3.2.1. Modelling
- 1.
Basic assumptions of the model
Because the actual project support structure, ground conditions, and construction situation are more complex, and the pit excavation is affected by spatial and temporal effects and other factors, the actual pit project is reasonably simplified and assumed to a certain extent to ensure that the calculation model can be optimized and the calculation efficiency can be improved without affecting the accuracy and authenticity of the calculation results. The specific assumptions and simplifications are as follows:
The length of the deep foundation pit in this subway station is large and the width of the pit is not completely uniform. The area near the monitoring section in
Figure 5 is selected and simplified as an equal-width pit for numerical analysis.
The soil and structural materials are isotropic, with a Moore–Coulomb elastic–plastic principal model for the soil, an elastic model for the concrete, and an elastic–plastic model for the steel pipe and DC joint.
Soils and diaphragm walls were simulated using 3D solid units, and DC joints and steel supports were simulated using 1D beam units.
The pit was constructed through out-of-pit descent, and the groundwater level near the pit was found to be below the bottom of the pit in the actual observation, so the effect of groundwater was not considered in the finite element model.
- 2.
Basic Dimensions of the Finite Element Model
The standard section of the foundation pit is about 21 m wide and 16.71 m deep, and the embedment depth of the diaphragm wall is 7.5 m. The steel supports are made of steel pipes with a 609 mm outer diameter and a 16 mm wall thickness. The spacing of the first steel support is 6 m, and the spacing of the second and third steel supports is 3 m. In order to reduce the influence of the model boundary effect on the numerical calculation of pit excavation, a 3–5-fold pit excavation depth is taken as the length of the model, and a 2–4-fold pit excavation depth is taken as the height of the model. Therefore, the length of the model is 120 m, the width is 42 m, and the height is 60 m. The X direction in the model corresponds to the east direction of the actual project, the Y direction in the model corresponds to the north direction of the actual project, and the Z direction in the model corresponds to the depth direction of the actual project; the finite element model is shown in
Figure 13. The solid cells are meshed with C3D8, and all meshes are hexahedral meshes. The beam cells are meshed with B31. The soil mesh in the range of one times the width of the pit is encrypted, and a total of 54,777 meshes are divided.
- 3.
Material Parameters
Due to the large size of the pit, it is difficult to establish a refined DC joint model. In order to simplify the calculation, the original DC joint is equivalent to a 1 m long section of steel pipe support with a 609 mm OD and 16 mm wall thickness, and in order to restore the bearing capacity of the DC joint, it is necessary to discount the performance of the equivalent section of steel support. According to the study on the weakening rate of the steel support at the DC joint in
Section 3.1, the yield load, initial compressive stiffness, and ultimate load at the DC joint are about 45.9% and 18.7% of the steel pipe support with an OD of 609 mm and a wall thickness of 16 mm. Therefore, the yield strength, elastic modulus, and ultimate strength of the equivalent section of the steel support are discounted according to this ratio, and the stress–strain relationship of the equivalent section of the steel support material after discounting is shown in
Table 4 [
22]. The stress–strain relationship of a normal steel support is selected according to
Table 5 [
20]. The underground diaphragm wall is made of C30 concrete and the bottom slab is made of C45 concrete. Other material parameters of the steel support, diaphragm wall, and base plate are shown in
Table 6.
The material parameters of each soil layer in the finite element model are shown in
Table 1.
- 4.
Pre-axial Force Application
The effect of applying pre-axial force is achieved by changing the temperature of the steel support in the equivalent section to make it expand. The initial temperature of the finite element model is set to 0 °C. The following relationship exists between the steel support pre-axial force (
Fa) and the temperature difference (Δ
T):
where
Eequ is the elastic modulus of the steel support of the equivalent section,
Aequ is the cross-sectional area of the steel support of the equivalent section, and
α1 is the coefficient of linear expansion of steel, which is taken as 1.25 × 10
−5/°C.
