Study on Influence of Tension Height of Steel Strand on Displacement of Foundation Pit Supported by Fish-bellied beams

The steel support system of prestressed fish-bellied beams can reliably control the deformation of foundation pit and provide open excavation space for foundation pit excavation, in which the triangle plate plays an important role in the fish-bellied beams system. But the deformation of the triangle plate and the steel strand is too large is a common problem in the foundation pit support, through the analysis of the stability of the triangle plate, it is found that the tension point height is an important factor leading to the deformation of too large. Through MIDAS/GEN analysis, it is found that the increase of the tension point height of the strand is conducive to the control of the displacement of the connecting part, and with the increase of the tension point of the strand, the anti-impact stability of the fish-bellied beams system is gradually enhanced. Therefore, by changing the tension height of the steel strand, the supporting system of the fish-bellied beams is optimized.


Introduction
Prestressed fish-bellied beams system has been widely used in practical foundation pit engineering because of its unique advantages.Many scholars through theoretical analysis, simulation test, field monitoring and other ways, through comparative analysis, proved that the prestressed fish-bellied beams system in the engineering application of excellent performance [1][2][3][4], in the future foundation pit support structure research occupies an important position [5][6][7][8].Among them, the triangle plate plays an important role in the fish-bellied beams system.Yu Xu [9] et al. took a foundation pit project in Hefei as an example to study the prestressed fish-bellied beams system by using mechanical analysis and finite element simulation.The withstand force analysis shows that the triangle plate is very important to the overall displacement control of the fish-bellied beams structure, and the control is the weakest.The structure will shift upward or downward under the action of external load, especially the deformation of the triangle plate and the steel strand will be obviously too large, which is a common problem in the foundation pit.If the deformation is too large, it will greatly reduce the bearing capacity of the fish-bellied beams, thus affecting the safety of the foundation pit.Therefore, in order to ensure the safety of the foundation pit, it is necessary to optimize the connection of the triangle plate and the steel strand in the fish-bellied beams system.

Theoretical analysis
The joint of the steel strand and the triangle plate is often the place where the force is weak and the deformation is large.This is because the connecting part is the meeting point of the opposite brace, the corner brace and the fish-bellied beams, the force is complicated and the role is important.The force analysis of the connecting piece shows that the interface shear V between the connecting piece and the section steel or waist beam is mainly composed of three parts: (1) the shear force generated by the tension of the steel strand; (2) the shear force generated by the splay brace or corner brace directly supporting the connecting part; (3) the shear force caused by bending of the composite wale, and the interface shear force V should be balanced by calculating the shear measures such as bolts (or anchor bolts) and Anti-shear parts set on the joint surface of the composite wale.Figure 1   According to the current specification, as shown in the figure, the tension point of the steel strand is low, that is, the h value is small, the bending moment value M is large, which is unfavorable to the displacement control at the connecting part, so it is necessary to optimize the tension point of the steel strand.

The influence of tension point height on foundation pit deformation
By changing the height of the tension point of the steel strand in the way shown in the figure 2, figure 3 below, the maximum displacement value of the connection part in the Y direction is analyzed and compared.0 point is the intersection point between the direct tension steel strand and the boundary of the triangle connecting part, the distance between 0 point and the vertex of the connecting part is 6 parts, so as to separate 5 intersection points, keep the length and position of the straight belly rod unchanged, adjust the intersection point of the steel strand and the connecting part.MIDAS/GEN is an analysis and design software widely used in the construction industry,so analyze and compare by MIDAS/GEN.The simulation results are sorted as follows: the horizontal coordinate is the tension point label of the steel strand in table 1, and the vertical coordinate in the figure 5 is the maximum displacement (mm) of the connecting part in the Y direction.It can be found that the increase of the tension point height of the strand is conducive to the control of the displacement of the connecting part, and with the increase of the tension point height, the maximum displacement of the foundation pit is gradually transferred from the connection point of the strand to both sides, that is, the local stiffness of the weak position of the connecting part is improved.Through simulation, a balance point can be found between the local stiffness and the overall stiffness, so that the overall resistance to deformation of the foundation pit can achieve the best.

