Prestressed cable-stayed bridges are subject to a variety of loads and temperatures, making them prone to cracks. The traditional finite element method cannot accurately depict the generation and propagation of cracks, and based on the continuous-discontinuous element method, combined with multiphysics coupling, the numerical simulation of the prestressed bridge deck is carried out, and the current fracture genesis and long-term evolution are analyzed. The results show that the gravity of the bridge deck, the cable force and the straightness of the bridge are not the main reasons for the cracks of the bridge, and the prestress of the steel bar hinders the crack development to a certain extent. The long-term temperature cycle plays a dominant role in the initial crack of the bridge deck, and the initial crack is further extended by repeated loading of the vehicle dynamic load in the later stage.
In addition to bearing its own weight and vehicle load during the service life of the bridge, it is also subjected to a large number of complex load effects such as temperature cycling, axial pressure caused by cable force, prestress in the box girder body, etc., which may cause deterioration and damage of bridge materials and lead to bridge cracking.
Although China has a large number of engineering practices in bridge large-volume concrete crack control, and also proposed control indicators such as concrete drying shrinkage rate and mold temperature, however, bridge large-volume concrete crack control has always been a problem in the engineering community. Meng Biaozhu summarizes and analyzes in detail the types of cracks common in reinforced concrete bridge engineering. Wang Ping et al. summarized the cracking of common prestressed concrete bridges, and analyzed the causes of cracks through typical prestressed bridges. ULM et al. studied the temperature-hydration-force coupling and established corresponding models to predict concrete shrinkage and cracking. Cervera et al. proposed that the thermal-hydration-force coupling model can simulate the hydration, aging, damage and creep of concrete, which is based on the reactive porous media theory, which can accurately predict the degree of hydration and the change of hydration heat production with time. Chen Zonghui et al. established a solid finite element model of the box girder through ANSYS software, and analyzed the causes of longitudinal cracks in the bottom plate of the box girder during the construction of the box girder segment. Tu Jian et al. used solid elements to establish a full-bridge numerical model and simulated it numerically, and analyzed the influence of two factors, temperature difference and shrinkage difference, on their stress. Based on the finite element method, Tan Guojin et al. explored the dynamic response of multi-piece girder bridges with conversion cracks under vehicle dynamic load conditions, and Liu Yufei et al. used numerical simulation software to study the effect of damage cracks of large quasi-coal special line bridges, and the results showed that bridge cracks have an impact on bridge deflection and strain. He Luo et al. explored the causes of cracks in concrete from the perspective of the actual construction of the Pingtang Special Bridge. Zhu Jinsong et al. proposed a three-dimensional dynamic stress strength factor solution method for crack tips based on the interaction integration method and axle coupling vibration analysis, which is used to study the propagation law of bridge cracks under vehicle dynamic load, and conclude the risk of bridge crack propagation and extension due to vehicle dynamic load. The above studies have analyzed the causes of cracks in concrete bridges through numerical simulation and experiments, which has led to a deeper understanding of the causes of cracks in the bridge.
Under the combined action of various factors such as day and night temperature difference and cold current erosion, the temperature of concrete bridge is constantly circulating, and due to the poor thermal conductivity of concrete, the temperature of the inner and outer surfaces of the box girder lags behind, so that the box girder section forms a nonlinear temperature distribution, resulting in the deformation of the bridge structure. In order to accurately grasp the distribution characteristics of the temperature field of the bridge, many scholars at home and abroad have successively used field tests and numerical simulation methods to carry out research. Elbadry et al. and Clark obtained the temperature field distribution characteristics of the bridge structure through the analysis of the measured data. Gu Bin et al. and Zhou et al. established a numerical model of the bridge temperature field through numerical simulation, and obtained the temperature field distribution characteristics of the bridge structure through theoretical calculation and analysis. Taking the No. 2 Bridge of Laotuanpo in Yunnan as the research background, Jia Jia et al. carried out the sensitivity analysis of bridge cracks to temperature effects, prestress loss and other factors through numerical simulation, and analyzed the causes of cracks during bridge construction in alpine areas.
