Keywords

1 Introduction

With the continuous growth of China's economy, new materials and new technologies are also emerging. CSW replace concrete webs to form a new type of bridge structure, which has been widely used in China [1]. Since France built the world's first highway bridge with CSW-Cognac bridge, it have been deeply studied and developed because of their unique “accordion effect” [2], small axial stiffness, reduced constraints on the roof and floor, improved prestress efficiency, less cracks in the webs, great shear performance [3], good energy dissipation capacity and seismic performance [4]. However, there are many errors in the cantilever casting construction of long-span CSW bridge, and there are errors between the actual construction state and the design theoretical state. In order to reduce the influence of error, the parameter sensitivity of CSW has been studied. It is analyzed that the main beam quality, concrete elastic modulus, prestress loss, shrinkage and creep are linear sensitivity parameters [5]. It is recognized that concrete density, elastic modulus and prestress loss are the main parameters of linear control, and temporary load is the secondary parameter [6]. The least square method is used to identify the parameters, combined with the grey system theory to predict the construction deflection error, compare it with the measured value, and the feedback is timely corrected, so as to form an adaptive control [7]. The influence of temperature difference and temperature gradient on bridge deformation is studied by numerical simulation and actual measurement. The error between the measured value and the calculated value of the model is used to identify and correct the design parameters and guide the subsequent construction [8].

At present, the parameter sensitivity research of long-span CSW bridge mostly focuses on the main beam alignment at the completion stage, and there is a lack of sensitivity research on the construction process and main beam stress. This paper mainly analyzes the parameter sensitivity of the alignment and stress in the maximum cantilever stage and the completion stage, monitors the changes of stress and alignment, and corrects the deviation in time to ensure that the main beam reaches the ideal design state.

2 Project Overview

A bridge has a total length of 319.0 m, crosses the river valley, with a span of 83 m + 153 m + 83 m. It is a three span PC composite continuous box girder bridge with CSW. The design standard is a two-way four lane expressway, the design reference period is 100 years, Fig. 1 show general layout of bridge.

Fig. 1.
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General layout of bridge (unit: m).

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The upper structure of the bridge is single box single chamber variable section CSW box girder, the roof and floor are made of C50 concrete, the width of the roof is 13.1 m, the length of the cantilever on both sides is 3.3 m, the thickness of the roof is 0.3 m, the thickness of the cantilever plate end is 0.2 m, the width of the floor is 6.5 m, and the thickness of the floor is 0.3 m~1.1 m. The height of the fulcrum is 8.8 m, the height of the side span end and the middle beam are 3.5 m. The thickness of the box girder floor varies from the fulcrum to the middle of the span according to a parabola of 1.8 times, Fig. 2 show standard transverse section.

Fig. 2.
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Standard transverse section (unit: m).

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Fig. 3.
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Dimension drawing of CSW (unit: mm).

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Figure 3 show dimension drawing of CSW. The type of CSWs used in the experiment is the BCSW-1600. The length of the flat subpanel and the horizontal projected length of the inclined are 430 mm and 370 mm, a height of 220 mm and the thickness is 10~22 mm.

3 Establishment of Finite Element Model

The bridge adopts Midas civil 2020 finite element software for numerical simulation calculation. Using the CSW section provided by the software, a total of 84 elements are established for the main beam. The single-side cantilever had 16 suspension casting sections with a length of 4.8 m, and the length of middle span and side span closure section was 3.2 m, adopting the method of side span first and then middle span closure, Fig. 4 show finite element model of the main bridge.

Fig. 4.
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Finite element model of the main bridge.

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4 Parameter Sensitivity Analysis

In order to reasonably control the alignment and stress and guide the design and construction, parameter sensitivity is vital to the alignment and stress control of the completed bridge. Therefore, the ±10% variation of the reference value of each parameter is taken to analyze its influence on the alignment and stress of the main beam, Table 1 show variation range of each parameter.

Table 1. Reference value and variation interval of design variables.
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4.1 Cast-In-Situ Section Weight

Due to the influence of concrete dense temperature variation, size error of formwork and other factors during cantilever pouring, the actual weight value of cast-in-place section always deviates from the theoretical value, resulting in the variation of section dead weight. Change the concrete dense to simulate the change of section weight, and monitor the change of main beam alignment and stress.

Fig. 5.
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Stress variation of main beam in bridge completion and cantilever stage under different concrete dense.

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Fig. 6.
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Deflection variation of main beam in bridge completion and cantilever stage under different concrete dense.

