CN117592154A - Method for designing analysis toughness of unbonded prestressed reinforced concrete pier - Google Patents
Method for designing analysis toughness of unbonded prestressed reinforced concrete pier Download PDFInfo
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Abstract
The invention relates to the technical field of pier earthquake resistance, in particular to a method for analyzing toughness design of a unbonded prestressed reinforced concrete pier, which comprises the following steps: determining design parameters of the unbonded prestressed reinforced concrete bridge pier, and obtaining the capacity of the bridge pier; obtaining the drift ratio and the residual drift ratio of the bridge pier according to the design parameters, and defining the damage state of the bridge pier; constructing a consistent damage model which represents the toughness design of the bridge pier through the relation among the capacity, the drift ratio and the residual drift ratio of the bridge pier; the design parameters of the bridge pier are input into the consistent damage model to analyze the toughness design of the bridge pier, and the structural and material parameters of the bridge pier are adjusted according to the analysis result.
Description
Technical Field
The invention relates to the technical field of pier earthquake resistance, in particular to a method for analyzing toughness design of a unbonded prestressed reinforced concrete pier.
Background
The bridge plays an important role in a traffic network, and once the bridge is destroyed after an earthquake occurs, the bridge cannot be used normally, so that traffic paralysis can be possibly caused, and rescue and reconstruction work after the disaster are affected. After an earthquake occurs, the bridge may collapse, or may not collapse but a large residual displacement occurs to lose its normal use function.
The toughness-based earthquake-resistant structure can quickly recover to a certain functional level after earthquake, and the structure is required to have smaller earthquake requirement and smaller residual displacement. Unbonded prestressed reinforced concrete (Unbonded Prestressed Reinforced Concrete, UBPRC) piers, as a self-centering member, have small residual displacement and are increasingly receiving attention in earthquake-resistant designs. The UBPRC bridge pier is designed to have toughness, so that the bridge can avoid losing normal use functions due to overlarge residual displacement, and the requirement of toughness and earthquake resistance is met, but the toughness design of the UBPRC bridge pier still needs a quick quantitative calculation method, so that the problem is to be solved.
Disclosure of Invention
In order to avoid and overcome the technical problems in the prior art, the invention provides a method for analyzing toughness design of a non-binding prestressed reinforced concrete pier. The invention can calculate the structure and material parameters of the bridge pier more accurately, thereby improving the earthquake resistance of the bridge pier.
In order to achieve the above purpose, the present invention provides the following technical solutions:
the method for designing the analysis toughness of the unbonded prestressed reinforced concrete pier comprises the following design steps:
s1, determining design parameters of the unbonded prestressed reinforced concrete bridge pier, and obtaining the capacity of the bridge pier;
s2, obtaining the drift ratio and the residual drift ratio of the bridge pier according to the design parameters, and defining the damage state of the bridge pier;
s3, constructing a consistent damage model for representing the toughness design of the bridge pier through the relation among the capacity, the drift ratio and the residual drift ratio of the bridge pier;
s4, inputting design parameters of the bridge pier into the consistent damage model to analyze the toughness design of the bridge pier, and adjusting the structure and material parameters of the bridge pier according to analysis results.
