Damage Research of the Cut-and-Cover Tunnel under Static and Seismic Load

This article uses the finite element software ABAQUS to establish an damage constitutive model for cut-and-cover tunnels, which studies the damage parameters for different filling heights under static load and damage evolution under seismic load. It is found that high filling has a significant impact on the damage of cut-and-cover tunnels, and earthquake waves affect the degree and distribution of lining damage. By studying the model of setting the LRL, it was found that it can effectively reduce the degree of damage. Therefore, it is necessary to set a LRL for high backfill cut-and-cover tunnels. And the damage parameters of different parts of the cut-and-cover tunnel are analyzed, and it was found that the arch crown and arch shoulder of the cut-and-cover tunnel were the most prone to damage. Therefore, reinforcement measures should be taken in the structural design.


Introduction
The Loess Plateau region of China is characterized by numerous ravines and fragmented terrain, with numerous mountains and limited land resources.The scarcity of land resources has become the biggest bottleneck for the development of comprehensive transportation hubs.Due to the influence of local planning and urban construction, in order to meet higher linear standards and adapt to the complex terrain of mountainous areas with crisscrossing gullies, more and more high backfill soil, heavy loads, and weak foundation cut-and-cover tunnel have emerged.
High backfill soil can cause excessive soil pressure on the structure, resulting in varying degrees of damage.Multiple locations of the lining structure may crack, leading to deformation and water seepage of the lining.A series of problems can pose a serious threat to the safety and stability of the structure.At present, research on high backfill tunnels mostly focuses on the stress performance of the lining [1][2][3][4][5][6][7][8], but does not consider the damage characteristics and evolution of high backfill tunnels under static and seismic load.The damage law of high backfill tunnels is a key factor affecting their long-term structural safety.
The existing research indicates that using numerical simulation software for damage identification is reliable [9][10][11][12].Therefore, this article uses Abaqus software to study the damage evolution law of cut-and-cover tunnel and identify the weak positions.It is necessary to effectively prevent disasters and avoid risks caused by safety hazards in newly built and constructed high backfill tunnels.The existing research indicates that using numerical simulation software for damage identification is reliable [9][10][11][12].Therefore, this article uses Abaqus software to study the damage evolution law of cut-and-cover tunnel and identify the weak positions.It is necessary to effectively prevent disasters and avoid risks caused by safety hazards in newly built and constructed high backfill tunnels.

Numerical simulation
Figure1.Numerical model for:(a) condition 1;(b) condition 2 Figure 1 shows the numerical model, including condition 1 of the CCT (cut-and-cover tunnel) and condition 2 of the CCT with LRL (load reduction layer).The length of the numerical model is 130m, the depth is 20m, and the height is 95m-115m.The foundation thickness is 50m, the lining structure is 15m high, and the width is 21m.The LRL laid on the top of the lining is set to be 1.5 times the lining width [13], which is 31.5m, with a thickness of 4m.The backfill above the lining top is backfilled in layers of 5m, with a total height of 30-50m.The angle between the slopes on both sides and the horizontal direction is 70 º.
The numerical analysis model includes five materials: foundation, slope, lining, backfill, and LRL.In numerical calculations, the Mohr Coulomb model is used for backfill and slope, the elastic model is used for foundation, and the CDP (concrete damage plasticity) embedded in ABAQUS is used for lining.The material parameters refer to the research results of Li Sheng [14], and are shown in Table 1.Due to the high stiffness of the foundation, slope, and lining themselves, the displacement of the soil at these locations during the backfilling process is very small.The properties of the contact surfaces between these locations and the soil have a small impact for CCT [14].Therefore, no contact surfaces are set between the backfill and the foundation, slope, and lining.The compression damage parameter and tensile damage parameter are determined based on the "Code for Design of Concrete Structures" (GB50010-2010) [16], and use the Sidoroff energy equivalence principle [17], which means that the elastic residual energy generated by damaged and non-destructive materials under stress is the same in form.Therefore, it is only necessary to replace the stress with equivalent stress or replace the elastic modulus with the elastic modulus at the time of damage.
The formula for obtaining the compression damage parameter is: The formula for obtaining the tensile damage parameter is: Calculate the Damage parameters of concrete based on the above formula, and the results are shown in Table 3.

