The Karnapuri River tunnel is located in Chittagong, Bangladesh and connects the east and west banks of Karnapuri River at the estuary. The shield tunnel is 2450 m long and is assembled with 1225 ring segments. The tunnel depth ranges from approximately 7–32 m, with a maximum water pressure of about 4 bar. The stratigraphic distribution of the tunnel site is shown in Figure 1.

The outer diameter of the tunnel is 10.8 m, and the thickness of the segment is 0.5 m, and the width of the segment is 2 m. Each ring lining consists of 1 K segment, two adjacent segments (L1, L2), and five standard segments (B1–B5). The longitudinal joints are connected by Class 8.8 M30 bolts, while the circumferential joints are connected by Class 8.8 M36 bolts. The central angle of the adjacent segments and the standard segments is 46.9°, and the central angle of the K segment is 31.7°. Each adjacent and standard segment has three force transfer platforms, and the K segment has two force transfer platforms. The thickness of the force transfer platform is 4 mm.

The dimensions of the segments, as well as the dimensions and positions of the force transfer platform, hand holes, and bolt holes as shown in Figure 2. It is worth noting that there was a 32-mm deviation between the center lines of the force transfer platforms and the center line of the segment (Figure 2B). As the positions of the force transfer platforms are the same as those of the jacks, the forces acting on the segment is always eccentric during the jacking process.

The shield machine is equipped with 23 jacks, which are divided into four zones. Jacks No. 21–23 and No. 1–3, No. 4–8, No. 9–15, and No. 16–20 are in the upper, right, lower and left zones, respectively. The central angles of the upper, lower, left, and right zones are 94°, 110°, 78°, and 78°, respectively (Figure 3A).

Guide bars are installed at the tail of the shield machine to avoid excessive jack deflection angles. The dimensions of the guide bars are 30 mm in height, 50 mm in width, 2795 mm in length and they are arranged in a circumferential direction, with a central angle of 8° between adjacent guide bars. The distance between the guide bar and the jack is 300 mm. There are four shield tail brushes at machine tail. The distances from the end of the guide bars for the four tail brushes are 200, 650, 1050, and 1500 mm, respectively (Figure 3B).

A total of 927 cracks were identified in the left tunnel, and the segment rings with cracks accounted for 47.7% of the total number of segment rings. The cracks could be divided into five types: positive, backward, handhole, corner and circumferential cracks. The handhole cracks started from the end of the bolts and developed obliquely (Figure 4).

The proportion of each crack type is illustrated in Figure 5. Positive cracks accounted for the largest proportion, followed by the backward and circumferential cracks. These three types of cracks accounted for 95% of the total cracks. The focus of the work was therefore on the causes of the longitudinal and circumferential cracks.

Considering that the dominant loads acting on segments were the thrust of the jacks before the segments were pushed out from the shield tail, the number of longitudinal cracks at locations of the 23 jacks was counted (Figure 6). The longitudinal cracks occurred mainly in the down zone of the jacks, followed by the left zone. Cracks in the lower and left zones accounted for 76% and 16.21% of the total cracks, respectively. Of the 23 jacks, the largest proportion of longitudinal cracks was found at jacks 13 and 14, which were mainly in the down zone closest to the left zone of the jack.

To investigate the relationship between the cracks and segment type, eight segments were divided into 23 zones (labelled as A–W), with the boundary of the adjacent zones being the bisector between the two force transfer platforms (Figure 7A).

Figure 7B lists the numbers of longitudinal cracks in each zone of the different segments. The largest proportion of longitudinal cracks was in zone J, followed by zone V. The segment with the most longitudinal cracks was B5, followed by L1, and the K segment had the least longitudinal cracks. For each segment, the zone with the largest proportion of cracks was the force transfer platform in the middle part, followed by the force transfer platform on the left.

The segments were assembled with staggered joints. Therefore, the segments could be divided into two types, namely, i.e., Type A and Type B according to the positional of the longitudinal joints of the front and rear rings in relation to and the segment of the objective ring, with the exception of the K segment. The proportion of longitudinal cracks in each type of segment is shown in Figure 8. Overall, 73.5% of the longitudinal cracks were observed in Type-A segments.