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It can be seen from Figs. 5 and 6 that the variation range of roof and floor stress is almost the same in the maximum cantilever stage and bridge completion, and the maximum variation of 0# block is 1.5 Mpa. With the increase of concrete dense the tensile stress of roof and compressive stress of floor increase. The maximum deflection variation is 12.5 mm at the quarter point of side span and middle span.

4.2 Modulus of Elasticity

The modulus of elasticity will increase with the pouring age, and the measured value of the modulus of elasticity is generally greater than the theoretical value after the completion of the bridge. it directly affects the stiffness of concrete, thus affecting the alignment and stress of the main beam, so the sensitivity analysis of the change of elastic modulus should be carried out.

Fig. 7.
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Stress variation of main beam in bridge completion and cantilever stages under different modulus of elasticity.

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Fig. 8.
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Deflection variation of main beam in bridge completion and cantilever stages under different modulus of elasticity.

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It can be seen from Figs. 7 and 8 that the variation of modulus of elasticity in the maximum cantilever and bridge completion has no obvious effect on the stress, the maximum value is 0.33 Mpa, and the change of roof stress is greater than that of the floor. The maximum deflection in the maximum cantilever and bridge completion is only 5.0 mm, and the modulus of elasticity has little effect on the alignment and stress of the main beam.

4.3 Temperature Gradient

For the temperature load, seasonal temperature difference load and sunshine temperature difference load are mainly considered in the construction, but the seasonal temperature difference load has no obvious influence on the structural stress and deformation. This paper only studies the influence of temperature gradient change on the alignment and stress of main beam in the construction and bridge completion.

Table 2. Stress variation of roof and floor of 0# block under different temperature gradient in the maximum cantilever stage.
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It can be seen from Table 2 that during the construction process, the cantilever structure is a static structure, the temperature secondary internal force does not change significantly, and only slight stress changes are generated in the cantilever 0# block [9].

Fig. 9.
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Stress variation of main beam in bridge completion stage under different temperature gradient.

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Fig. 10.
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Deflection variation of main beam in bridge completion under different modulus of elasticity.

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It can be seen from Figs. 9 and 10 that the change of roof stress is greater than that of floor stress at bridge completion stage. The stress change of floor stress is within 1.2 Mpa, and the maximum change of roof stress can be up to 5.7 Mpa, the maximum deflection in the bridge completion stage is 9 mm. The change of temperature gradient has a significant impact on the stress and alignment of the main beam in the bridge completion stage.

5 Sensitivity Calculation

There is no clear functional relationship between design parameters and objective parameters, so it is difficult to obtain the analytical solution of objective function accurately. In order to facilitate parameter analysis and reasonably optimize the alignment and stress during construction. Parameter sensitivity is introduced to quantify the impact of each parameter on target parameters [10].

$$ \eta = \mathop {\lim }\limits_{{\Delta }x\to ^{yields} 0} \frac{{{\Delta }y/y}}{{{\Delta }x/x}} $$
(1)

Where, y is the target control parameter, i.e. stress and deformation in cantilever state and bridge completion state. x is the design parameter.

According to Formula (1), take ±10% of the change of each parameter to calculate the sensitivity of it to alignment and stress. The calculation results are shown in the Table 3.

Table 3. Sensitivity of design parameters in bridge completion and maximum cantilever stages.
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It can be seen from Table 3 that the sensitivity of concrete dense and temperature gradient is strong, and the sensitivity of modulus of elasticity is weak.

6 Conclusion

  1. (1)

    The concrete dense and temperature gradient have great influence on the alignment and stress of the main beam, which is the key control parameter, and the elastic modulus has little influence, which is the secondary control parameter. The parameters of midspan closure section, midspan and side span quarter points and cantilever 0# blocks vary greatly, so the above positions should be monitored during construction to ensure that the stress and alignment of the bridge meet the design value.

  2. (2)

    During construction, real-time monitoring of concrete dense changes, according to the specification of concrete vibration and formwork. Select the appropriate temperature to close the bridge, monitor the temperature field and temperature gradient effect, avoid the structure being affected by the temperature gradient, and ensure the smoothness of the bridge alignment.

  3. (3)

    There are abrupt changes in stress and deflection corresponding to parameter changes at the closure of mid span and side span, which is related to the closure method, closure sequence, age and weight of closure section. There are abrupt changes in stress and deflection corresponding to parameter changes at the closure of mid span and side span, which is related to the closure method, closure sequence, age and weight of closure section.