In this study, relying on the bridge cracking project of the Huanglongbelt Special Bridge, a three-dimensional numerical model was established based on the continuum-discontinuum-element-method (CDEM) to analyze the causes of bridge cracks. The coupling algorithm of stress and heat conduction is introduced, and the influence of anchor cable force, prestress of prestressed ribs, temperature field and their coupling effect on bridge durability is analyzed. At the same time, the variable separation method and parametric inverse analysis method are used to obtain the internal force and displacement of the bridge under different conditions and different working conditions, and further analyze the causes of bridge cracking.
Project overview
Hanzhuang Canal Longdai Special Bridge is located in the Malantun section of the Xintai-Taierzhuang (Lusujie) highway, and the bridge crosses the river for the Zaozhuang section of the Beijing-Hangzhou Canal (Hanzhuang Canal). The Huanglong belt special bridge bridge is divided into left and right 2 parts, the maximum longitudinal slope of the bridge deck is 3.00%, the plane is located on the circular curve and the easing curve with a radius of 1800m, the main girder structure is a prestressed concrete variable section box girder, the box girder height is 3.80~6.00m, the width of the bottom plate is 12.50m, and the width of the wing plate is 4.00m (Figure 1, Figure 2). Table 1 is a table of the distribution characteristics of cracks inside and outside the main bridge box, and Figure 3 shows the distribution of existing cracks in the bridge deck.
Figure 1 Elevation of the main bridge
Figure 2 Standard cross-section of main beam
Figure 3 Fracture distribution
Table 1 Distribution characteristics of cracks inside and outside the main bridge box
Numerical methods and mechanical models
Numerical methods
This numerical simulation is based on the CDEM principle, and the numerical model of the Yellow Dragon Belt Bridge is established through the BlockDyna module of GDEM (Graphic-augemented-CDEM). Figure 4 shows the calculation flowchart of the CDEM method.
Figure 4 Calculation process of CDEM method
A block in GDEM consists of one or more finite element elements, with a continuous constitutive used inside the block and a discontinuous constitutive for the block boundary. GDEM divides each finite element element in the bridge model into tetrahedral elements as shown in Figure 5. The discontinuous deformation between the blocks is mainly achieved by springs, as shown in Figure 6, and the cracking and slippage of the model material are characterized by the fracture of the spring.
Figure 5 Tetrahedral unit
Figure 6 Block and interface in CDEM
The continuous-discontinuous element method is an explicit dynamic numerical analysis method in which finite elements and discrete elements are coupled to each other. The theoretical basis of CDEM is the Lagrange equation:
where , is a generalized coordinate , L is the energy of the Lagrange system, and work is done for the nonconservative force.
GDEM uses the stiffness matrix method to solve the internal forces of the element. Since GDEM adopts dynamic relaxation technology, it does not need to form an overall stiffness matrix, but only needs to take the unit stiffness matrix of each unit, calculate the unit's own nodal force through equation (2) at each iteration step, and distribute this nodal force to the node corresponding to the cell.
where is the nodal force vector of element i; is the nodal displacement vector of element i; is the element stiffness matrix of element i.
A schematic diagram of the normal and tangential springs at the GDEM interface is shown in Figure 7.
Figure 7 Contact surface normal and tangential springs
The spring force is calculated as
where , respectively, the normal and tangential forces of the jth spring; , respectively, the normal and tangential stiffness of the jth spring; , normal and tangential displacement of the jth spring, respectively.
When performing the failure calculation, the Mohr-Coulomb criterion is used to correct the spring force in the formula, and the correction formula is
where T is the tensile strength; φ is the internal friction angle; C is cohesion. The ,、、 in Figure 7 shows the cohesion.