Figure 9 displays the distribution of the occurrence time of the longitudinal cracks. The current ring jacking indicates that the cracks were produced in the n-th segment when the n-th segment was jacked. The last ring jacking represents that the cracks were generated in the n-th segment when the (n+1)-th segment was jacked. The third ring jacking denote that the cracks were developed in the n-th segment when the (n+2)-th segment was jacked.

Figure 9, demonstrates that more than half of the cracks were formed during the current ring jacking stage. However, unlike different from previous studies, 38% of the cracks were formed during the last ring jacking stage. Considering that 93% of the cracks were formed in the current and last ring jacking stages, this study only concentrated on the cracks developed in these two jacking stages.

Since the segment cracks were primarily longitudinal, the main causes of the segment cracks were considered to be the same. Previous studies have linked formation of cracks to the thrust, torque, jacking speed, and posture of the shield machine. Therefore, the values of these tunneling parameters were utilized to analyze the causes of cracks. The equation for calculating the shield attitude adjustment could be given as: Δ = y f , n − y f , n − 1 + y t , n − y t , n − 1 2 + x f , n − x f , n − 1 + x t , n − x t , n − 1 2 (1) where Δ is the adjustment amount of the shield attitude between two segment rings; y f , n and y f , n − 1 are the vertical deviations of the shield head of the nth and (n−1)-th segments, respectively; y t , n and y t , n − 1 are the vertical deviations of the shield tail of the nth segment and the (n−1)-th segments, respectively; x f , n and x f , n − 1 are the horizontal deviations of the shield head of the nth and the (n−1)-th segments, respectively; x t , n and x t , n − 1 are the horizontal deviations of the shield tail of the nth and the (n−1)-th segments, respectively.

The average shield thrusts and cutter torques of the segments with and without cracks are indicated in Figure 10A. It can be seen that the average thrusts and cutter torques of the segments with cracks were lower than those without cracks, demonstrating that excessive thrusts and cutter torques were not the main causes of cracking in the segments.

The average tunneling speeds and attitude adjustment values of the segments with and without cracks are displayed in Figure 10B. It is indicated which shows that the average tunneling speed for the segments with cracks were lower than those without cracks. Hence, the large tunneling speed was not the main cause of cracking in the segments. However, the attitude adjustment value of the segments with cracks was 1.64 times higher than that without cracks, implying the attitude adjustment of the shield machine may be the cause of cracking in the segments.

For an individual segment ring, the jacking pressure in different zones and the shield tail clearance may cause cracks in the segments. As can be seen from Figure 10C, the largest average jacking pressure was found in the down and left zones. Excessive jacking pressure may have contributed to the cracking in the segments as the cracks in the down and left zones accounted for 76% and 16% of total cracks, respectively.

It can be seen from Figure 10D that the lower and left zones of the jacks with larger shield tail clearance values had a greater proportion of cracks compared to the up and right zones, indicating that the shield tail clearance was not the cause of cracking in the segments.

The analysis from the data in the previous sections, the B4 segment had the largest number of cracks. The positional of the segment ring with cracks and its front and rear rings was Type-A. Moreover, most cracks occurred in the current and the last ring jackings stage. Therefore, these two rings containing B4 segments were chosen for the further study. The n-th segment was divided into B3n, B4n, and B5n, while the (n+1)-th segments was divided into B3n+1 and B4n+1.

Figure 11 illustrates the finite element model constructed in this study. In order to simulate the interactions between the segments, circumferential pedestals were built for B3n, B5n, B3n+1, and B4n+1, and longitudinal pedestals were created for B3n, B4n, and B5n. For the B4n segment, there were two longitudinal pedestals, S and H, to simulate the uneven longitudinal support and assembly angles of the segments. Guide bars were set on the outer arc surfaces of the segments. Longitudinal bolts were adopted for the longitudinal and circumferential joints of the segments, and the clearance between the bolt and bolt hole was neglected. The handholes were simplified to be of a rectangle cross section. Steel rebars were placed in the segments of B4n, B3n+1, and B4n+1. In the numerical model, the solid elements were employed to simulate segments, bolts and pedestals, while the Truss elements were utilized to simulate the steel rebars (Zhang LB. et al., 2023a; Zhang JC. et al., 2023b).

