2.3.2. Numerical Simulation of Supporting Structure

The supporting structure around the foundation pit is a concrete diaphragm wall with concrete C35 and a thickness of 1000 mm, which extends into the soil layer at the bottom of the foundation pit to twice the depth of the foundation pit by underwater pouring technology. A concrete crown beam is set at the top of the concrete diaphragm wall and a concrete structure is adopted for the purlin of the foundation pit with concrete C30. A steel crown beam and a steel waist beam are arranged along the vertical height of the steel assembly bracing. Both the crown beam and waist beam adopt the section steel with the same specification, i.e., H400 × 400 × 13 × 21 (Q355b), and the upright column also adopts section steel H400 × 400 × 13 × 21 (Q355b).

Based on the above situation, the S4R element, that is, a four-node curved thin shell element with hourglass control, is used for the diaphragm wall and the surrounding concrete purlin plate where the global element size is 1.0 m and the number of the elements is about 28,000. The B31 element, i.e., a two-node spatial linear beam element, is adopted in the model for the steel assembly bracing, steel purlin beam, section steel column and concrete crown beam in which the global element size is 1.0 m and the number of the elements is about 52,000. The thermal expansion coefficient of steel is <sup>α</sup> = 1.2 × <sup>10</sup>−5, the damping coefficient of steel is ζ<sup>S</sup> = 0.02, and that of reinforced concrete is ζ<sup>C</sup> = 0.02. The material parameters of each component of the foundation pit supporting structure are shown in Table 2, and the finite element model is shown in Figure 4. The outer soil and diaphragm wall have face-to-face contact, and the normal contact is set as hard contact which means that the normal pressure can be transmitted between the two contact surfaces only when they are not separated [22,23]. The penalty function is adopted in the tangential direction, and the friction coefficient is taken as 0.2.

**Table 2.** Physical and mechanical parameters of steel assembly bracing.


**Figure 4.** Numerical model of foundation pit braced by section steel assembly.

With the help of engineering experience, it can be concluded that the stiffness of reinforced concrete diaphragm walls, cement mixing pile and reinforced concrete brace around the wall is much larger than the vertical stiffness of steel assembly bracing, and the low-order natural frequency of the foundation pit support system should occur in the steel assembly bracing, which has been also proved by numerical results. The low-order vertical natural frequencies of the steel assembly bracing system are mainly concentrated in (6.16 Hz~7.02 Hz), and the first four natural frequencies and the corresponding vertical vibration modes are shown in Figures 5–8 as follows.

**Figure 5.** Vertical first-order vibration mode (6.16 Hz).

**Figure 6.** Vertical second-order vibration mode (6.31 Hz).

**Figure 7.** Vertical third-order vibration mode (6.59 Hz).

**Figure 8.** Vertical fourth-order vibration mode (7.02 Hz).

It can be found that the low-order natural frequencies of the steel assembly bracing are mainly concentrated on the T01 steel support shown in Figure 1, and it is easier to cause T01 vibration when the earthwork truck drives over the concrete trestle bridge. The numerical analysis results preliminarily prove the problems reflected by construction workers.

#### 2.3.3. Acting Load

It has been proved that the internal force changes of steel bracing under the action of temperature cannot be ignored. Considering the abnormal vibration of T01 complained of by workers in this project, it is necessary to consider the combined action problem of temperature and vibration of the steel assembly bracing in both field monitoring and calculation analysis. When the site-monitoring system was established, the construction stage was in the binding steel bars and pouring concrete on the right foundation pit bottom plate near T01, while the left side was in the stage of outward soil transportation. Therefore, the working conditions of the construction site were complicated. As far as temperature changes are concerned, from August to November 2022, the 100 consecutive days of monitoring showed that the strain and temperature monitoring data of the steel assembly bracing changed little at night, while the steel surface temperature of the first steel assembly bracing of T01 ranged from 10.9 ◦C to 51.6 ◦C during the day, and the compressive strain of the brace decreased or increased with the temperature obviously. During the 100 days of real-time online monitoring, even in October when the temperature drops, for example, the lowest temperature of steel was 26.0 ◦C at 4 am on October 3, the highest temperature of steel was 51.6 ◦C at 14 pm, and the temperature difference between high and low was 25.6 ◦C. On that day, the axial static compressive strain SSTS-01 increased by 156.3 με with the temperature, and the similar high temperature environment frequently occurred within three months. The temperature changes of the steels from 12 August to 22 November is shown in Figure 9.