According to
Table 2, the design values of the pre-axial force of the first, second, and third steel supports are 180 kN, 300 kN, and 345 kN, respectively, while in the actual erection process, the pre-axial force is greatly lost in a short time after the erection is completed. In order to make the numerical results more accurate, the pre-axial force of each steel support in the finite element model is adopted as the corresponding pre-axial force before the soil excavation below. Therefore, the preloaded axial forces of the second and third steel supports are 210 kN and 231.2 kN. The preloaded axial force of the first steel support is basically stable after 12 h of erection because the soil below has not been excavated for a long period of time after erection, and the preloaded axial force of the first steel support is adopted as the preloaded axial force 12 h after erection, which is 117 kN. The preloaded axial forces of the three steel supports are about 70% of the design value.
- 5.
Contact Forms and Boundary Conditions
According to the collected data of the axial force of steel supports in the foundation pit, it can be seen that the steel support is always under pressure, which means that it is always in compression and always connected with the underground diaphragm wall, so the binding constraint is used between the steel support and the underground diaphragm wall. The soil body of the diaphragm wall is synergistically stressed by friction, and the contact form between the soil body and the diaphragm wall is set as surface-to-surface; the normal direction is set as hard contact and separation after contact is allowed; and the tangential direction is defined as penalized friction, isotropic, and the coefficient of friction is 0.577 [
23]. Specific forms of contact between the individual components in the model are shown in
Table 7.
The boundary conditions of the finite element model are set in the initial step of the ground stress equilibrium, and the displacement along the x direction is limited for the boundaries on the east and west sides of the soil body; the displacement along the y direction is limited for the boundaries on the south and north sides of the soil body and the underground diaphragm wall; and the displacement along the arbitrary direction is limited for the bottom of the soil body. The boundary conditions of the finite element model are shown in
Figure 14.
- 6.
Construction Process
In the actual project, the foundation pit excavation is a layered excavation, not a one-time excavation to the bottom of the foundation pit. In order to simulate the dynamic process of the foundation pit excavation in the actual project, six processes are set up according to the actual construction sequence, as shown in
Table 8.
Since this research focuses on the influence of the steel support system on the stability of the enclosure structure without considering the influence of the diaphragm wall, the diaphragm wall will be set up in the process of geostatic stress balance in the soil body. Construction loads of 30 kPa and personnel loads were applied at the bottom of the pit after each step of soil excavation.
3.2.2. Analysis of Numerical Results
- 1.
Comparative Analysis of the Numerical and Measured Results of the Axial Force of the Steel Support
The numerical results of the axial force of the first steel support and the measured results are shown in
Figure 15a. The numerical results are larger than the measured results, but the general trends of the two coincide. Especially before the excavation of the third soil layer, the maximum error between the numerical results and the measured results is not more than 12%. In the excavation of the third layer of soil and the subsequent construction process, the numerical results showed an increasing trend, while the monitoring results showed a gradual decrease and finally remained stable, which is mainly due to the fact that in these steps, the construction site is in the stage of the largest workload, both soil excavation and structural operations, so the steel support is more disturbed, which is prone to causing the DC joint to loosen and reducing the axial force of the steel support. Zhang [
16] applied a DC joint in this pit project and monitored the steel support axial force, and the change rule of the monitored steel support axial force was more consistent with the numerical simulation results in this section; especially after the removal of the third steel support, the axial force of the first steel support increased significantly. Therefore, it is further verified that the decrease in the first steel support axial force in the third soil excavation and the subsequent construction process is caused by the shortening of the steel support due to the loosening of the steel wedge.
A comparative analysis of the numerical results and measured results for the second steel support under each construction process is given in
Figure 15b. The numerical results are still larger than the measured results, but the overall trend matches. The axial force of the second steel support increased rapidly during the excavation of the second soil layer and the early stage of the excavation of the third soil layer. In the monitoring data, the maximum value of the second steel support axial force during the excavation of the third layer of soil and the application of bedding and subgrade is 893 kN, and in the numerical results, the maximum value of the second steel support axial force after the completion of subgrade is 1024 kN; the error of the two is only 14%. Similar to the pattern in
Figure 15a, the measured data after the removal of the third steel support were relatively smooth; the second steel support axial force did not increase rapidly, while the numerical results showed that the second steel support axial force increased by 223 kN in this process. The same numerical results showed that the pattern coincided with the pattern of change in the axial force of the DC joint steel support with BFW applied, which was monitored in [
16].
