Analysis of Displacement Influence of Span of Prestressed Fish-Belly Beam on Foundation Pit Plane

As a new technology of antagonistic internal support, prestressed fish-bellied steel support system has been widely used in various foundation pit projects because of its advantages such as reutilization, effective displacement control and large mechanical operation space. But at present, the plane layout depends on experience, and has not yet formed a set of complete and reasonable plane layout methods. In the plane layout, the corner brace is arranged according to the condition of the plane stress balance of the corner brace, then the brace is arranged based on the corner brace balance theory, and finally the optimal span of the fish-belly beam is selected. The displacement diagram of supporting structure is obtained by using Midas/Gen with the span of fish-belly beam as the variable, the influence of the span of fish-belly beam on the horizontal displacement of foundation pit is analyzed, the relationship formula between the span of fish-belly beam and the size of foundation pit is obtained, and the plane layout method of prestressed fish-belly beam system is proposed.


Introduction
Compared with the traditional reinforced concrete support system or steel support system, the prestressed fish-belly beam support system can provide open excavation space for the foundation pit and facilitate the earthmoving; Secondly, through the application of prestress, the fish-belly beam system can adjust the vertical and horizontal displacement of the surrounding soil layer for deformation control, to meet the safety and normal use requirements.The deformation control ability and effect of the system are good, especially in soft soil areas or when there are sensitive pipelines and other key protection objects around the foundation pit [1][2][3] .However, from both domestic and international perspectives, the existing pre-stressed fish-belly beam system lacks a proven plan layout method, so it mainly relies on the experience of designers to realize the layout.In practical engineering, because of the unreasonable design, the deformation of the corner brace is often too large.For example, the angle of the corner brace was not selected at 45°according to the specification "Prestressed fish-belly type foundation pit steel support technical regulations" [4]mentioned in the selection process of prestressed fish-belly beam is as follows: First, on the basis of considering the geological conditions of foundation pit engineering, environmental protection requirements and excavation depth of foundation pit, calculate and determine the number of vertical support channels, and then select the applicable model of prestressed fish-belly beam according to the horizontal force of each support, and finally consider the shape of foundation pit, earth excavation and underground structure construction, complete the support plane layout.It is also necessary to carry out the overall plane or three-dimensional calculation, and review the displacement, so as to finally determine the specifications of all components.However, the specific how to choose the type and size of the fishbelly beam and the layout of the plane and other component specifications are not explained, so the following how to choose the best span of the prestressed fish-belly beam, how to rationally arrange the plane of the prestressed fish-belly steel support and how to determine the selection of component specifications are studied and analyzed.

Based on the Angle brace balance theory of the basic principles of brace layout
The main components of the flat surface of prestressed fish-belly beams are the corner brace, the opposite brace, the fish-belly beam, etc.When the plane layout of the foundation pit is ready to be deployed, Because corner brace and opposite brace are prone to deformation in the project,the layout of the corner brace and the opposite brace can be started firstly.The corner brace is set between the two sides of the foundation pit, or the horizontal compression bar between the side wall of the foundation pit and the support.From the point of force analysis, it is caused by the unbalanced force on both sides of the corner brace.As shown in figure 1, suppose there is a long pit, the short side size Lx, the long side Ly is arranged with a opposite brace, according to the code recommended Angle 45,0 arranged at m.According to the supporting range of the corner brace on the short and long sides, the conditions of the balance of the corner brace can be analyzed from the Angle of the force.As shown in figure 1, the support range of the corner brace on the short side of the foundation pit is (m+a), and the support range on the long side is (m+b).Such problems will occur under some foundation pit sizes: The supporting range of the corner brace on the long side of the foundation pit is different from that on the short side of the foundation pit, resulting in different earth pressure on both ends of the corner brace.The force imbalance on both sides of the corner brace leads to the deformation of the side with greater force in the foundation pit is too large, and the side with less force is reversed to the foundation pit.The displacement of the foundation pit at the corner brace is difficult to control.[5][6][7] According to this condition, the area immediately adjacent to the short side of the foundation pit should be square.This condition can only be realized by the opposite brace, whose essence is to determine the opposite brace layout position of the prestressed fish-belly beam supporting structure.Therefore, one of the principles of the plane layout of the prestressed fish-belly beam supporting structure: the layout of the opposite brace should be based on the size of the foundation pit, select the appropriate number of brace paths, so that the area next to the short side of the foundation pit is separated into a square.
After determining the angle of the corner brace, number and position of the opposite brace, how to choose the span of the fish-belly beam is the core problem of the plane layout.Therefore, finite element software can be used to carry out numerical simulation and theoretical analysis of foundation pit plane, so as to explore the law of the influence of the span of fish-belly beam members on the overall displacement of foundation pit, and finally get the optimal span of fish-belly beam in the corresponding foundation pit.