Basic theory of buckling analysis of impact load
Structural stability analysis methods include linear buckling analysis (eigenvalue buckling analysis) and nonlinear buckling analysis (geometric nonlinear instability analysis).In practical projects, the buckling of many structures is close to the linear branch buckling, and the linear buckling analysis can reflect the stability of the structure to some extent.The analysis in MIDAS/GEN mainly [10]focuses on linear analysis.Subspace iteration method is used for buckling analysis.The buckling analysis of MIDAS/GEN can be used for stability analysis under specific loads.In buckling analysis, most attention is usually given to the minimum load that causes the structure to buckle or the eigenvalue [11][12]of the first order buckling mode.After completing the buckling analysis, look at the eigenvalue of the first order buckling mode, which is the critical load factor.
The impact load and boundary conditions of the model should be set reasonably to explore the influence of the change of tension point height on the anti-impact stability of the fish-bellied beams system.The loading time of the impact load is short, and the magnitude of the load varies considerably in a very short period of time, so the acceleration varies drastically and is not easy to measure directly.In MIDAS/GEN, there are two methods to simulate the impact load, namely equivalent static load and time-history load, and the dynamic response of the structure under the impact load can be obtained.
(a) Equivalent static load: When the impact load is equivalent to the static load, it needs to be multiplied by the impact coefficient, which can be determined according to the actual situation and can be approximated as 1.1~1.3.The impact load is applied by the node load; (b) time history load: time history analysis is a dynamic analysis method, through the gradual integration to solve the structural motion differential equation, mostly used in seismic analysis and research.The impact load can be defined by function in engineering.This is achieved [13]by setting the time history load function and applying the node dynamic load.
Considering that when the prestress is applied to the fish-bellied beams system, the structure will squeeze the soil under the action of the prestress, so as to stimulate the passive earth pressure of the soil.Therefore, it is necessary to set a normal spring only under pressure on the joints around purlin to approximate the passive earth pressure of the soil.When the elastic action of the surrounding soil is not considered, the surrounding nodes of the structure are restrained in degrees of freedom by means of general supports.

Influence of tension point height on structural stability
From the above, it can be seen that the increase of the tension point height of the strand is conducive to the control of the displacement of the connecting part.Therefore, the influence of the change of tension point height on the anti-impact stability of the fish-bellied beams system is explored here, as shown in figure 6.A group of five different tension points of the strand are set and the deformation of the structure is checked through MIDAS/GEN analysis.It can be seen that the buckling characteristic value of the structure gradually increases with the increase of the tension point of the strand, which means that the stability of the fish-bellied beams system against impact tends to increase with the increase of the tension point of the strand.
It can be seen from the Technical Regulations on Steel Support for Foundation Pit of Prestressed fish-bellied beams that the Angle between the end span of the fish-bellied beams and the upper string beam should not be greater than 40°.At the same time, it can be seen from the above numerical simulation that the higher the tensile point height of the steel strand, the stronger the anti-impact stability of the fish-bellied beams, so the tensile point height of the steel strand can be selected at position 5. Therefore, it is recommended that the tensile point height of the strand should be chosen at 2/3 of the side length of the triangle plate.

Conclusion
By analyzing the stability of the triangle plate, it is concluded that the height of the tension point of the steel strand has an influence on the displacement control of the triangle connecting part, which can be obtained by changing the height of the tension point of the steel strand.
(1) The increase of the height of the tension point of the steel strand is conducive to the control of the displacement of the connecting part, and with the increase of the height of the tension point, the maximum displacement of the foundation pit is gradually transferred from the connection of the steel strand to both sides, that is, the local stiffness of the weak position of the connecting part is improved.
(2) With the increase of the tension point of the steel strand, the anti-impact stability of the fish-bellied beams system is gradually enhanced.It is concluded that the best choice of the tension point height of the strand is 2/3 of the side length of the triangle plate.
is a schematic diagram of the force of the triangular connecting part.

Figure 1 .
Figure 1.Force diagram of triangular connecting part

Figure 5 .
Figure 5.The maximum displacement at different tension points

Figure 6 .
Figure 6.Diagram of steel strand tensioning points

Figure 7 .
Figure 7.The First order eigenvalues of buckling for structures under different tensioning points

Table 1 .
Maximum displacement of plane under different tension points