The pedestals and guide bars were fully constrained, and Coulomb friction was assigned between the longitudinal and circumferential joints, as well as between the segments and the guide bars. The coefficient of friction was 0.5 between the longitudinal and circumferential joints (Zhang et al., 2021), and was 0.2 between the segments and the guide bars. The steel rebars and bolts were embedded in the model (Li et al., 2023).

The model was run in three phases (Figure 12). In the first phase, the n-th segment was jacked. The (n+1)-th segment and the corresponding bolts in the longitudinal and circumferential joints were not activated. In the second phase, the (n+1)-th segment was just assembled and was about to be jacked. In the third phase, the jacking of the (n+1)-th segment was completed, and the n-th segment was thrust out from the shield tail.

The loads applied to the segment are depicted in Figure 13. The designed pre-tightening forces of the longitudinal, and the circumferential bolts were 150 kN and 100 kN, respectively. The calculated handhole stresses of the longitudinal and circumferential bolts were 12.9 and 8.6 MPa, respectively. The jacking pressures in the down and left zones were similar, and the same was true for up and right zones, so the average pressures in the down zone (i.e., 23 MPa) and the up zone (i.e., 14.5 MPa) were taken as the jacking pressures. When the shield tail clearance was 110 mm (i.e., 0.5 MPa), the pressure in the down jacking zone was taken as the shield tail brush pressure for the n-th segment of the second phase and the (n+1)-th segment of the third phase (Wei, 2021). The shield tail sealing grease was set to 0.6 MPa based on actual practical conditions. In the third phase, when the n-th segment was thrust out from the shield tail, and the water and soil pressure of 0.45 MPa was at its maximum for the duration of the shield construction.

The above analysis confirmed that the shield attitude adjustment and poor assembly were two possible causes of the segment cracks, and they were which therefore selected for the further analysis. Attitude adjustment may cause jack eccentricity and deflection of the jack, while the transform platform lead to a 32-mm eccentricity of the boot (Figure 2B). Hence, the additional eccentricity was not studied. Six deflection angles (0°–5°) were studied in the sensitivity analysis of attitude adjustment. The distances between the segment and the guide bar in three cases were varied between 0 mm and 8 mm (Figure 14A). The clearance in the longitudinal and circumferential joint was not considered in the sensitivity analysis of attitude adjustment.

The assembly quality was reflected by the uneven longitudinal supports and V-shaped openings of the longitudinal joints. The uneven longitudinal support was at a distance of 1 mm, and the assembly angle of the longitudinal joint was 0.1°. The assembly clearance values of circumferential joints ranged from 0 to 4 mm. In this study, assembly clearance values of 0 and 4 mm were investigated. As shown in Figure 14B, the simulation scenarios included the uneven longitudinal support, V-shaped longitudinal opening, inverted V-shaped longitudinal opening, and continuous uneven longitudinal support. The jack pressures for the shield attitude adjustment conditions were set at 23 and 14.5 MPa, respectively. The jack deflection was not considered in the sensitivity analysis of assembly condition, while the jacking pressure was fixed at 23 MPa, and the distance between the segment and the guide bar was kept at 50 mm.

Although concrete damage is not necessarily manifested in the form of cracks, damage evolution is a precondition for the development of the cracks (Behnam et al., 2018). Hence, the concrete damage plasticity (CDP) model was introduced to evaluate crack development. When the tensile damage coefficient D t or the compressive damage coefficient D c were 1, the concrete was completely damaged, and when D t or D c becomes 0, the concrete was in an elastic state (Lubliner et al., 1989). The ratio of the biaxial yield stress to the uniaxial yield stress σ b 0 / σ c 0 was set to 1.16. The expansion angle ψ θ − f i and the change of expansion angle ε θ − f i under hydrostatic pressure condition were 35° and 0.1, respectively. The ratio of the tensile to the compressive stress was a constant with a value of 0.667, and the concrete viscosity parameter was 0.0005 (Jiang et al., 2020).