Introduction to Finite element software
MIDAS/GEN is a kind of analysis and design software widely used in the construction industry.It was developed by PoSCO Group of South Korea since 1989.After several years of development and improvement, it has been widely used in many engineering projects,especially in the design [8]of super tall buildings, stadiums and long-span Bridges.It has fully proved its powerful function and the accuracy of the results.
Compared with other sxisting finite element analysis software, Midas/Gen's performance can be compared with large finite element analysis software such as ANSYS, and its price is low, the interface and analysis steps are simple, which provides great convenience for the technical personnel engaged in finite element analysis.Its modeling is fast and convenient, built-in rich Chinese design specifications and a variety of analysis functions, so choose this software for application.

Basic assumptions and parameter Settings
The selection of component elements according to the relevant specifications "Technical Regulations for steel support of prestressed fish-belly foundation pit", the following basic assumptions are made when modeling: the structure is analyzed as a plane problem; The level applied to the waist beam is considered according to the uniform distribution load.The waist beam and the belly bar are beam units, the opposite brace and the corner brace and the oblique belly bar are rod units, the steel strand is only the tension unit, and the connector can be considered as the rigid zone relative to the single H-beam steel, so the connector is the flat plate unit.

Setting of boundary conditions and load application
At the four corner points of the foundation pit, limit the movement of the plane in the X and Y directions, and the rotation in the Z direction.The load transferred by the retaining structure to the internal support should take the fulcrum force obtained in the analysis of the retaining structure, calculate the vertical enclosure structure q=118kN, and take the calculated support reaction force as uniform distribution load and add it to the enclosing [9][10][11][12] purlin.The design value of the axial force of the fish-belly beam steel strand is calculated according to the standard calculation method.According to formula (4), the prestress applied by the fish-belly beam steel strand is 0.70~0.75 of the design value of the axial force of the steel strand.

Result Analysis
In order to explore the influence of the span of the fish-belly beam on the displacement of the foundation pit plane, on the basis of determining a foundation pit plane, change the span of the fishbelly beam, check the deformation of the structure, and analyze the influence of the span of the fishbelly beam on the displacement control of the structure plane.
In 30m*30m foundation pit plane to change the span of the fish-belly beam, through analysis, obtained different spans of fish-belly beam under the structure of the plane in the Y direction of the deformation results are as follows:  Check the deformation of the structure in the Y direction, and select the maximum displacement of the fish-belly beam structure as shown in table 1:

Table 1. Span and maximum displacement of fish-belly beam
The span of the fish-belly beam L(m) Dfish-belly beam max(mm) Figure 3 shows the maximum horizontal displacements under fish-belly beam with different spans.As can be seen from the results, when the span of fish-belly beam is small, the maximum displacement of the structure in the Y direction increases slowly with the increase of the span of fish-bellied beam, and the increment is negligible, indicating that increasing the span of fish-belly beam has no obvious effect on improving the stiffness of the structure.However, when the span of the fish-belly beam is 17m, the displacement value decreases somewhat, and the continuous increase of the span leads to a substantial increase in the displacement value.
Through the stiffness study of the fish-belly beam structure, the average equivalent stiffness of the fish-belly beam can be calculated [13]according to equation ( 5 Where: EwIw is the bending stiffness of enclosing purlin/N•m2 ; φ is the coefficient related to the bending stiffness of enclosing purlin, axial stiffness, axial stiffness of steel strand, the height and span ratio of fish-belly beam; η is the prestress coefficient of the steel strand of the fish-belly beam, usually 0.6~0.75 in engineering; λ is the vector span ratio of the fish-belly beam; α is the Angle /°between the end steel strand and the enclosing purlin; L is the span of the fish belly beam /m.Through the formula, the equivalent stiffness of the fish-belly beam is inversely proportional to the cube of the span of the fish-belly beam.From this, it can be concluded that the smaller the span of the fish-belly beam, the higher the stiffness.
Through the formula, the equivalent stiffness of the fish-belly beam is inversely proportional to the cube of the span of the fish-belly beam.From this, it can be concluded that the smaller the span of the fish-belly beam, the higher the stiffness.However, considering that when the span of the fish-belly beam is too small, more corner brace members are needed to control the displacement of the foundation pit, and when the span of the fish-belly beam is too large, the number and length of the straight belly rod increase, resulting in an increase in the prestress loss of the steel strand, thus the stiffness is lost.Therefore, the Angle of plane deformation control and material budget can be comprehensively considered, and the fish-belly beam with 17m span can be selected for layout.
It can be seen from the above that the span of the fish-belly beam cannot be reduced simply in order to improve the stiffness, and the amount of corner brace members and the loss of prestress of the steel strand should be taken into account at the same time.