Mechanical model
The unit adopts the linear elastic constitutive and the calculation formula is
where is the stress tensor; is the incremental stress tensor; Δεij is the incremental strain tensor; Δθ is the volume strain increment; K is the bulk modulus; G is the shear modulus; Mark for Kronecker; is the current time step; is the next step in time.
In order to depict the extension and extension of bridge deck cracks, the interface adopts brittleMC brittle fracture constituent.
Application of multiphysics
For the application of steel bar prestress, the tension process of the prestressed bar is simulated by applying the joint force to the steel bar in the bridge deck, and the applied stress value is calculated according to the tension control stress of the prestressed bar in the bridge deck.
For the application of cable-stayed cable force, according to the frequency of the cable, the cable force of the cable is calculated based on the frequency method, and it is decomposed into two directions, x and y, and the surface force is applied to the surface of the bridge deck.
For the application of the temperature field, according to the temperature change range of Guangdong Province in 2020, the peak temperature field of the bridge body is deduced, and the cyclically changing temperature field is applied to the bridge body.
For the application of vehicle dynamic load, the vehicle load is applied to the bridge deck surface by surface force, and the segmented application method indicates that the vehicle is driving on the bridge deck surface at a speed of 80km/h.
Numerical simulation
Numerical model and working condition settings
Because the bridge structure is a complex curved beam form, the main bridge box girder structure is complex, the volume is large, which will not only increase the difficulty of modeling, but also may lead to a large number of divided elements, and increase the calculation time, considering the symmetry of the bridge deck model shape and working condition setting, so this study selects 1/4 of the box girder structure for modeling, and uses GID software to establish a three-dimensional solid calculation model of the box girder. The simplified model is shown in Figure 8, the grid size is selected 0.70m, the calculation model is divided into 93894 tetrahedral elements, and the number of nodes is 26671. The calculation input parameters refer to the parameters of C60 reinforced concrete, and the prestressed bars are equivalent to the bolt unit. The mechanical parameters of concrete are: density 2551kg/, elastic modulus 3650MPa, Poisson's ratio 0.2, cohesion 24.2MPa, tensile strength 20.4MPa.
Figure 8 Box girder simplified model and its meshing
In order to obtain the internal force and displacement of the model under various working conditions, three information monitoring points are set along the center line of the top plate and the bottom plate of the box girder, and the monitoring points from one end of the sota to the middle end of the span are A1, A2, B1, B2, C1, C2 (Note: the monitoring point is located in the internal center of the bridge deck instead of the surface), the specific location is shown in Figure 9.
Fig. 9 Location distribution of monitoring points of box girder of main bridge
In order to explore the causes of the occurrence and propagation of bridge deck cracks, qualitatively and quantitatively analyze their main controlling factors, and provide guidance for the repair and subsequent maintenance of the bridge, this study adopts the variable separation method and parametric inverse analysis method, and sets up a total of 6 different working conditions, namely: curve box girder gravity + prestress analysis, curve box girder gravity + cable force analysis, curve box girder gravity + temperature action analysis, curve box girder gravity + prestress + cable force + temperature action coupling analysis. In order to investigate whether the existence of curved box girder bending moment affects the generation and propagation of bridge deck cracks, a control group was set up: linear box girder gravity + prestress + cable force + temperature action coupling analysis.
Gravity + prestress analysis of curved beams
In the Huanglong belt special bridge, the roof, floor and web of the box girder of the main bridge are provided with longitudinal prestressed steel bars along the axis direction, the web is provided with vertical prestressed steel bars, and the roof and transverse partitions are provided with transverse prestressed steel bars, the distribution of which is shown in Table 2, due to the large types and number of prestressed ribs and complex distribution, only longitudinal prestressed ribs and some transverse prestressed ribs are considered in this working condition. The prestressed ribs are modeled using the anchor/anchor element in the GDEM software, taking into account the coupling calculation with the solid element.
