Design and optimization of an innovative lining structure for high-pressure water transmission tunnels subjected to strike-slip fault creep

The analysis presented in this section was based on the previous numerical modeling approach and structural arrangement. The effects of factors on the internal force response and fracture resistance of the tunnel structure were analyzed. These factors include the length of the concrete segment, the thickness of the cushion, and the number of bellows joints.

Effect of concrete segment length

This section investigates the impact of the concrete segment length on the structural behavior. In light of the common practice in tunnel construction, where concrete lining trolleys usually range from 6 to 12 m^9,19, concrete segment lengths of 6, 8, and 10 m were employed. While keeping the other parameters of the lining combination scheme constant, the concrete segment length was varied. The von Mises stress of the steel pipe and the deformation of the bellows joint showed negligible changes as the length of the segment increased from 6 to 10 m. Instead, the change mainly occurred in the concrete.

The analysis showed that the tensile damage of the concrete, which was predominantly caused by the water pressure, remained similar in the schemes with the three lengths. However, Fig. 19a shows that the maximum compressive damage values occurred at the bottom of the concrete tube in all the schemes, which increased with the increase in the lining segment length. Shortening the concrete segment length could simultaneously reduce the damage scope and extent. The established damage division intervals were employed to calculate the relative damage ratio by comparing the volume of the compressed damage elements in each interval, taking the segment length of 10 m as the reference. To gain further insight into the impact of the segment length, the relative damage ratio is presented in Fig. 19b.

Compressive damage of concrete for three length schemes: (a) damage contour and (b) relative damage ratio based on 10-m scheme.

Based on the results in Fig. 19b, it is clear that reducing the length of the concrete segments is an effective method for mitigating compressive damage in tunnels. Compared to the 10-m calculation scheme, the 6- and 8-m segments exhibited 50% and 20% less damage, respectively, in the 0–0.3 interval. Moreover, the 6-m scheme achieved a damage reduction of up to 70% in the 0.3–0.6 level, and there were no damaged elements in the greater-than-0.6 interval for both the 6- and 8-m schemes.

Based on the analysis of the axial force within the concrete (in Fig. 20) and a comparison with the unsegmented scheme, it is apparent that the inclusion of flexible joint segments could greatly diminish the axial force along the concrete. Further reduction of the concrete length could lead to even smaller axial forces. However, the use of shorter concrete segments could result in increased construction difficulties and project costs, which should be carefully considered in the design process.

Axial forces inside concrete for different schemes.

Effect of flexible joint length

Flexible joints often experience damage before the concrete segments due to their low moduli and large amounts of deformation. They can effectively absorb the deformation caused by the fault and protect the concrete sections from failure. To investigate the effect of the flexible joint length on the tunnel’s structural response, three commonly used lengths of 0.05, 0.5, and 1 m were adopted in this study, while keeping the other numerical parameters of the lining combination scheme constant. As the length of the flexible joint increased from 0.05 to 1 m, the von Mises stress of the steel pipe and the deformation of the bellows joints underwent little change, and the change mainly occurred in the concrete. The concrete compressive damage and its corresponding relative damage ratio are shown in Fig. 21a, b, respectively. The tensile damage of concrete and its corresponding relative damage ratio are shown in Fig. 21c, d, respectively.

Compressive and tensile damage of three flexible joint lengths: (a) compressive damage contours, (b) compressive relative damage ratio based on 0.05-m scheme, (c) tensile damage contour, and (d) tensile relative damage ratio based on 0.05-m scheme.

When using flexible joints with a length of 0.05 m, typical diagonal shear cracks appeared in the concrete within the fracture zone. Additionally, the tensile damage area showed a wide belt-like distribution. Meanwhile, as the length of the flexible joint increased to 0.5 m, the compressive damage zone showed a discontinuous block-like distribution, while the area of tensile damage showed a relatively narrow stripe shape. As the length of the flexible joint continued to increase, the degree of damage decreased further.

In the 0.5-m scheme, most of the compressive element damage values were concentrated in the 0–0.3 interval range, and only a few sporadic compressive areas existed at the waist of the concrete pipe in the 1-m scheme. The distribution and level of concrete tensile damage were approximately the same in the 0.5- and 1-m schemes. As shown in Fig. 21b, d, increasing the length of the flexible joint sharply decreased the concrete damage in tension and compression. It is important to note that a too long of a flexible joint may reduce the effectiveness of the concrete lining support.

Effect of cushion thickness

In the MFL structure, the cushion layer plays a crucial role. To investigate the effect of the cushion layer thickness on the stress and deformation of the lining structure, the cushion layer thickness was assumed to be 0.1, 0.4, 0.7, and 1 m. As the thickness of the cushion layer was increased from 0.1 to 1 m, the range of damage caused by compressive and tensile stresses on the concrete gradually expanded, while the degree of damage gradually decreased. The changes in both were not particularly significant. Furthermore, the thicker the cushion layer was, the lower the water pressure transmitted outward from the steel pipe to the concrete became. The von Mises stress of the steel pipe outside the fault range increased sharply, and the maximum stress of the steel pipe within the fault range decreased slightly when the cushion thickness increased from 0.1 to 0.4 m (Fig. 22). However, as the cushion thickness continued to increase, the rate of increase of the von Mises stress gradually decreased.