Foundation pit with a length and width of 25m
The above simulation and analysis are carried out, and the analysis results are as follows figure 4: It can also be seen that when the span of fish-belly beam is small, the maximum displacement value of fish-belly beam increases slowly or even does not increase with the increase of the span of fishbelly beam.However, when the span of fish-belly beam increases to 14m, the displacement value begins to increase significantly.Therefore, considering the overall consideration, the 14m span of the fish-belly beam can be selected.

Foundation pit with length and width of 35m
The analysis results obtained by simulation are as follows figure 5: It can be seen that when the span of the fish-belly beam increases from 18m to 19m, the displacement of the fish-belly beam in the Y direction suddenly increases.This is because according to the Technical Regulations of Steel Support for Prestressed fish-belly foundation Pit, the model of the fish-belly beam is FS when the span is 18m, and the steel strand of the lower string of the fish-belly beam is applied and fixed through the anchorage end.The model is FA when the span is 19m.The lower string steel strand of the fish-belly beam is applied and fixed by the anchor on the connecting piece, and the application of prestress is the key to control the deformation of the foundation pit of the prestressed fish-belly steel support system.According to the formula of the calculation of the prestressed steel strand(Ref.3.3), Ln is the net distance between the ends of the fish-belly beam connector.When the fish-belly beam model is FS and becomes FA type, Ln decreases.Therefore, the prestress value also decreases accordingly, resulting in an increase in the displacement of the fishbelly beam.Comprehensive consideration can choose 18m span fish-belly beam.

Foundation pit with length and width of 40m
The analysis results obtained by simulation are as follows figure 6: It can be seen that when the span of fish-belly beam increases to 23m, the displacement value begins to increase significantly.Comprehensive consideration can choose 23m span of fish-belly beam.

Foundation pit with a length and width of 45m
The analysis results obtained by simulation are as follows figure 7: It can be seen that when the span of fish-belly beam increases to 24m, the displacement value begins to increase significantly.Comprehensive consideration can choose 24m span of fish-belly beam.
The results of each size foundation pit are settled as follows, and the relationship between the span of the fish-belly beam and the size of the foundation pit can be obtained, that is In the formula: L is the span of the fish-belly beam /m; a is the foundation pit size /m in figure 8.

Conclusion
By establishing finite element models of prestressed fish-belly beam systems with different spans, the following conclusions can be drawn by comparing the test results: 1) When the size of the foundation pit and the span of the fish-belly beam are small, changing the size of the fish-belly beam has little influence on the horizontal displacement of the foundation pit.With the increase of the span of the fish-belly beam, the maximum displacement has a small increase, but when the span of the fish-belly beam increases to a certain value, the displacement of the foundation pit will increase obviously and suddenly; 2) By analyzing the influence law of the span of the fish-belly beam on the multi-size foundation pit, the formula for the change of the span of the fish-belly beam with the size of the foundation pit is obtained, that is

Figure 1 .
Figure 1.Diagram of the support range of the angle brace Set the uniform distribution load of soil as q and the length of the right angle side of the corner brace as m.Considering the principle of symmetrical arrangement and convenient calculation, the length of the right angle side of the eight-figure 2 support is also m.According to the support range, the balance conditions at both ends of the corner brace are:

Figure 2 .
Figure 2. The supporting structure displacement diagram of the Y

Figure 3 .
Figure 3.The maximum displacement of fish-belly beam varies with the span

Figure 4 .
Figure 4.The maximum displacement of fish-belly beam varies with the span

Figure 5 .
Figure 5.The maximum displacement of fish-belly beam varies with the span

Figure 6 .
Figure 6.The maximum displacement of fish-belly beam varies with the span

Figure 7 .
Figure 7.The maximum displacement of fish-belly beam varies with the span

Figure 8 .
Figure 8.The span of fish-belly beam under different pit dimensions