As still further aspects of the invention: determining the numerical value of each design parameter of the bridge pier, wherein the design parameters comprise the height, slenderness ratio, axial pressure ratio, longitudinal reinforcement arrangement rate, stirrup arrangement rate, compressive strength of concrete, yield strength of longitudinal reinforcement, prestress reinforcement arrangement rate and prestress degree of the bridge pier;
the damage states of the bridge pier comprise two types, namely a drift ratio damage state and a residual drift ratio damage state;
the damage state of the bridge pier when the drift ratio is taken as the bridge pier engineering demand parameter is called a drift ratio damage state, and the drift ratio damage state corresponds to the capacity of the bridge pier when the drift ratio is taken as the bridge pier engineering demand parameter, and the capacity is called a drift ratio capacity;
the damaged state of the bridge pier when the residual drift ratio is taken as the bridge pier engineering demand parameter is called as a residual drift ratio damaged state, and the residual drift ratio damaged state corresponds to the capacity of the bridge pier when the residual drift ratio is taken as the bridge pier engineering demand parameter, and the capacity is called as a residual drift ratio capacity;
the specific energy of drift of the bridge pier is calculated as follows:
X T ＝[1ln(A r ) ln(α c ) ln(ρ l ) ln(ρ s ) ln(f c ) ln(f y ) ln(ρ p ) ln(αp a )]
wherein delta i The capability value of the pier in the ith drift ratio damage state is represented, namely the ith drift ratio capability; x represents a parameter matrix formed by each design parameter of the bridge pier; t represents matrix transposition;when the bridge pier is in the ith drift ratio damage state, a coefficient matrix consisting of each coefficient to be determined corresponding to the design parameters of the bridge pier is represented;
ln represents a logarithmic function; a is that r Representing the slenderness ratio of the bridge pier; alpha c Representing the axle pressure ratio of the bridge pier; ρ l Representing the longitudinal reinforcement ratio of the bridge pier; ρ s Representing the stirrup arrangement rate of the bridge pier; f (f) c Representing the compressive strength of the pier concrete; f (f) y Representing the yield strength of the longitudinal steel bars of the bridge pier; ρ p Expressing the reinforcement ratio of prestressed reinforcement of the bridge pier; alpha ps The prestress degree of the bridge pier is represented.
As still further aspects of the invention: the specific steps for obtaining the drift ratio and the residual drift ratio of the bridge pier are as follows:
S2A1, simulating a main body of a pier by using a nonlinear beam column unit in OpenSees finite element analysis software, wherein the nonlinear beam column unit takes a plastic hinge length of 6 times;
S2A2, simulating unbonded prestressed reinforcement in the pier by using truss units in OpenSees finite element analysis software, wherein the truss units are connected with bottom and top nodes of the main body;
S2A3, simulating bonding slip of steel bars in the bridge pier by using a zero length unit in OpenSees finite element analysis software, so as to form a finite element model of the bridge pier, wherein the axis of the bridge pier in the finite element model of the bridge pier is a prestressed steel bar, core concrete is coated on the outer side of the prestressed steel bar, longitudinal steel bars are arranged on the outer side of the core concrete in a surrounding manner, and protective layer concrete is coated on the outer side of the longitudinal steel bars;
S2A4, inputting the numerical value of each design parameter of the bridge pier into a finite element model, and obtaining a drift ratio corresponding to the bridge pier through simulation;
S2A5, inputting the obtained drift ratio and design parameters corresponding to the bridge pier under the drift ratio into a prediction formula of the residual drift ratio to calculate the residual drift ratio; the prediction formula is specifically as follows:
wherein,a matrix of 4 multiplied by 1, which represents the corresponding residual drift ratio of the bridge pier in the damaged state of the four residual drift ratios; y is a matrix of four rows and one column, and represents the corresponding drift ratio of the bridge pier in the damage state of the four drift ratios; x represents a parameter matrix formed by nine design parameters of the bridge pier; b represents a coefficient matrix composed of coefficients corresponding to nine design parameters of the bridge pier.
As still further aspects of the invention: the drift ratio damage state definition process is as follows:
S2B1, when the strain of the protective layer concrete reaches the maximum strain, the bridge pier is damaged, the damage is defined as slight damage, and the first drift specific energy is corresponding to the second drift specific energy;
S2B2, when the yield strength of the longitudinal steel bars reaches the yield limit, the bridge pier is damaged, the damage is defined as medium damage, and the second drift specific energy corresponds to the second drift specific energy;
S2B3, when the stress of the core concrete reaches the maximum stress, the bridge pier is damaged, the damage is defined as serious damage, and the third drift specific energy is corresponding to the damage;
S2B4, when the strain of the core concrete reaches the maximum strain, the bridge pier is damaged, the damage is defined as complete damage, and the fourth drift specific energy is corresponding to the damage;
as still further aspects of the invention: the residual drift ratio damage state definition process is as follows:
S2C1, when the value of the residual drift ratio is [0,0.25 percent ], the bridge pier is not damaged;
S2C2, when the value of the residual drift ratio is 0.25 percent and 0.5 percent, the bridge pier is damaged, and the bridge defines the damage as slight damage and corresponds to the first residual drift ratio capacity;
S2C3, when the value of the residual drift ratio is 0.5% and 0.75%, the bridge pier is damaged, the damage is defined as medium damage, and the second residual drift ratio capability is corresponding to the bridge pier;
S2C4, when the value of the residual drift ratio is 0.75% and 1%, the bridge pier is damaged, the damage is defined as serious damage, and the damage corresponds to the third residual drift ratio capacity;
S2C5, when the value of the residual drift ratio is 1 percent and +infinity, the bridge pier is damaged, the damage is defined as complete damage, corresponding to a fourth residual drift specific energy capacity.
