30 high-strength bolts. The cross-sectional dimension is the theoretical calculation of bending stiﬀness of trans- shown in Figure 4. 10.9-10 indicates that the bolt has verse joint. a tensile strength of 1000 MPa, and 9 indicates that the When Left ¼ 0:5H, the results of the two models ratio of yield strength to tensile strength is 0.9. Thus, the agree well with each other. Therefore, it is recom- yield strength of bolt is 900 MPa. M30 indicates that the mended that Left be 0.5 H in the theoretical calculation bolt has a diameter of 30 mm. Bolts made of low-carbon model for determining the bending stiﬀness of joints. alloy steel or medium-carbon steel and subjected to heat From the comparison of the results of theoretical treatment (quenching and tempering) are known as high- calculation model and numerical model, it can be strength bolts, and the remaining are collectively referred observed that although the two joint models show to as ordinary bolts (Todut, Dan, and Stoian 2014). Figure similar changes, there are still some diﬀerences. The 24 shows a reinforcement drawing of the test piece. The comprehensive analysis has the following reasons: 216 P. WANG ET AL. strength grade and waterproof grade of the test piece Sidewall loading is performed by applying equivalent concrete are C40 and S6, respectively. A groove is monotonic static loading synchronously to the four reserved at the abutted seam of the test piece joint, and sidewalls of the overall structure test pieces, as a 821-BF type water swelling rubber is pasted. In the shown in Figure 25. The test simulates multiple loads theoretical calculation model, the eﬀect of water swelling of the overall structure, including standard load condi- rubber is neglected. Other experimental parameters are tions, design load conditions, 1.5 times design load shown in Table 2. conditions, two times design load conditions, three times design load conditions, and ultimate failure. According to the design requirements of a utility tun- 6.2. Loading method and test content nel structure, the sidewall loads P of the overall struc- tural test piece under standard load conditions and The test loading can be divided into two stages: tigh- design load conditions are 50 kN and 80 kN, tening the bolt and applying the sidewall load. Figure 24. The reinforcement drawing of the test piece. Table 2. Test parameters. 2 5 2 4 2 Test parameters h (mm) h(mm) A (mm) f (N/mm ) E (10 N/mm ) l (mm) E (10 N/mm ) 2 b b b b c Joint section 100 300 706 903 2.01 500 3.52 Figure 25. Install strain gauges and loading installation. JOURNAL OF ASIAN ARCHITECTURE AND BUILDING ENGINEERING 217 respectively. In the test loading device, a 10,000 kN 6.4. Analysis and comparison of results microcomputer was used to control the electrohydrau- To verify the accuracy of the established theoretical lic servo multifunction testing machine system. calculation model of utility tunnel joint, the test results Notably, because of a larger size of the test piece, the were compared with the theoretical calculation results, overall structural test piece was rotated by 90° in the as shown in Table 3, where indicates the angle of test to satisfy the space size requirement of testing opening at joint beam, and indicates the bending machine. The testing content of overall structural moment at the joint. The result of theoretical calcula- stress performance test mainly includes the following: tion is consistent with the experimental result as Strain in high-strength bolts and ordinary steel bars a whole, indicating that the theoretical calculation and the opening amount of beam of transverse joint model and method developed for determining the and seam corner, including the mid-span deﬂection of bending stiﬀness of transverse joint of prefabricated sidewall of beam (Chen et al. 2017). utility tunnel can accurately describe the deformation and internal force state of joint during the whole pro- cess of stress (Chen et al. 2019). 