The stress-strain relationship of concrete under compression is determined by Eqs 2–6 (China Architecture and Building Press, 2010). σ c = 1 − d c E c ε c (2) d c = 1 − ρ c n n − 1 + x n   x ≤ 1 1 − ρ c α c x − 1 2 + x   x > 1 (3) ρ c = f c r E c ε c r (4) n = E c ε c r E c ε c r − f c r (5) x = ε ε c r (6)

In the equations, σ c is the concrete compressive stress, ε c is the concrete compressive strain, E c represents the concrete elastic modulus, d c is a uniaxial compressive damage evolution parameter, α c denotes the parameter of the descending segment of the concrete’s uniaxial stress-strain curve, f c r is the standard uniaxial compressive strength of concrete, and ε c r represents the peak compressive strain of concrete corresponding to f c r .

The stress-strain relationship of concrete under tension is determined by Eqs 7–10 (China Architecture and Building Press, 2010). σ t = 1 − d t E c ε t (7) d t = 1 − ρ t 1.2 − 0.2 x 5   x ≤ 1 1 − ρ t α t x − 1 1.7 + x   x > 1 (8) ρ t = f t r E c ε t r (9) x = ε ε t r (10) where σ t is the tensile stress of concrete, ε t is the tensile strain of concrete, d t is the damage evolution parameter of concrete under uniaxial tension, α t is the parameter value of the descending section of the stress–strain curve of concrete under uniaxial tension, f t r is the standard uniaxial tensile strength of concrete, and ε t r is the peak tensile strain of concrete corresponding to f t r .

Due to the linear stress-strain relationship of concrete in CDP, which is inconsistent with the specifications, it is necessary to manually set the yield points of concrete under compression and tension. If the yield points of tension and compression are set to σ t o = 0.8 f t r and σ c o = 0.6 f c r , respectively, the corresponding strains are ε t o = σ t o / E c and ε c o = σ c o / E c , respectively (Figure 15).

Once the modified stress-strain curve of concrete is obtained, the tensile damage factor and compression damage factor of concrete can be calculated based on the energy loss (Krajcinovic and Lemaître, 1007) as shown in Table 1. D t = 1 − ∫ σ t d ε t E c ε t 2 / 2 (11) D c = 1 − ∫ σ c d ε c E c ε c 2 (12)

The elastic modulus and Poisson’s ratio of the concrete were taken as 36 GPa and 0.2, respectively. , and the concrete Poisson’s ratio was 0.2. Reinforcement and bolts adopted a double-line constitutive law. The elastic modulus and the Poisson’s ratio of steel were 206 GPa and 0.31, respectively. The yield stress and plastic strain of the steel rebars and bolts are displayed in Table 2. The CDP model was adopted to describe the B4n, B4n+1, and B3n+1 segments. The elastic concrete model was applied to B5n, B3n, and the pedestals. A steel elastic model was assigned to the guide bars.

As segmental cracks could only be observed inside the tunnel, the analysis in this section concentrated on the cracks occurred on the segment inner surface. Figure 16 illustrates the damage results of the B4n segment in the first phase under various shield attitude adjustment conditions. The DAMAGET threshold for crack occurrence was defined as 0.95. Two major tensile cracks occurred in all the studied scenarios regardless of the deflection angle, while the crack lengths increased with the increasing deflection angle. Figure 17 shows the influence of the spacing between the guide bar and segment as well as the and deflection angle on the crack length.

When the jack deflection was 0°, the crack length remained constant regardless of the spacing between the guide bar and the segment, which was caused by the eccentricity of the platform. There was an upper limit to the crack length for each case of deflection angle. This was due to the outward bending moment of the segment induced by the jack deflection. Since the outer surface of the segment was constrained by guide bars, the segment did not deform towards the outer arc surface, thus preventing positive cracks from occurring. However, the restraining effect of guide bars was weakened when the distance between the outer arc surface of the segment and the guide bars became larger. The segment was constrained by the adjacent segments and bolts. On the other hand, the formation of cracks was inhibited when the spacing between the guide bar and the segment was small enough to restrain the deformation.

Figure 18 presents the crack lengths in three phases, where the positive cracks in the B4n segment caused by the jack deflection did not develop in the second and third phases. Therefore, the positive cracks caused by jack deflection mainly occurred during the current ring jacking stage, and subsequent tunneling contributed little to the development of positive cracks.

As shown in Figure 19, the crack lengths decreased significantly when the jacking pressure was 14.5 MPa, and the positive cracks were no longer obvious when the jack deflection angle was less than 3°.