As still further aspects of the invention: the specific contents of the establishment of the consistent damage model are as follows: taking the drift ratio and the residual drift ratio as pier engineering requirement parameters simultaneously, and recording the probability that the pier reaches complete damage simultaneously in a drift ratio damage state and a residual drift ratio damage state as a set threshold value, wherein the damage state of the pier is called a consistent damage state; then constructing a toughness design analysis model according to the consistent damage state;
the analytical formula of the toughness design analytical model is expressed as follows:
wherein ω (X) is a consistent damage status value; beta 0 、β 1 、…、β 8 Representing regression coefficients corresponding to each design parameter when the bridge pier is in a residual drift ratio damage state; gamma ray i0 、γ i1 、…、γ i8 Representing undetermined coefficients corresponding to each design parameter when the bridge pier is in an ith drift ratio damage state;the capability value of the pier in the damaged state of the ith residual drift ratio is shown, namely the capability of the ith residual drift ratio.
As still further aspects of the invention: determining the values of each regression coefficient and the parameters to be determined, and inputting the values of each design parameter of the bridge pier into the toughness design analysis model for calculation; the calculation results are as follows:
when ω (X) =0, the bridge taking the drift ratio and the residual drift ratio as the pier engineering requirement parameters is in a consistent damage state;
when omega (X) is more than 0, the drift ratio reaches a set threshold value before the damage state, and the pier belongs to the toughness design, wherein the toughness design is a target design mode;
when omega (X) is less than 0, the residual drift reaches a set threshold value before the damage state, and the pier belongs to a non-ductile design;
and adjusting each design parameter of the bridge pier according to the calculation result so as to enable the design mode of the bridge pier to be toughness design.
As still further aspects of the invention: the set threshold is 50%.
Compared with the prior art, the invention has the beneficial effects that:
1. the invention defines the damage state of the structure by taking the drift ratio and the residual drift ratio as engineering requirement parameters. And deducing an analysis formula of the toughness design according to a capacity formula of the UBPRC bridge pier and a prediction formula of the residual drift ratio. According to the analysis formula, the values of the parameters when the structure reaches 50% damage probability simultaneously under two engineering demand parameters can be calculated. Meanwhile, the value range of each parameter in the process of toughness design is calculated. The toughness design method can be used for conveniently calculating the values of all structural and material parameters in the toughness design, and can be applied to the preliminary design of unbonded prestressed reinforced concrete piers.
Drawings
FIG. 1 is a flow chart of the main parsing steps of the present invention.
Fig. 2 is a schematic structural diagram of a finite element model of a pier according to the present invention.
FIG. 3 is a diagram of alpha in the present invention c Structural seismic damage probability change plot at=0.06.
FIG. 4 is a diagram of alpha in the present invention c Structural seismic impairment probability variation graph at =0.106.
FIG. 5 is a diagram of alpha in the present invention c Structural seismic impairment probability variation graph at=0.2.
FIG. 6 is a view of alpha in the present invention ps Structural seismic impairment probability variation graph at=0.02.
FIG. 7 is a view of alpha in the present invention ps Structural seismic damage probability change plot at =0.051.
FIG. 8 is a view of alpha in the present invention ps Structural seismic impairment probability variation graph at =0.18.
FIG. 9 is ρ in the present invention p Structural seismic impairment probability variation graph at =0.006.
FIG. 10 is a graph of ρ in the present invention p Structural seismic impairment probability change plot at =0.014.
FIG. 11 is ρ in the present invention p Structural seismic impairment probability variation graph at=0.02.
FIG. 12 is ρ in the present invention l Structural seismic impairment probability variation graph at =0.006.