6.3. Failure process of test piece There are two main reasons for the error between the First of all, it is required to tighten the bolts, and then experimental and theoretical values: First, the members in completely seal the joint of test piece before applying the test are larger in size and diﬃcult to be controlled, and load on the side wall. In the process of applying load errors will inevitably occur in the assembly and measure- on the side wall, the test piece experienced three ment. Manufacturing errors are present in the ﬂatness stages: cracking, yielding and ultimate failure. During and reserved groove size at the joint. As the opening this process, the cracks ﬁrst appeared on the outer width at the joint increases, the error between the theo- edge section of the haunched area at the end of the retical experimental values decreases, mainly because the cast-in-place side wall of the test piece, and the joint joint is subjected to more uniform force when the load seam was still closed at this moment. With the increase increases, and the actual force at the joint can better of the load, the cracking area gradually extended to comply with the assumption of theoretical model. the middle of the side wall span when the joint seam gradually opened. When P (the load on side) reached 6.5. Two-stage value method for bending two times of the design load, the joint seam opened stiﬀness of transverse joints for about 3 mm; when P reached three times of the design load, the tensile longitudinal bar at the end of Figure 26 shows that the bending stiﬀness of joint is the test piece yielded and the joint seam opened for not ﬁxed during the change in the bending moment of 8 mm. With the increase of P, the concrete in the joint (Zhang and Fang Ruo-Quan 2017). Therefore, it is compression zone of the joint peeled oﬀ; meanwhile obviously unreasonable to take a ﬁxed value of bend- the overall deformation of the structure increased ing stiﬀness in the mechanical calculation of tube gal- rapidly and reached the ultimate limit state. At this lery. According to the curve obtained in this study, the time, the bolt strain was about 80% of the yield strain, bending stiﬀness is revalued (Feng Kun and Ming-Qing and the opening of joint seam is about 24 mm. 2016). Table 3. Comparison of theoretical calculation results and test results. Theoretical calculation results and test results Theoretical experimental Theoretical values/experi- Force stage values values mental values Before yielding θ ¼ 0:0004 M/(KN·m) 35.8 28.7 1.25 –3 High-strength bolt strain (10 ) 2.632 2.096 1.26 Maximum crack width/mm 0.52 0.54 0.96 θ ¼ 0:005 M/(KN·m) 57.5 48.1 1.20 –3 High-strength bolt strain (10 ) 3.366 2.948 1.15 Maximum crack width/mm 3.34 3.16 1.06 θ ¼ 0:012 M/(KN·m) 74.2 62.8 1.18 –3 High-strength bolt strain (10 ) 4.269 3.625 1.17 Maximum crack width/mm 7.07 6.42 1.10 θ ¼ 0:02 M/(KN·m) 77.5 70.3 1.11 –3 High-strength bolt strain (10 ) 4.812 4.263 1.13 Maximum crack width/mm 12.41 10.25 1.21 θ ¼ 0:03 M/(KN·m) 80.1 75.6 1.06 –3 High-strength bolt strain (10 ) 6.274 5.631 1.12 Maximum crack width/mm 15.28 16.36 0.93 θ ¼ 0:04 M/(KN·m) 85.7 83.2 1.03 –3 High-strength bolt strain (10 ) 7.265 6.948 1.05 Maximum crack width/mm 25.96 23.62 1.10 Ultimate bearing M/(KN·m) 87.2 91.6 0.95 capacity 218 P. WANG ET AL. When the bending moment of joint section is simulation results were compared to obtain the varia- small, the section angle of joint is small. As the tion trend of bending stiﬀness of transverse joints. bending moment increases, the amount of opening A method is proposed for determining the bending of joint section increases, the concrete in the com- stiﬀness of transverse joints. pression zone collapses, and the bolt yields. At this (1) According to the change process of transverse stage, the bending stiﬀness of the joint decreases, joint section, a calculation model and analytical for- even by an order of magnitude (Li Xin-Xing and Cao mula are proposed for the bending stiﬀness of trans- 2015). Figure 26 shows a two-stage method for verse joint. A comparison between the calculation determining the bending stiﬀness of a transverse results and simulation results shows that they agree joint. The two phases are the stable phase OA and well. thenonsteady phaseAB. TheslopesK1and K2 (2) When the bending moment of transverse joint corresponding to the OA segment and AB segment section is small, the bending moment-corner curve are the joint bending