**Figure 9.** Temperature–strain diagram of steel assembly bracing during monitoring period (12 August to 22 November 2022).

As for the vertical vibration problem of steel bracing, since the site is in the construction stage, the vibration sources of structure include: (1) the vibration caused by earthwork truck running; (2) the vibration caused by pouring concrete in the foundation pit bottom plate; (3) the vibration caused by tower crane running and hoisting construction materials, and vibration caused by various construction machines and tools. Frankly speaking, it is extremely difficult to accurately analyze the steel assembly bracing under the action of each vibration source. The multi-day vibration monitoring data show that the vertical vibration of the reinforced concrete trestle bridge and steel assembly bracing increases obviously when the earthwork truck passes through the trestle bridge, which further shows that the earthwork truck passing through the trestle bridge is the main reason for the significant vibration of T01. Video monitoring of the speed of earthwork trucks on the trestle is about 10 km/h. The truck is fully loaded and the roof soil layer is neatly covered, and the average total mass weighed is 20,000 kg. In order to obtain the moving load of the truck running on the trestle, a vertical vibration sensor is installed on one of the trucks to collect the vertical vibration monitoring data of the vehicle. The vibration action during the driving process of the vehicle is shown in Figures 10 and 11 below. The vertical vibration responses of trestle ground vibration acceleration monitoring point 3AS-01 and steel support vibration acceleration monitoring point 3AS-02 at the same time are shown in Figures 12 and 13. It can be seen from the vibration time history and frequency spectrum curves in Figures 10 and 12 that the first-order frequency (Figure 10) of the vehicle action when the truck passes through the concrete trestle is basically consistent with the first-order dominant frequency of the vertical trestle response. The trestle vibration contains forced vibration components, and the frequency components are complex. The first frequency of the vibration response in Figure 13 is 6.661 Hz, which is close to the vertical natural frequency of the bracing in Figure 7 of numerical analysis. The vertical vibration of the bracing is mainly caused by resonance.

During numerical analysis, the vibration effect of earthwork truck as the unique vibration source is considered and the static and dynamic strain of steel assembly bracing at the highest temperature difference are only considered. With regard to the vibration calculation input, the amplitude modulation input model of Figure 10 is calculated based on the maximum value Atbt.max of the vibration response of the concrete trestle bridge (purlin) in Figure 14, such that Atbt.max of Figure 12 is equal to Atbt.max of Figure 14. The time history curve of vehicle vibration acceleration after amplitude modulation in Figure 10 was taken as the calculation input.

**Figure 10.** Vibration action of earthwork truck.

**Figure 11.** Test system of vehicle vibration.

**Figure 12.** Vibration response of concrete trestle bridge.

**Figure 13.** Vibration response of steel assembly bracing.

In order to simulate the influence of the vertical vibration of vehicles, eight concentrated forces are set in this model to represent the mass distribution of vehicles on the trestle bridge. The numerical values are calculated according to the vehicle weight and the vehicle mass distribution percentage. The first half of the earthwork vehicle accounts for 36% of the total mass of the vehicle, and the second half accounts for 64% of the total mass of the vehicle, and then the mass is evenly distributed to the concentrated force in the area located. During numerical analysis, the total mass of the vehicle is taken as 20,000 kg, and the front

and rear wheels of the vehicle are distributed in proportion, in which the concentrated forces exerted by the front wheels RP-1 to RP-4 are all 1800 kg, and the concentrated forces exerted by the rear wheels RP-5 to RP-8 are all 3200 kg, as shown in Figure 15. The time history curve of vehicle vibration acceleration after amplitude modulation is assigned as the amplitude curve which is multiplied by the above mass of the vehicle to obtain the dynamic load-time history curve. Finally, the dynamic load action can be analyzed. It is assumed that the most unfavorable working condition is considered, that is a linear combination of the maximum temperature difference of steel assembly bracing and the maximum vibration response amplitude of the trestle which occur at the same time.

**Figure 14.** Maximum vibration response of trestle bridge during monitoring period.

**Figure 15.** Mass distribution of front and rear wheels of earthwork trucks.