FIG. 13 is ρ in the present invention l Structural seismic impairment probability variation graph at =0.0114.
FIG. 14 is ρ in the present invention l Structural seismic impairment probability variation graph at =0.03.
FIG. 15 shows PGV with alpha in the present invention c Schematic change.
FIG. 16 shows PGV with alpha in the present invention ps Schematic change.
FIG. 17 shows PGV with ρ in the present invention p Schematic change.
FIG. 18 shows PGV with ρ in the present invention l Schematic change.
Fig. 19 is a consistent damage state diagram in the present invention.
FIG. 20 is a view of a in the present invention c Consistent injury status plot at=0.06.
FIG. 21 is a view of a in the present invention c Consistent injury status plot at =0.12.
FIG. 22 is a view of a in the present invention c Consistent injury status plot at =0.18.
FIG. 23 is a view of a in the present invention c ρ when=0.06 l And alpha ps The parameter plane divides the graph.
FIG. 24 is a view of a in the present invention c ρ when=0.12 l And alpha ps The parameter plane divides the graph.
FIG. 25 is a view of alpha in the present invention c ρ when=0.18 l And alpha ps The parameter plane divides the graph.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
Referring to fig. 1, in the embodiment of the invention, the method for designing the analytical toughness of the unbonded prestressed reinforced concrete pier mainly comprises the following steps:
building UBPRC bridge pier finite element model
As shown in fig. 2, a finite element model of UBPRC bridge pier is built in openses. The bridge pier height H is 9.8m, the section is square with the side length D of 1.4m, and the slenderness ratio A of the bridge pier r =h/D is 7. Ratio of axial pressure alpha c 0.095. The bridge pier is simulated by using nonlinear beam column units, and the length of each unit is 6 times of the length of each plastic hinge. In the discrete fiber section, both the protective layer concrete and the core concrete were modeled using a Kent-Scott-Park model, concrete strength f c 31.25MPa. Longitudinal reinforcement bar arrangement rate ρ l Yield strength f of longitudinal steel bar of 0.012MPa y Is the pressure of the water at 400MPa,stirrup rate ρ s 0.0138, was modeled using a Steel02 constitutive model. The prestressed reinforcement in the pier is modeled by truss units that connect the bottom and top nodes and run through the entire UBPRC pier. Prestressed reinforcement arrangement rate ρ p 0.0085, modeling by adopting a Steel02 constitutive model, and prestress degree alpha ps Is 0.04. The zero length unit in the finite element model simulates the Bond slip effect of the longitudinal rebar modeled using bond_sp01 constitutive model. Specific values of each design parameter in the UBPRC pier model are shown in table 1.
TABLE 1 design parameters of pier
2. Definition of damage states based on drift ratio and residual drift ratio
The damage limit state with the drift ratio as the engineering requirement parameter is defined by the stress-strain relationship of the steel bar and the concrete, and the results are shown in table 2. Wherein the slight damage state is defined as the strain epsilon of the concrete of the protective layer cc Reaching maximum strain epsilon cu0 . At this stage, the structure exhibits slight damage without affecting its normal functioning. When the yield strength epsilon of the longitudinal steel bars s Reaching the yield limit epsilon y At this time, a moderate injury state is reached. When the stress sigma of the core concrete c Reaching its maximum stress f c1 When the structure reaches a severely damaged state. The complete damage state is defined as strain epsilon of core concrete c Reaching maximum strain epsilon cu1 At this point, the structure loses its load carrying capacity entirely.
TABLE 2 definition of damage limit conditions with drift ratio as engineering demand parameter
When drift ratios are used as engineering requirement parameters, the ability of the structure in the damaged state for each drift ratio can be calculated using the equations below. X is x i For each parameter corresponding to Table 1, γ ij And representing the undetermined coefficient corresponding to the design parameter of the jth bridge pier in the ith drift ratio damage state as the corresponding undetermined coefficient.