The change rule of the third steel support axial force in measured data and numerical simulation is given in
Figure 15c. Because the numerical simulation involves the excavation of the third layer of soil and the construction of the bedding and subgrade combined into one calculation step, there are only two data points, which can not fully reflect the change rule in this section of the process. However, during the process of the excavation of the third layer of soil and the construction of the bedding and subgrade, the maximum measured axial force of the third steel support is 973 kN and the numerical result is 1014 kN, which are in good agreement with each other.
- 2.
Comparative Analysis of Numerical and Measured Horizontal Displacements of Diaphragm Walls
Figure 16 shows the comparison analysis of the numerical results of the horizontal displacement of the wall body under each process with the measured results, as well as showing the measured data for the removal of the third steel support after the horizontal displacement of the wall, and the numerical results of process 6 for the same construction step. It can be seen that the change rule of the two curves is almost the same, and the maximum displacement of the wall after the removal of the third steel support appeared at the original location of the third steel support. The numerical results are slightly smaller than the measured data, and the difference is about 2.4 mm. From process 2 to process 5, the maximum horizontal displacement of the wall body increases gradually, and the location of the maximum horizontal displacement of the wall body moves downward gradually with the excavation of the foundation pit.
Figure 17 gives the change rule of the maximum horizontal displacement of the diaphragm wall’s numerical results and measured results under each process. The overall rule of change is more consistent, especially in the second layer of soil body excavation before the numerical results and measured results match better. After the excavation of the second layer of soil and in the early stage of the excavation of the third layer of soil, the measured data have a larger increase than the numerical results in the construction process, which is mainly due to the fact that, for numerical analysis, the third layer of soil excavation and the construction of bedding sub-slabs are combined into a single step, and the sub-slabs limit the horizontal deformation of the diaphragm walls. During the removal of the third steel support, the numerical results increased more than the measured data; this is due to the fact that the removal of the steel support in the actual project is gradual, the data have a significant increase when the steel support is removed around the measurement point, and the removal of the subsequent support is accompanied by the construction of other structures, so the data at the point of measurement begin to level off and the increase is small. In the finite element analysis, the steel support removal was an overall removal; therefore, the removal of the third steel support in the numerical results caused a sharp increase in the maximum horizontal displacement of the wall.
- 3.
Comparative Analysis of Numerical and Measured Results of Surface Settlement
Figure 18 shows the numerical results of the settlement curve around the pit and the comparative analysis of the measured data; the change rule of the settlement curve at the three measurement points is in good agreement, and the farther away from the pit, the closer the monitoring data are to the numerical results. The main reason is that the closer the measurement point is to the pit, the greater the influence of pit excavation and enclosure structure construction, and the actual construction environment is much more complex than the numerical simulation. The numerical results of the settlement curves at the three measurement points and the measured data are basically in line with the rule of change of the numerical analysis results and are more satisfactory; the settlement is smaller. In the excavation of the third layer of soil and the application of bedding slabs, also due to the numerical simulation of these two steps being combined into one construction step, under the limitations of the subgrade, the numerical analysis of the surface settlement change is smaller. In the process of removing the third steel support, both the numerical results and the measured data showed a slight increase in settlement values, but the increase was smaller.
According to the comparative analysis of the numerical results and measured data of the steel support axial force, the horizontal displacement of the diaphragm wall, and the surface settlement around the foundation pit, the numerical results are in complete agreement with the trend of the measured data. It is verified that the simulation method in this section for the DC joint equivalent to steel support is feasible. And before the excavation of the third layer of soil, the numerical results are in good agreement with the measured data, and the errors are all within 20%. In the subsequent construction process, due to the disturbance of the complex construction environment at the construction site, the steel wedge at the DC joint was loosened, and the axial force of the steel support was not well maintained, so the axial force of the steel support in the measured data did not increase, while the deformation of the enclosure structure increased more, resulting in a slight difference between the numerical results and the measured data. However, the results of the comparative analysis show that the numerical model established in this paper with the corresponding pit project of Beijing Metro Line 17 is basically able to reflect the force and deformation law of the pit, and the material parameters, contact form, and boundary conditions set in the model are reasonable, which can be used to analyze the influence of the local weakening of steel support on the stability of the enclosure structure under different conditions.