Von Mises stress curves for steel pipes with different cushion thicknesses.

To investigate the relationship between the deformation of the bellows joints and the cushion thickness, we assigned numbers 1–11 to the bellows joints based on their order from the hanging wall to the footwall. The effect of the cushion thickness on the deformation of the bellows joints is shown in Fig. 23.

Relationship between bellows joint deformation and cushion thickness: (a) total cumulative deformation of all bellows joints and (b) individual deformation of bellows joints within fault zone under different cushion thicknesses.

As per conventional understanding, a thicker cushion layer allows for more space for the bellows joint, which can increase the overall flexibility of the steel liner. This makes the structure more susceptible to deformation, resulting in greater total cumulative deformation. It is interesting that with the increase in the cushion thickness, the total cumulative deformation and individual deformation of the bellows joints showed a trend of increasing before decreasing. To explain this phenomenon, the axial displacement difference between the top and bottom points of the cross sections at both ends of each pipe segment were extracted, as shown in Fig. 24. This value reflected the degree of deflection of the steel segment. It can be seen that the rotation of the pipe segments was more pronounced near the middle of the fault zone.

Axial displacement difference curves of top and bottom points of pipe cross section.

The cushion layer in the MFL structure served dual purposes: on the one hand, it reduced the deformation transmitted from the concrete to the steel pipes by providing a buffering effect; on the other hand, it created the deformation space for the bellows joints and the steel pipe, thereby regulating the overall flexibility of the structure. Initially increasing the cushion layer thickness allowed for greater deformation of the bellows joints, resulting in an increase in the total cumulative deformation of the joints. This suggested that within a reasonable range, increasing the thickness of the cushion layer could better facilitate the displacement compensation function of the bellows joints. At this point, the second purpose of the cushion layer became dominant. Subsequently, as the cushion layer thickness continued to increase, the cushion partially absorbed displacement of the concrete, thereby decreasing the transmission of displacement from the concrete to the steel pipe. At this stage, the first purpose of the cushion layer became dominant. Additionally, the rotation of the steel pipe also contributed to the absorption of the displacement caused by the fault, leading to reduced compensation at the bellows joints.

In terms of the anti-fracture design of the lining structures, using an overly thick cushion layer is beneficial for minimizing the extent of the concrete damage. Nevertheless, such an approach may augment the von Mises stress of the steel pipe and diminish the displacement compensation function of the bellows joint. The thicker the cushion layer is, the larger the tunnel diameter is, and the less economical the project becomes. Consequently, the ideal thickness of the cushion layer should be ascertained via precise calculations.

Effect of number of bellows joints

The extrusion deformation of a steel pipe is mainly absorbed by bellows joints, and the number of bellows joints will directly affect the adaptability of the MFL structure to fault dislocations. With the engineering fortification distance and other parameters of the numerical model of the combination scheme unchanged, the number of bellows joints was varied by adjusting the lengths of the steel pipe segments. The number of bellows joints was set to six, 11, and 16. Increasing the number of bellows joints resulted in shorter lengths of the steel pipe segments, making the overall structure more flexible, as shown in Fig. 25a. This makes it easier for the steel lining to deflect in the direction of the fault dislocation, thereby reducing the damage caused by the extrusion of the steel pipe itself and the concrete. The effect of changing the number of bellows joints on the concrete was limited, with the main impact being on the stresses of the steel pipes and the deformation of the bellows joints.

(a) Axial displacement difference curves of top and bottom points of pipe cross section and (b) relationship between bellows joint deformation and number of bellows joints.

In contrast to the stress level of 184.8 MPa observed when using only six bellows joints, the use of shortened-steel pipe segments with 16 bellows joints resulted in a lower maximum von Mises stress of 154.7 MPa, representing a reduction of 16.3%. The total cumulative deformation values of all the bellows joints for different numbers of bellows joints are plotted in Fig. 25b.

The total deformation of the bellows joints remained near 160 mm with a small variation range; in all three cases, the bellows joints with the largest deformation were located at the intersection of the hanging wall with the fault zone, and the maximum deformation of a single bellows joint reached 60.64 mm when the number of bellows joints was six, while the value was 24.55 mm when the number of bellows joints was 16, which was 2.47 times greater than the value with six bellows joints. However, the value was 25.2 mm when the number of bellows joints was 11, which was not significantly different from the scheme with 16 joints.

From the perspective of the anti-fault design of the lining structure, using more bellows joints was beneficial for improving the ability of the tunnel to resist fault displacement. However, there was a marginal diminishing effect when increasing the number of bellows joints. That is, after reaching a certain number, further increasing the number of bellows joints had limited effects. The deformation differences between each bellows joint were also significant. Bellows joints with noticeable deformation were predominantly concentrated within the fault zone. When there were too many bellows joints, the deformation of the bellows joints near the edge of the engineering fortification zone was very small and did not have a corresponding effect. Therefore, excessive use of bellows joints in engineering projects can substantially increase the project costs. However, when there are too few bellows joints, deformation is likely to concentrate on a small number of such joints, which can cause structural breakdown and loss of normal operating capacity.