δ 4×1 ＝Γ 4×9 ·X 9×1
Wherein delta 4×1 The capacity matrix of the bridge pier in a drift ratio loss state is represented, and the dimension is 4 multiplied by 1; Γ -shaped structure 4×9 The coefficient matrix which is composed of all the coefficients to be determined when the bridge pier is in a drift ratio loss state is represented, and the dimension is 4 multiplied by 9;representing a coefficient matrix formed by corresponding undetermined coefficients when the bridge pier is in a first drift ratio loss state; />Representing a coefficient matrix formed by corresponding undetermined coefficients when the bridge pier is in a first drift ratio loss state; />Representing a coefficient matrix formed by corresponding undetermined coefficients when the bridge pier is in a first drift ratio loss state; />And the coefficient matrix is formed by corresponding undetermined coefficients when the bridge pier is in the first drift ratio loss state.
X 9×1 T ＝[x 0 x 1 x 2 x 3 x 4 x 5 x 6 x 7 x 7 ]
The following equation set is established:
the values of the undetermined coefficients are shown in table 3.
TABLE 3 gamma ij Is of the value of (2)
Residual displacement is a key indicator for evaluating post-seismic structural function and repairability. A specific description of the four damage states defined based on the residual drift ratio is given in table 4. When the residual drift ratio is less than 0.25%, the structure does not need to be repaired. With residual drift ratios between 0.25% and 0.5%, the structure reaches a moderately damaged state, and small parts of the structure need to be repaired. When the residual drift ratio is greater than 0.5% but less than 0.75%, the structure may reach a severely damaged state, requiring maintenance of the main components. When the residual displacement reaches or exceeds 1%, the structure reaches a fully damaged condition, making repair difficult or uneconomical, in which case removal is often preferred.
TABLE 4 definition of damage limit states with residual drift ratio as engineering demand parameter
3. Prediction formula of residual drift ratio
Wherein,a matrix of four rows and one column, representing the residual drift ratio of the structure in the four damage states defined above; y is a matrix of four rows and one column, representing the drift ratio of the structure in the four damage states defined above. The values of the regression parameters in the matrix B are shown in Table 5.
TABLE 5 regression coefficient values
4. Creation of a toughness design analytical model
When the drift ratio and the residual drift ratio are used as engineering requirement parameters, the probability that the structure can reach complete damage simultaneously is 50%. In the case of both engineering demand parameters, the probability of damage to the structure to reach 50% simultaneously is called consistent damage. When the damage probability of the structure reaches 50%, the seismic requirement of the structure is the same as the bearing capacity of the structure. When drift and residual drift ratios are used as engineering demand parameters, it can be expressed as:
wherein y is a matrix of four rows and one column, and represents the drift ratio of the structure in the four damage states defined above. Delta sumThe ability of the device to correspond to four damage states can be calculated by the formulaThe calculation can be obtained from table 4.
According to the prediction formula of the residual drift ratio and the capacity calculation formula of the UBPRC bridge pier, the method can be as follows:
the analytical formula of the toughness design analytical model is expressed as follows:
wherein the following steps:
then there are:
where ζ is a matrix of corresponding coefficients representing a vector of the ability of the damage state to be defined in terms of residual drift ratio. When ω (X) =0, this means that the UBPRC pier will reach 50% probability of damage at the same time, i.e. the structure reaches a consistent damage state, using the drift ratio and the residual drift ratio as pier engineering requirement parameters at the same time. If ω (X) > 0, it is shown that the drift ratio is used as the pier engineering demand parameter, the total damage in the damaged state reaches 50% damage probability first. In contrast, if ω (X) < 0, it is indicated that the residual drift ratio is used as the pier engineering demand parameter, the damage probability of the complete damage in the damaged state reaches 50% first.
5. Parameter design based on consistent damage
The proposed matrix-based analytical formula can be used to evaluate and design the earthquake-resistant performance of UBPRC piers. Taking the UBPRC bridge pier as an example, the parameters of the bridge pier are shown in Table 1, and the fourth loss is calculatedThe wound status was studied. Given a consistent damage to the structure, the design parameters (α c ,α ps ,ρ p ,ρ l ) Is a value of (a). In order to clearly present the results, the definitions provided in table 6 are used.
Table 6 description of the results
Taking the fourth damage state as an example, the values of the corresponding coefficients in the analytical formula are shown in table 7.