Table 2 Distribution of prestressed ribs
In this working case, considering the coupling effect of gravity and prestress, the boundary conditions are set to: the displacement of the box girder semi-structure pier side is limited to 3 directions to 0, which simulates the supporting effect of the main bridge cable tower on the box girder. The displacement of the two ends of the diaphragm beam is limited to 0 in three directions, which simulates the supporting effect of the cable. The box girder semi-structure spans the middle side and sets the horizontal 2 directions, and the displacement is 0.
As shown in Figure 10, the displacement at both ends of the box girder is small, which is due to the fact that both ends of the box girder semi-structure are supported by the tower and constrained by the box girder of the bridge on the other side, and the end of the diavid beam is constrained by the cable. At the position of the center line of the top plate of the box girder, the vertical displacement of this area is the largest, the value is about 3.5mm, which is because the diaphragm beam can be regarded as a solid support beam under this working condition, so the vertical displacement reaches the maximum there; because the displacement on both sides of the box girder is constrained, the box girder can be regarded as a cantilever beam fixed at the sota, and the unit is tensile at the end roof, and the stress value is about 2.5~4.0MPa; Similarly, tensile stresses occur at both ends of the diaphragm. Due to the action of prestress, most of the area in the box girder body is in a state of compression, and the stress value is about 1.59MPa. The tensile area near the centerline area at the bottom of the box girder is the tensile area, but the stress level is low, which shows that the application of rebar prestress can reduce the tensile stress of the box girder under its own weight, avoid the appearance of new cracks due to tensile failure, and hinder the propagation and extension of existing cracks.
Figure 10 Vertical displacement and maximum principal stress cloud
Curve beam gravity + cable force analysis
In this case, the coupling effect of gravity and cable force is considered, and the mechanical behavior of the curved box girder under the influence of the deflection axial force caused by the cable force is studied. Boundary conditions are set: the displacement of the box girder semi-structural pier side is limited to 3 directions to 0; The displacement of the box girder semi-structure in the middle side of the span is 0 in 2 directions; Both ends of the diaphragm constrain the vertical displacement and apply the axial force caused by the cable force. Due to the large number of cable-stayed force data, in order to simplify the calculation, only the maximum value of each cable-stayed cable is selected for simulation in this working condition. Considering that the steel bars in the reinforced concrete structure of the box girder will have a good distribution effect on the cable force, and in order to avoid the concentration effect, the axial force of this working condition is applied to the diaphragm beam and its nearby area in the form of surface force, and the input stress level is the cable force monitoring value divided by the applied area area.
Observing Figure 11, due to the constraint of the sota and the other side of the bridge, the vertical displacement of both ends of the box girder is small, and the maximum displacement is about 0.13m, which shows that the vertical displacement of the box girder is large without prestress, in addition, the cable-stayed cable will stretch and lengthen when stressed, so it will also affect the vertical displacement of the box girder. In addition, transverse cracks appeared at the roof plate on the middle side of the box girder span, and stress concentrations appeared at the tip and near the cracks. The maximum tensile stress can reach 18.40MPa, which is because the direction of the cable force is far away from the middle side of the span, so the action of the cable force will make the concrete of the middle part of the box girder span tensile, resulting in transverse tensile cracks; at the same time, under the action of its own weight, the concrete of the bottom plate of the span part is compressed, which effectively eliminates the role of tensile stress caused by the cable force there, so under this working condition, the crack only appears at the top plate of the span. Since the displacement of the box girder on the side of the tower is constrained, it can be regarded as a fixed support, under the action of gravity, the top plate of the box girder is subjected to tensile stress, and the bottom plate is subjected to compressive stress; Under the action of cable force and gravity, the middle floor of the box girder is subjected to tensile stress, and the top plate is subjected to compressive stress, the tensile stress level is about 10.24MPa, and the compressive stress level is about 3.35MPa. If the role of steel prestress is considered at the same time under this working condition, part of the tensile stress can be effectively offset and the cracking load of the box girder concrete can be increased.