Result analysis
The degree of structural damage is divided into four stages based on the maximum damage parameter: normal-ues、temporarily-ues、maintenance-reinforcement、structural-safety、complete-destruction [18].Figure3 shows the damage parameter and degree at different backfill heights for condition 1 and condition 2. For the compressive damage of the structure, as the backfill height increases, the damage parameter of the lining increases, and the damage degree of the lining increases, indicating that the higher the backfill the more unfavorable it is for structural compression damage.The maximum compressive damage parameter for Condition 1 is 0.2384, and the maximum compressive damage parameter for Condition 2 is 0.05506, both occurring when the backfill height is 50m.Compared to condition 1, the maximum compressive damage parameter in condition 2 decreased by 76.9%, indicating that the LRL reduces the soil pressure above the lining by transferring the soil pressure of the inner soil column outward, while effectively reducing the degree of damage to the lining.When the height of the backfill soil is within 50m, condition 1 transitions from normal-ues to temporarily-ues at 30m, while condition 2 remains in the normal-ues stage.This indicates that if the backfill soil height of HFCCT needs to be set above 30m, load reduction measures should be taken to avoid affecting the long-term safety of the structure.
For the tensile damage of the structure, the damage parameters and degree of the lining will still increase with the increase of the backfill height, indicating that higher backfilling is unfavorable for both compressive and tensile damage of the structure.The maximum tense damage parameter for Condition 1 is 0.989, and the maximum tense damage parameter for Condition 2 is 0.106, both occurring at the backfill height of 50m, which is 4.148 times and 1.925 times the maximum compressive damage parameter.Compared to compressive damage, the lining in the tense damage within 50m of backfill has transformed from reaching the temporarily-ues stage to further reaching the complete-destruction stage, while condition 2 has transformed from normal-ues to further reaching the temporarily-ues stage.This indicates that due to the brittle nature of concrete, its tensile damage is more severe compared to the compressive damage of the lining.Condition 1 transitions from normalues stage to temporarily-ues stage at a backfill height of 30m, from maintenance-reinforcement stage at a backfill height of 32m, and from structural-safety stage at a backfill height of 32.5m.It is complete-destruction at a backfill height of 37.5m.However, condition 2 is still in the normal-ues stage when the backfill height is within 47.5m, and in the temporarily-ues stage when the backfill height is within 50m.Setting the LRL can effectively reduce the tension damage of the structure ， increase the backfill height of CCT.
Due to the severe tensile damage, the tensile damage parameters of different parts of HFCCT under two conditions were extracted, as shown in Figure 4.As the height of the backfill soil increases, the tensile damage of the lining in Condition 1 starts from the arch crown and arch waist, that is, tensile damage begins at 30m and increases dramatically at 32.5m and 35m.Therefore, HFCCT is more prone to damage at the arch crown and arch waist, as the arch crown of HFCCT is subjected to greater pressure from the backfill soil above, and the arch waist is located at the tangent point of the lining (i.e. the point of discontinuity in the arc), both of which are more prone to stress concentration.Afterwards, tensile damage occurred at the arch shoulder at a distance of 45m, and the damage parameter directly changed to 0.940, indicating that tensile damage only occurred at the arch shoulder and arch bottom after the structure was completely damaged.Moreover, when pressure was applied again after the structure was completely damaged, the arch shoulder could not bear the pressure and reached the complete damage stage in an instant.
Due to the fact that condition 2 reached the temporary use stage when backfilling soil at 50m, HFCCT only suffered damage at the arch crown and waist, and tensile damage began at 40m.The damage parameters of the arch crown are slightly greater than those of the arch waist, indicating that the arch crown is the most vulnerable area to damage.Corresponding measures to improve tensile strength should be designed in structural design, and key monitoring of the arch crown should be carried out in subsequent maintenance to ensure structural safety.

Dynamic analysis Figure 5. Acceleration time history curve
From the above, it can be seen that compared to CCT without LRL, which has a better damage situation under static action, condition 2 is still in normal-use within a filling height of 27.5m.At present, the filling height of CCT in China is usually 25m, so the CCT with a filling height of 25m with LRL is selected for dynamic analysis.
According to the "Seismic Parameter Zoning Map of China" (GB18306-2015) , the basic peak acceleration of the engineering site is 0.30g.Therefore, this article selects the EL-Centro wave with a peak acceleration of 0.3g as the seismic input.The acceleration time history curve of the seismic wave is shown in Figure 5.

Figure 3 .
Figure 3. Damage parameter and degree at different backfill heights under: (a) compressive stress; (b) tensile stress

Figure 4 .
Figure 4. Damage parameter in different parts of the HFCCT for: (a) condition 1; (b) condition 2

Figure 6 .
Figure 6.Damage cloud atlas of CCT under seismic load Figure 6 shows the damage cloud atlas of CCT under seismic load.The lining structure began to show damage from the inside of the arch bottom at 0.83 seconds, with a maximum damage parameter of 0.0385.At 3.56s, the damage at the bottom of the arch penetrated and developed upwards, with damage occurring at both the arch waist and crown.The maximum damage parameter was 0.404, reaching the stage of requiring maintenance and reinforcement.The lining structure reaches the complete-destruction stage at 7.29 seconds, during which multiple damages occur, with the arch shoulder and arch bottom being the most severely damaged, and the arch waist also reaching the structural-safety stage.Therefore, in the seismic design of CCT structures, it is necessary to reinforce weak points such as the arch bottom, arch shoulder, and arch waist.

Table 1 .
ModelFor other damage parameters of the CDP model, after multiple numerical simulations and combined with the modeling experience of ABAQUS software, show in Table2.

Table 2 .
Model parameters

Table 3 .
Damage parametersBased on the data in the table 2, draw the stress-strain curve of C30 concrete, as shown in Figure2.