TABLE 7 value of the corresponding coefficient in the fourth damaged condition
The structure can reach 50% damage probability at the same time by adjusting the values of the related parameters according to the analytic formula. Reinforcement Rate ρ of longitudinal reinforcing steel for selected UBPRC bridge pier l Prestressed reinforcement arrangement rate ρ p Prestress degree alpha ps And an axial pressure ratio alpha c The structure reached consistent damage when the values were 1.14%,1.40%,0.051,0.106, respectively. When one of the parameters is adjusted, the remaining parameters remain unchanged.
Figures 3 to 14 show the following alpha c ，α ps ，ρ p ，ρ l A change in the probability of structural seismic damage. Dr represents the drift ratio, RDr represents the residual drift ratio, and PGV represents the ground peak velocity. It can be observed from fig. 3 to 8 that the axial compression ratio α follows c And prestress degree alpha ps The failure behavior of UBPRC pier is gradually changed from a non-ductile design to a ductile design. This indicates that when alpha c And alpha ps Less, neglecting the effect of residual displacement in the anti-seismic design may result in significant residual displacement. And as shown in fig. 12 to 14, the longitudinal reinforcement ratio ρ is increased l The opposite effect would result. In addition, fig. 9 to 11 show that the reinforcement ratio ρ of the prestressed reinforcement p The change in (c) has less impact on the probability of damage.
Fig. 15 to 18 show the change in PGV as the parameter value increases when the probability of damage of UBPRC column reaches 50%. The transition point from the non-ductile design to the ductile design may be determined from fig. 15-18. At this point, the structure reaches a consistent damage state. As shown in fig. 15 to 18, when the reinforcement ratio ρ of the longitudinal reinforcement is l Prestressed reinforcement arrangement rate ρ p Prestress degree alpha ps And an axial pressure ratio alpha c The values of (2) are 1.14%,1.40% and 0.051,0.106, respectively, and a damage probability of 50% is achieved. This is consistent with the results obtained from the proposed expression.
6. Parameter value range based on analytic design method
Design parameter alpha according to toughness design analysis formula c ,α ps ,ρ l Is designed according to the value range of the number. As shown in table 8, the values of the remaining parameters remain unchanged.
Table 8 parameter values
For the fourth damage state, the toughness design analytical formula can be written as follows:
each ζ used in the pair is a corresponding coefficient shown in table 7. According to Table 4, the capacity value in the completely damaged state is 1%.
According to Table 8, the above formula is divided by α c 、α ps And ρ l Other parameters are known, and the formula can be written as:
wherein:
ω 0 ＝ξ 40 +ξ 41 ln(A r )+ξ 44 ln(ρ s )+ξ 45 ln(f c )+ξ 46 ln(f y )+ξ 47 ln(ρ p )
and then the following calculation formula is obtained:
when the structure reaches a consistent damage, i.e., ω=0.
When ω=0 is established, the structure reaches a uniform damage, as shown by the curved surface in fig. 19. When the parameter is located above the curved surface shown in fig. 19, the structure first reaches 50% of damage probability, i.e. non-ductile design, with the residual drift ratio as the engineering requirement parameter. And when the parameter value is located below the curved surface shown in fig. 19, the structure belongs to the toughness design.
As shown in fig. 20 to 25. Fig. 23 to 25 show the intersection between the curved surface and the plane ω=0 corresponding to fig. 20 to 22. Intersecting line will ρ l And alpha ps The parameter plane is divided into two distinct regions. In fig. 23 to 25, the ω value in the right area of the intersection is larger than 0, and in this case, the damage probability in the completely damaged state with the residual drift ratio as the engineering demand parameter reaches 50% first, and the structure is of a non-ductile design. In contrast, the ω value in the left region of the intersection is smaller than 0, and in this case, the damage probability of the completely damaged state with the drift ratio as the engineering demand parameter reaches 50% first, and the structure is designed to be ductile.
The foregoing is only a preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art, who is within the scope of the present invention, should make equivalent substitutions or modifications according to the technical scheme of the present invention and the inventive concept thereof, and should be covered by the scope of the present invention.