Fig. 11 Vertical displacement and maximum principal stress cloud
Analysis of gravity + temperature action of curved beam
Located in Guangdong Province, the Yellow Dragon Belt Bridge has a subtropical monsoon climate with an average annual climate of about 26 °C, especially in summer, when the temperature can reach 40 °C. In summer, the bridge deck is directly exposed to the sun, and continuous exposure can cause the temperature of the bridge to be much higher than the temperature. The specific heat capacity of concrete materials is large, and the thermal conductivity is small, so the conduction of heat on the bridge body will be very slow, resulting in a large temperature gradient, forming a large temperature stress, which is very likely to lead to temperature cracks on the concrete surface or interior, resulting in deterioration and damage of the bridge concrete. According to the temperature of the bridge location, such as Table 3 and the temperature change range of the box girder in summer, the internal force distribution, deformation, crack generation and propagation of the box girder under the action of temperature are studied.
Table 3 Temperature variation range in Guangdong Province in 2020
The boundary conditions of this working condition are set: the displacement of the box girder semi-structural pier side is limited to 3 directions to 0; The box girder semi-structure spans the middle side of the span with two horizontal displacements of 0. Both ends of the diaphragm constrain vertical displacement. Set the initial temperature of the bridge body to 20°C, and apply a temperature boundary that changes and the temperature-cooling cycle on the bridge deck and bottom of the bridge. The temperature boundary was uniformly raised from 20°C to 70°C within 30 days for 2 months, and then uniformly cooled from 70 °C to 20 °C within 30 days for 2 months, simulating the temperature change in the area where the bridge is located for half a year, and analyzing the influence of temperature action on the bridge deck.
As shown in Figure 12, the displacement and stress cloud of the curved bridge under the coupling of gravity and temperature, under the action of the heating-cooling cycle, due to the limitation of the tower and the cable, the vertical displacement of the box girder in these areas is small, and the vertical displacement occurs in the center area of the box girder roof and bottom plate, the maximum value is 3.6mm, due to the temperature action, several cracks appear at the connection between the diaphragm beam and the box girder roof plate, which shows that temperature is the main reason for the cracks in the box girder. From the maximum principal stress cloud, it can be found that there is a large tensile stress in the area where the top plate of the box girder and the diaphragm beam are connected, up to 11.6MPa locally, but due to the low thermal conductivity and large specific heat capacity of the concrete material, the heat conduction rate is slower, resulting in a large temperature gradient. From Figure 12, it can be found that part of the tensile stress area appears at the bottom of the top plate of the box girder, which is due to the temperature action on the surface of the roof plate, the thermal expansion of the material, the lower surface temperature is low, and the level of unit expansion is not high, so that the concrete on the lower surface restricts the expansion of the upper surface concrete, so the higher temperature area is pressurized, and the lower temperature area is tensile. There is a sudden concave and convex angle at the junction of the top plate and the diaphragm, which is easy to cause stress concentration in this area, so this is also one of the reasons for the high stress level in this area.
Fig. 12 Vertical displacement and maximum principal stress cloud
Due to the slow heat conduction speed of concrete materials, there will be a large temperature difference between the box girder at the end of heating and the end of cooling, and the temperature difference can reach 30 °C after the end of the heating stage of a single heating-cooling cycle, and the temperature difference of close to 10 °C in the cooling stage. Therefore, after each temperature cycle, the temperature of some areas does not return to the original level, resulting in residual temperature, which may cause the residual temperature stress inside the box girder.
Coupled analysis of gravity + prestress + cable force + vehicle load of curved beam
At this stage, the dynamic load of the vehicle is applied, and three lanes 1, 2 and 3 are installed on the bridge deck (fig. 13). The vehicle load is applied to the surface of the bridge deck by surface force, and the blue square in the figure indicates that the vehicle is in the middle of the bridge deck span, and the segmented application indicates that the vehicle is driving on the bridge deck surface at a speed of 80km/h. The working condition is divided into three calculations, driving on three lanes in turn, and analyzing the influence of vehicle load on the bridge deck.