Figure 20 presents the simulation results of a single-ring segment with the presence of uneven longitudinal support. When the assembly clearance was 0 mm, the right end of the B4n segment was deformed in the negative Z-axis direction during the jacking of the n-th segment, causing the tension on the end face and the formation of positive tensile cracks. Moreover, due to friction of the right-side segment and the constraint of the bolts, there was shear at the rear end of the uneven support, which resulted in backward shear cracks. During the jacking of the (n+1)-th segment, the positive cracks did not propagate, the length of the backward crack increased by 150 mm, and there were no cracks in the B3n+1 and B4n+1 segments. All cracks were formed in the current jacking stage, and the total number of cracks was 2. When the assembly clearance was 4 mm, the maximum length of the positive cracks was 600mm, which was an increase of 350 mm compared to the case of the tense assembly model. Meanwhile, during the last ring jacking stage, two positive tensile cracks developed on B4n+1, one backward shear crack developed on all B4n, B3n+1, and B4n+1 and one circumferential tensile crack developed on both B4n and B4n+1 the total number of cracks increased to 14.

Figure 21 shows the results of a single-ring segment with a V-shaped opening in the longitudinal joint. When the assembly clearance was 0 mm, the front end of B4n was under tension during the jacking of the n-th segment. Consequently, a positive tensile crack formed in the middle segment. The left end of B4n was subjected to the friction from the adjacent segment and the constraint from the bolts during deformation, which resulted in a circumferential tensile crack. During the jacking of the (n+1)-th segment, there was a clearance between B4n and pedestal H, and the left end of B4n continued to deform in the negative Z-axis direction. Due to frictional constraint at the left end, the length of the circumferential crack increased by 300 mm, and a new backward shear crack generated at the rear of B4n. The total number of cracks was 9. When the assembly clearance was 4 mm, the both ends of B4n were only constrained by the bolts, and the deformed in the negative Z-axis direction and were in contact with pedestals S and H. The maximum length of the positive cracks was 850mm, whereas in the tense assembly model the length was only 300 mm. Meanwhile, during the last ring jacking stage one positive tensile crack developed on B4n+1, one backward shear crack developed on B4n+1, two backward shear crack developed on B3n+1, and one circumferential tensile crack developed on B4n, the total number of cracks increased to 18.

Figure 22 presents the results of a single-ring segment with an inverted V-shaped opening in the longitudinal joint. When the assembly clearance was 0 mm, B4n was a simply supported beam that was restrained at both ends during the jacking of the nth segment. The rear end was under tension, so that multiple longitudinal shear and tensile cracks formed in the middle part of the segment. During the jacking of the (n+1)-th segment, the backward crack did not propagate and there were no cracks developed on the B3n+1 and B4n+1 segments due to the friction constraints on both ends of B4n. One positive tensile crack on B3n+1 occurred in the last ring jacking stage, and the total number of cracks was 7. When the assembly clearance was 4 mm, the length of the backward crack during jacking of the n-th segment was 250 mm longer than that when the assembly clearance was 0 mm due to the lack of friction constraints. The maximum length of the backward tensile crack was 1300 mm, while in the tense assembly model the length was 700 mm. Meanwhile, one positive tensile crack on B3n+1 and two backward shear cracks on B4n formed in the last ring jacking stage, the total number of cracks increased to 12.

Figure 23 shows the segment cracks formed due to the continuous uneven support. Compared with Figure 20, when the assembly clearance was 0 mm, the front and rear rings on the right end of B4n were not sufficiently restrained during the jacking of the (n+1)-th segment. The pressure on the segment led to the shear on the uneven platform and a new backward shear crack was formed. The left end of B4n+1 was deformed in the negative Z-axis direction, and one backward shear crack was generated due to the friction of the B3n+1 segment and the constraint of the bolts. One backward shear crack on B3n+1 occurred in the last ring jacking stage and the total number of cracks was 7. When the assembly clearance was 4 mm, the maximum length of the positive tensile crack was 500 mm, while in the tense assembly model the length was 200 mm. Meanwhile, one positive tensile crack developed both on B3n+1 and B4n+1, and one circumferential tensile crack developed on B4n in the last ring jacking stage, the total number of cracks increased to 12.