Claims (8)
1. The method for designing the analysis toughness of the unbonded prestressed reinforced concrete pier is characterized by comprising the following design steps of:
s1, determining design parameters of the unbonded prestressed reinforced concrete bridge pier, and obtaining the capacity of the bridge pier;
s2, obtaining the drift ratio and the residual drift ratio of the bridge pier according to the design parameters, and defining the damage state of the bridge pier;
s3, constructing a consistent damage model for representing the toughness design of the bridge pier through the relation among the capacity, the drift ratio and the residual drift ratio of the bridge pier;
s4, inputting design parameters of the bridge pier into the consistent damage model to analyze the toughness design of the bridge pier, and adjusting the structure and material parameters of the bridge pier according to analysis results.
2. The method for analytical toughness design of unbonded prestressed reinforced concrete piers according to claim 1, wherein the numerical values of each design parameter of the pier are determined, and the design parameters include the height, slenderness ratio, axial compression ratio, longitudinal reinforcement bar arrangement rate, stirrup arrangement rate, compressive strength of concrete, yield strength of longitudinal reinforcement bar, prestressed reinforcement bar arrangement rate and prestress degree of the pier;
the damage states of the bridge pier comprise two types, namely a drift ratio damage state and a residual drift ratio damage state;
the damage state of the bridge pier when the drift ratio is taken as the bridge pier engineering demand parameter is called a drift ratio damage state, and the drift ratio damage state corresponds to the capacity of the bridge pier when the drift ratio is taken as the bridge pier engineering demand parameter, and the capacity is called a drift ratio capacity;
the damaged state of the bridge pier when the residual drift ratio is taken as the bridge pier engineering demand parameter is called as a residual drift ratio damaged state, and the residual drift ratio damaged state corresponds to the capacity of the bridge pier when the residual drift ratio is taken as the bridge pier engineering demand parameter, and the capacity is called as a residual drift ratio capacity;
the specific energy of drift of the bridge pier is calculated as follows:
X T ＝[1 ln(A r ) ln(α c ) ln(ρ l ) ln(ρ s ) ln(f c ) ln(f y ) ln(ρ p ) ln(α ps )]
wherein delta i The capability value of the pier in the ith drift ratio damage state is represented, namely the ith drift ratio capability; x represents a parameter matrix formed by each design parameter of the bridge pier; t represents matrix transposition;when the bridge pier is in the ith drift ratio damage state, a coefficient matrix consisting of each coefficient to be determined corresponding to the design parameters of the bridge pier is represented;
ln represents a logarithmic function; a is that r Representing the slenderness ratio of the bridge pier; alpha c Representing the axle pressure ratio of the bridge pier; ρ l Representing the longitudinal reinforcement ratio of the bridge pier; ρ s Representing the stirrup arrangement rate of the bridge pier; f (f) c Representing the compressive strength of the pier concrete; f (f) y Representing the yield strength of the longitudinal steel bars of the bridge pier; ρ p Expressing the reinforcement ratio of prestressed reinforcement of the bridge pier; alpha ps The prestress degree of the bridge pier is represented.
3. The method for analytical toughness design of unbonded prestressed reinforced concrete piers according to claim 2, wherein the specific steps of obtaining the drift ratio and the residual drift ratio of the piers are as follows:
S2A1, simulating a main body of a pier by using a nonlinear beam column unit in OpenSees finite element analysis software, wherein the nonlinear beam column unit takes a plastic hinge length of 6 times;
S2A2, simulating unbonded prestressed reinforcement in the pier by using truss units in OpenSees finite element analysis software, wherein the truss units are connected with bottom and top nodes of the main body;
S2A3, simulating bonding slip of steel bars in the bridge pier by using a zero length unit in OpenSees finite element analysis software, so as to form a finite element model of the bridge pier, wherein the axis of the bridge pier in the finite element model of the bridge pier is a prestressed steel bar, core concrete is coated on the outer side of the prestressed steel bar, longitudinal steel bars are arranged on the outer side of the core concrete in a surrounding manner, and protective layer concrete is coated on the outer side of the longitudinal steel bars;
S2A4, inputting the numerical value of each design parameter of the bridge pier into a finite element model, and obtaining a drift ratio corresponding to the bridge pier through simulation;
S2A5, inputting the obtained drift ratio and design parameters corresponding to the bridge pier under the drift ratio into a prediction formula of the residual drift ratio to calculate the residual drift ratio; the prediction formula is specifically as follows:
wherein,a matrix of 4 multiplied by 1, which represents the corresponding residual drift ratio of the bridge pier in the damaged state of the four residual drift ratios; y is a matrix of four rows and one column, and represents the corresponding drift ratio of the bridge pier in the damage state of the four drift ratios; x represents a parameter matrix formed by nine design parameters of the bridge pier; b represents a coefficient matrix composed of coefficients corresponding to nine design parameters of the bridge pier.