Figure 13 Bridge deck lane distribution
Figure 14 is the maximum principal stress cloud diagram of the vehicle driving in different lanes, it can be seen in the figure that the maximum principal stress in the three cases is mainly manifested as compressive stress, the stress size is about 3MPa, and at the same time, under the coupling of gravity, prestress, cable force and vehicle dynamic load, cracks appear in the middle of the span of the bridge deck. Through the analysis of different working conditions of vehicles driving in 3 lanes and comparing with the gravity + cable force case of curved beam, it can be concluded that the bridge deck will produce a certain amount of cracks under the vehicle load, but it has little to do with the vehicle driving lane.
Figure 14 Cloud of maximum principal stress of vehicles driving in different lanes
Coupled analysis of gravity + prestress + cable force + temperature action of curved beam
This working condition considers the combined effects of gravity, prestress, cable force and temperature, and the prestress and cable force are set according to the same parameter values of the first working condition and the second working condition. Set the initial temperature of the bridge body to 20°C, and apply a temperature boundary that changes and the temperature-cooling cycle on the bridge deck and bottom of the bridge. The temperature boundary was uniformly raised from 20°C to 70°C within 30 days for 2 months, and then uniformly cooled from 70 °C to 20 °C within 30 days for 2 months, simulating the temperature change in the area where the bridge is located for half a year, and analyzing the influence of temperature on the box girder. The boundary conditions of this working condition are set to: the displacement of the box girder semi-structural pier side is limited to 3 directions, which is 0; The box girder semi-structure spans the middle side of the span with two horizontal displacements of 0. Both ends of the diaphragm constrain vertical displacement.
As shown in Figure 15 is a vertical displacement cloud diagram, the box girder under the action of gravity and cable force, vertical displacement, due to the large weight of the bridge itself, and due to the tension of the cable, the cable is elongated, resulting in the phenomenon of downward displacement of the bridge body. In the middle of the bridge span, due to the supporting force of the bridge tower, the vertical displacement in the middle of the span is small, the displacement is about 1.2cm (the green part in the upper left corner of Figure 15), and the vertical displacement on the side away from the bridge tower is large, and the vertical displacement is about 5.0cm.
Figure 15 Vertical displacement cloud
The maximum principal stress cloud is shown in Figure 16, the box girder is mainly subjected to tensile stress under the combined action of gravity, temperature lifting cycle, cable force and steel prestress, and the tensile stress value is about 2.35MPa, and the local stress concentration is large, which is about 10.30MPa, causing local damage. And it can be seen from the stress cloud diagram that there are partial compressive stress areas at the top and bottom of the box girder, mainly because the box girder will undergo heat conduction under the action of temperature, but due to the low thermal conductivity of concrete materials and large specific heat capacity, the heat conduction speed is slower, resulting in a large temperature gradient. It can be found from the figure that part of the tensile stress area appears at the bottom of the top plate of the box girder, which is due to the temperature action on the surface of the roof plate, the thermal expansion of the material, the lower surface temperature is low, and the level of unit expansion is not high, so that the concrete on the lower surface restricts the expansion of the upper surface concrete, so the higher temperature area is pressurized, and the lower temperature area is tensile. There is a sudden concave and convex angle at the junction of the top plate and the diaphragm, which is easy to cause stress concentration in this area, so this is also one of the reasons for the high stress level in this area.
Figure 16 Maximum principal stress cloud
In Figure 16, it can also be seen that there are more cracks in the top plate and bottom plate of the box girder, and the reasons for the cracks are as follows: in the initial stage of applying temperature, due to the small thermal conductivity of reinforced concrete, the heat conduction process is slow, and the heat conduction at this time is mainly in the box girder roof, bottom plate and flange plate, which has little influence on the web, resulting in a large temperature difference between the upper and lower surfaces of these areas. When the temperature continues to rise and the temperature gradient increases, the temperature stress will also increase (the high temperature side of the plate is compressed, and the low temperature side is tensed). As the box girder is subjected to multiple cycles of heating-cooling, the residual temperature stress in the plate will continue to be superimposed, so that the stress level of the plate will also increase. At the same time, considering that concrete is a non-uniform medium, the thermal conductivity and thermal expansion coefficient of various materials are different, so the uneven expansion between the materials inside the concrete will also produce different levels of thermal expansion stress in the plate.
