CN113704859A - Concrete bridge flood vulnerability analysis method considering bridge pier failure mode - Google Patents
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Abstract
The invention discloses a concrete bridge flood vulnerability analysis method considering a bridge pier failure mode, which comprises the following steps: 1. determining basic information of a bridge to be researched, wherein the basic information comprises bridge deck size, pier structure and reinforcement information; 2. calculating the shearing resistance bearing capacity of the bridge pier based on the basic information of the bridge pier; 3. constructing a bridge numerical analysis model in OpenSees based on the bridge basic information; 4. determining the water flow depth, further applying uniform load at the corresponding depth of the bridge, and performing push-coating analysis until the bridge pier reaches the maximum bearing capacity; 5. determining the water flow acting force when the bridge pier reaches the maximum bearing capacity, and calculating the water flow speed at the moment; 6. obtaining the water flow velocity of the bridge pier at different depths when the bridge pier collapses, and fitting to obtain a bridge flood vulnerability curve; the method provides a scheme for analyzing the vulnerability of the bridge under the action of flood, simultaneously considers the response influence of the shear failure mode of the bridge pier on the vulnerability of the bridge under the action of flood impact, and is favorable for accurately evaluating the vulnerability of the concrete bridge under the action of flood.
Description
Technical Field
The invention relates to a performance analysis method of a concrete bridge under the action of flood, in particular to a concrete bridge flood vulnerability analysis method considering a bridge pier failure mode.
Background
China is a country with frequent flood, and particularly in southern areas, the rain is abundant in summer and the phenomenon of flood waterlogging is frequent. When a flood occurs, huge water flow acting force can cause huge safety influence on the bridge. Therefore, the safety performance of the concrete bridge under the action of flood impact can be analyzed, guidance can be provided for disaster relief rescue, and help can be provided for bridge maintenance decision. However, an analysis method for vulnerability of the concrete bridge under the action of flood impact is still lacked at present, and particularly, an analysis method for shear damage of pier columns possibly occurs when the depth of flood is shallow and the flow rate is high is considered. The invention provides a concrete bridge flood vulnerability analysis method considering a bridge pier failure mode. Vulnerability characterizes the probability of structural failure under different disaster intensities. The method can provide the probability of bridge collapse under different water flow speeds and water flow depths, and has very important guiding significance for judging the safety performance of the bridge.
Disclosure of Invention
The invention aims to provide a concrete bridge flood vulnerability analysis method considering a pier failure mode, which can give the collapse probability of a bridge under the action of flood according to the design parameters of the bridge, the water flow speed and the water flow depth and help to judge the safety performance of the bridge under the flood disaster.
The technical scheme adopted by the invention is as follows: a concrete bridge flood vulnerability analysis method considering bridge pier failure modes comprises the following steps:
(1) determining basic information of a bridge to be researched, wherein the basic information comprises bridge deck size, pier structure and reinforcement information;
(2) calculating the shearing resistance bearing capacity of the bridge pier based on the basic information of the bridge pier;
(3) constructing a bridge numerical analysis model in OpenSees based on the bridge basic information;
(4) determining the water flow depth, further applying uniform load at the corresponding depth of the bridge, and performing push-coating analysis until the bridge pier reaches the maximum bearing capacity;
(5) determining the water flow acting force when the bridge pier reaches the maximum bearing capacity, and calculating the water flow speed at the moment;
(6) and (5) repeating the steps (4) and (5), obtaining the water flow velocity when the piers collapse under different depths, and fitting to obtain a bridge flood vulnerability curve.
Further, the basic information of the bridge in the step (1) mainly comprises: the bridge span L, the bridge deck width De, the bridge deck height Dh, the concrete strength fc, the steel bar yield strength fy, the pier height ColH, the pier section width Cb, the pier section height Ch, the longitudinal bar reinforcement ratio pl, the stirrup reinforcement ratio pt, the bridge abutment foundation pile number Pn, the support number Bn, the support friction coefficient Cof, the bridge deck and bridge abutment gap Agap and the bridge deck and shear key gap Sgap.
Further, the calculation formula of the shear resistance bearing capacity of the bridge pier in the step (2) is as follows:
wherein VshearFor bridge pier shear-resisting bearing capacity, fcThe strength of the concrete is the strength of the concrete,ais the height of the pier, d is the effective height of the section of the pier, P is the axial force of the pier, AgIs the cross-sectional area of a pier, AsTotal area of stirrups parallel to the direction of loading, fyThe yield strength of the stirrups and s the distance between the stirrups.
Further, the initial stiffness of the pier shear response in step (3) is assumed to be infinite, i.e., the pier shear deformation is not considered, and only the influence of the shear load is considered.
Further, in the step (4), when the water flow depth does not reach the bottom of the bridge deck, only the acting force of the water flow on the pier is considered, and the water flow force exerted on the pier is assumed to be the pressure p uniformly distributed along the height.