4. A method of analytical toughness design for a unbonded prestressed reinforced concrete pier according to claim 3, characterized in that the drift ratio damage condition defining process is as follows:
S2B1, when the strain of the protective layer concrete reaches the maximum strain, the bridge pier is damaged, the damage is defined as slight damage, and the first drift specific energy is corresponding to the second drift specific energy;
S2B2, when the yield strength of the longitudinal steel bars reaches the yield limit, the bridge pier is damaged, the damage is defined as medium damage, and the second drift specific energy corresponds to the second drift specific energy;
S2B3, when the stress of the core concrete reaches the maximum stress, the bridge pier is damaged, the damage is defined as serious damage, and the third drift specific energy is corresponding to the damage;
S2B4, when the strain of the core concrete reaches the maximum strain, the bridge pier is damaged, the damage is defined to be complete damage, and the fourth drift specific energy is corresponding to the fourth drift specific energy.
5. The method for analytical toughness design of a unbonded prestressed reinforced concrete pier according to claim 4, wherein the residual drift ratio damage state defining process is as follows:
S2C1, when the value of the residual drift ratio is [0,0.25 percent ], the bridge pier is not damaged;
S2C2, when the value of the residual drift ratio is 0.25 percent and 0.5 percent, the bridge pier is damaged, and the bridge defines the damage as slight damage and corresponds to the first residual drift ratio capacity;
S2C3, when the value of the residual drift ratio is 0.5% and 0.75%, the bridge pier is damaged, the damage is defined as medium damage, and the second residual drift ratio capability is corresponding to the bridge pier;
S2C4, when the value of the residual drift ratio is 0.75% and 1%, the bridge pier is damaged, the damage is defined as serious damage, and the damage corresponds to the third residual drift ratio capacity;
S2C5, when the value of the residual drift ratio is 1 percent and +infinity, the bridge pier is damaged, the damage is defined as complete damage, corresponding to a fourth residual drift specific energy capacity.
6. The method for analytical toughness design of a unbonded prestressed reinforced concrete pier according to claim 5, wherein the specific contents of the establishment of the consistent damage model are as follows: taking the drift ratio and the residual drift ratio as pier engineering requirement parameters simultaneously, and recording the probability that the pier reaches complete damage simultaneously in a drift ratio damage state and a residual drift ratio damage state as a set threshold value, wherein the damage state of the pier is called a consistent damage state; then constructing a toughness design analysis model according to the consistent damage state;
the analytical formula of the toughness design analytical model is expressed as follows:
wherein ω (X) is a consistent damage status value; beta 0 、β 1 、…、β 8 Representing regression coefficients corresponding to each design parameter when the bridge pier is in a residual drift ratio damage state; gamma ray i0 、γ i1 、…、γ i8 Representing undetermined coefficients corresponding to each design parameter when the bridge pier is in an ith drift ratio damage state;the capability value of the pier in the damaged state of the ith residual drift ratio is shown, namely the capability of the ith residual drift ratio.
7. The method for analyzing toughness design of the unbonded prestressed reinforced concrete pier according to claim 6, wherein the numerical values of each regression coefficient and the undetermined parameter are determined, and the numerical values of each design parameter of the pier are input into a toughness design analysis model for calculation; the calculation results are as follows:
when ω (X) =0, the bridge taking the drift ratio and the residual drift ratio as the pier engineering requirement parameters is in a consistent damage state;
when omega (X) is more than 0, the drift ratio reaches a set threshold value before the damage state, and the pier belongs to the toughness design, wherein the toughness design is a target design mode;
when omega (X) is less than 0, the residual drift reaches a set threshold value before the damage state, and the pier belongs to a non-ductile design;
and adjusting each design parameter of the bridge pier according to the calculation result so as to enable the design mode of the bridge pier to be toughness design.
8. The method of claim 7, wherein the set threshold is 50%.
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