Coupling analysis of gravity + prestress + cable force + temperature action of linear beam
The cable is one of the force transmission members of the cable-stayed bridge, and the cable-stayed cable is connected to the diaphragm to transmit the force of the box girder body to the sota. Due to the structural characteristics of the cable, in addition to the vertical upward force, it will also produce horizontal force along the longitudinal direction of the bridge, which is manifested as the axial force acting on the beam body, and in the case of curved bridge, these axial forces are eccentric, so that the beam body produces bending moments, causing the local area to be tensile, resulting in cracks generation and expansion; In the case of straight bridges, the horizontal forces caused by the cable-stayed cables at both ends of the tower balance each other without bending moments. In summary, the bridge body is remodeled here, this time as a straight bridge, that is, there is no offset in the horizontal direction of the bridge body. The computational model is divided into 95994 tetrahedral elements, and this model contains 27671 total nodes with a mesh size of 0.70 m, as shown in Figure 17. The linear linear elastic constituent is used in the unit, and the brittleMC brittle fracture constituent is adopted at the interface. The calculation input parameters refer to the parameters of C60 reinforced concrete, and the prestressed bars are equivalent to the bolt unit.
Figure 17 Straight bridge model mesh
This working condition also considers the combined effects of gravity, prestress, cable force and temperature, and the prestress and cable force are set according to the same parameter values of the first and second working conditions. Set the initial temperature of the bridge body to 20°C, and apply a temperature boundary that changes and the temperature-cooling cycle on the bridge deck and bottom of the bridge. The temperature boundary was uniformly raised from 20°C to 70°C within 30 days for 2 months, and then uniformly cooled from 70 °C to 20 °C within 30 days for 2 months, simulating the temperature change in the area where the bridge is located for half a year, and analyzing the influence of temperature on the box girder. The boundary conditions of this working condition are set to: the displacement of the box girder semi-structural pier side is limited to 3 directions, which is 0; The box girder semi-structure spans the middle side of the span with two horizontal displacements of 0. Both ends of the diaphragm constrain vertical displacement.
Under the action of gravity, prestress, cable force and temperature heating-cooling cycle of the bridge body, the vertical displacement cloud of the linear box girder is shown in Figure 18, the box girder under the action of gravity and cable force, vertical displacement is generated, due to the large weight of the bridge itself, and due to the tension of the cable, the cable is elongated, so that the bridge body is displaced. In the middle of the bridge span, due to the supporting force of the bridge tower, the vertical displacement in the middle of the span is small, the displacement is about 0.74cm (yellow area in the upper left corner of the figure), and the vertical displacement of the side away from the bridge tower is large, and the vertical displacement is about 1.60cm. The maximum principal stress cloud is shown in Figure 19, the linear box girder is mainly subjected to tensile stress under the combined action of gravity, temperature lifting cycle, cable force and steel prestress, and the tensile stress value is about 2.35MPa, and the local stress concentration is large, about 10.30MPa, causing local damage. And from the stress cloud diagram, it can be seen that there are partial compressive stress areas at the top and bottom of the box girder, the main reason is similar to the above curved box girder, and the local stress is different due to temperature transfer.