stiﬀness values of the stable increases linearly. As the bending moment increases, phase and unstable phase. The diﬀerence between the concrete crushes, and the bolt yields. The curve K1 and K2 is larger. When the bending stiﬀness of grows slowly. When the inﬂuencing depth of concrete joint is K1, the joint is in the normal stable working compressive strain in the compression zone is 0.5 H, state; when the bending stiﬀness of joint is K2, the the theoretical calculation result and numerical simu- joint section is in a nonsteady state, usually with lation result are closer. Therefore, it is recommended to cracks. take 0.5 H as the inﬂuencing depth of concrete com- Figure 26 shows that under the condition of diﬀer- pressive strain in the compression zone in the theore- ent axial force and bending moment combination con- tical calculation model of transverse joint bending ditions, when the joint section is subjected to a stable stiﬀness. force, the bending stiﬀness of joint does not change, (3) The performance of transverse joint bending and it becomes its own attribute of the joint and has stiﬀness is less aﬀected by the bolt tightening force, nothing to do with the external load. In the calculation increasing the tightening force of the bolt; the joint of an actual pipe corridor design, the bending stiﬀness section angle is reduced slightly; the joint bending of the joint can be selected by using the method of stiﬀness is increased. The radial position of the bolt two-stage bending stiﬀness of transverse joint pro- aﬀects the stability of compression section of joint posed in this paper. section. When the axial force increases, the eﬀect of bolt position on the bending stiﬀness of joint is reduced. The thickness of transverse joint signiﬁcantly 7. Conclusions aﬀects the joint stiﬀness. The thicker the joint, the greater the height of joint section of joint, and the In this study, a mechanical model which can character- constraint on the joint section is correspondingly ize the various stages of transverse joint from force to increased, that is the space and capacity of joint sec- failure and the corresponding theoretical analytical tion are reduced correspondingly, resulting in an expressions were established. Then, a sensitivity analy- increase in the bending stiﬀness. sis of the factors aﬀecting the bending stiﬀness of the (4) According to the variation trend of bending joint was carried out by numerical simulation. Finally, stiﬀness curve of transverse joint, the bending stiﬀness the theoretical calculation results and the numerical Figure 26. Phase stiﬀness model of transverse joints relationship diagram. JOURNAL OF ASIAN ARCHITECTURE AND BUILDING ENGINEERING 219 of transverse joint can be divided into the unsteady Jiang Jian-jing, L. X.-Z., and Y. Lie-ping. 2005. “Finite Element Analysis of Concrete Structures.” Journal of Tsinghua stage stiﬀness and stable stage stiﬀness, and the two- University(Science and Technology) 32 (1): 47–48. stage bending stiﬀness value method is proposed for Julian Canto, P., J. Curiel-Esparza, and V. Calvo. 2013. the transverse joint of utility tunnel joint. “Criticality and Threat Analysis on Utility Tunnels for Planning Security Policies of Utilities in Urban Underground Space.” Expert Systems with Applications 40 (5): 4707–4714. doi:10.1016/j.eswa.2013.02.031. Disclosure statement Lbobb, L., O. Blanpain, and F. Buyle-Bodin. 2004. “Promoting No potential conﬂict of interest was reported by the authors. the Urban Utilities Tunnel Technique Using a Decision-making Approach.” Tunneling and Underground Space Technology 12 (3): 256–261. Li Xin-Xing, Y. Z.-H., and W.-H. Cao. 2015. “Model Test Study Funding on Joint Stiﬀness of Super-tunnel Assembled Segment Joints.” China Civil Engineering Journal 23 (S2): 315–320. This work was conducted with supports from the National Li Yu-Jie, H. P. 2012. “Inﬂuence Analysis on Longitudinal Natural Science Foundation of China (Grant Nos. 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Journal
Journal of Asian Architecture and Building Engineering
– Taylor & Francis
Published: May 3, 2020
Keywords: Precast prestressed utility tunnel; transverse joint; high-strength bolts; bending mechanical model