Figure 18 Vertical displacement cloud of linear box girder
Fig. 19 Maximum principal stress cloud of linear box girder
Comparative analysis of curved beam and linear beam results
The maximum principal stress of the B2 monitoring point of curved box girder and linear box girder was monitored, and the maximum principal stress time history curve was drawn as shown in Figure 20, from which it can be seen that the maximum principal stress of the bridge deck fluctuates with the increase and decrease of temperature in the two cases, and the maximum principal stress time history curve of curved box girder and linear box girder is highly similar. In order to further explore the influence of bending moment on the cracks of the bridge deck, the dimensionless parametric fracture degree is introduced and the time history curve of the fracture degree is plotted as shown in Figure 21, and it can be seen that the two curves are highly similar. In summary, there is little difference between curved bridges and linear bridges, that is, the existence of bridge bending moments under the same working conditions will not further aggravate the cracking of the cracks, and the existence of bending moments is not the cause of the cracks in the bridge deck.
Fig. 20 Comparison of maximum principal stress at monitoring points
Figure 21 Comparison of fracture degree time history curves
discuss
Referring to the boundary conditions imposed by the actual project, the force transmission path of the box girder is: the box girder load is transmitted to the diaphragm, and then from the septum beam to the cable at both ends, from the cable to the foundation through the tower, or the box girder load is directly transmitted from the tower pier to the foundation. Under the coupling of self-weight stress, temperature stress and expansion stress, the box girder is very likely to crack in the above potentially dangerous cross-section, resulting in longitudinal cracks. A large number of longitudinal cracks appeared on the upper and lower edges of the top, bottom and flange plates of the box girder, and the simulation results were consistent with the test results.
With the conduction of heat, the temperature gradient of the lower side of the top plate and the flange plate gradually decreases, and the temperature of the lower side of the plate gradually increases, at this stage, the heat will be conducted from the top plate and the flange plate to the web in contact with it, due to the large height of the web, the heat conduction in the web is very slow, resulting in a large temperature gradient of the web along the height direction, resulting in a larger temperature stress.
Due to the uneven and convex corners at the web and roof junctions, stress concentrations may occur in these areas, and the stress level is larger than the surrounding area, so these areas can easily become dangerous sections. At the junction of the wings, diaphragms and webs, obvious oblique cracks appeared. The main reason may be that a large stress concentration occurs in the corner, resulting in failure, and oblique rupture occurs under the influence of temperature stress and self-weight. Due to the action of temperature gradient, there is temperature stress in the web, and at the same time, due to the difference in concrete composition materials, the degree of thermal expansion inside the concrete is different, and one or several vertical cracks are generated on the web under the simultaneous action of temperature stress and expansion stress. At the same time, the long-term effect of vehicle load will further promote the propagation of existing cracks and reduce the service life of the bridge.
conclusion
According to the test report of the Huanglong Belt Special Bridge, considering the coupling effect of gravity, steel prestress, cable force, vehicle load and temperature, a three-dimensional numerical model was established based on CDEM for numerical simulation, and the cause of cracks in the bridge deck was analyzed, and the main work and conclusions are as follows.
1) Considering the mechanical behavior of the bridge deck under the action of gravity, steel bar prestress and cable force, the results show that gravity, steel bar prestress and cable force are not the main causes of cracks in the bridge, and the steel bar prestress has the effect of hindering the crack development to a certain extent.
2) The maximum principal stress and rupture degree of curved bridge and linear bridge under the coupling of gravity, cable force, steel prestress and vehicle dynamic load are compared, and the difference between curved bridge and linear bridge is not much, and the existence of bending moment is not the cause of cracks in the bridge deck.
3) The cause of cracks is mainly due to the action of temperature residual stress to cause cracks in concrete, and then under the continuous action of vehicle load, the existing cracks are further expanded.
The authors of this article: Gan Jianfeng, Zhong Yunping, Rao Faqiang, Qin Kaiqiang, Cao Ruyang, Zhang Yiming
About author:GAN Jianfeng, Guangzhou Daguang Expressway Co., Ltd., engineer, research direction is highway and bridge engineering construction and management; Zhang Yiming (corresponding author), Professor, School of Civil Engineering and Transportation, Hebei University of Technology, specializes in geotechnical engineering.
The original article was published in the 11th issue of Science and Technology Review in 2023, welcome to subscribe to view.