When the water flow depth exceeds the height of the pier in the step (4), the water flow force applied to the bridge deck needs to be considered besides the acting force of the water flow on the pier.
The water flow force applied on the bridge deck is buoyancy, the direction of the water flow force acts on the center line of the bridge deck vertically and upwards, and the calculation method of the buoyancy comprises the following steps:
Ff＝ρsgdhwd
wherein, FfFor buoyancy forces exerted on the deck of the bridge, psIs the density of the water flow, g is the acceleration of gravity, dhThe depth of the water flow on the bridge deck, wd the width of the bridge deck.
The method for defining the maximum bearing capacity of the pier in the step (4) comprises the following steps: if maximum base shear FcBefore the displacement of 5 percent of the bridge pier occurs, the maximum bearing capacity of the bridge pier is directly taken as the maximum base shearing force F at the momentc(ii) a If maximum base shear FcWhen the maximum bearing capacity of the bridge pier is 5 percent of the base shearing force F after the displacement of the bridge pier is 5 percentc-5。
Further, the method for determining the water flow acting force when the bridge pier reaches the maximum bearing capacity in the step (5) comprises the following steps: according to the maximum bearing capacity of the bridge pier determined in the step (4), assuming that the corresponding water flow pressure applied to the bridge pier at the moment is p, the corresponding water flow acting force is as follows:
Fflood＝ph
wherein, FfloodH is the water flow depth applied to the pier at this time.
The method for determining the water flow speed when the bridge pier reaches the maximum bearing capacity in the step (5) comprises the following steps:
where ρ issIs the density of the water stream, deltaDAnd B is the water flow impact coefficient, B is the section width of the pier facing the water flow, and v is the water flow velocity.
In the method for determining the water flow speed when the bridge pier reaches the maximum bearing capacity in the step (5), the water flow density rhosCoefficient of water flow impact deltaDConsider notThe impact of the certainty is that,
wherein, the density of the water flow accords with the uniform distribution, and the distribution function is as follows:
wherein, a is 1000kg/m3，b＝1250kg/m3。
Preferably, the values of a and b can be determined by surveying the water area data of the bridge or by field test.
Wherein, the water flow impact coefficient accords with the even distribution, and its distribution function is:
wherein c is 1.0 and d is 2.
Preferably, the values of c and d can be determined according to the water area data investigation of the bridge or the field test.
Adopting a Monte-La-Luo simulation method to determine the water flow speed when the bridge pier reaches the maximum bearing capacity in the step (5), specifically, sampling 10000 water flow density values and 10000 water flow impact coefficient values, and further according to the formula in the step (5)
And respectively calculating the water flow speed value under each water flow density and water flow impact coefficient.
Further, in the step (6), a calculation formula of the bridge flood vulnerability curve at different depths is as follows:
wherein Φ is a cumulative distribution function;
for causing pier collapse under corresponding heightMedian water velocity of betavIs the standard deviation of the water velocity.
Has the advantages that: aiming at the concrete bridge under the action of flood, the invention can accurately give the collapse probability of the bridge under the action of flood impact only according to the bridge design information, the flood water flow speed, the depth, the density and other information; the influence of a potential shear failure mode of the pier under shallow water flow and fast water speed can be considered; the method has very important guiding significance for judging the safety performance of the bridge under the action of flood, and can provide help for bridge performance evaluation in a flood-prone area.
Drawings
FIG. 1 is a schematic flow diagram of the present invention.
Fig. 2 is a schematic view of the application of water flow on a bridge.
Fig. 3 is a schematic diagram illustrating a method for defining a maximum bearing capacity of a bridge pier.
Detailed Description
The invention is further described with reference to the following figures and detailed description.
As shown in fig. 1, a method for analyzing a concrete bridge flood vulnerability considering a pier failure mode includes the following steps:
the method comprises the following steps: determining basic information of a bridge to be researched, wherein the basic information comprises bridge deck size, pier structure and reinforcement information;
the basic information of the bridge in the first step mainly comprises the following steps: the bridge span L, the bridge deck width De, the bridge deck height Dh, the concrete strength fc, the steel bar yield strength fy, the pier height ColH, the pier section width Cb, the pier section height Ch, the longitudinal bar reinforcement ratio pl, the stirrup reinforcement ratio pt, the bridge abutment foundation pile number Pn, the support number Bn, the support friction coefficient Cof, the bridge deck and bridge abutment gap Agap and the bridge deck and shear key gap Sgap.
Step two: calculating the shearing resistance bearing capacity of the bridge pier based on the basic information of the bridge pier;
and in the second step, the formula for calculating the shearing resistance and bearing capacity of the bridge pier is as follows:
wherein VshearFor bridge pier shear-resisting bearing capacity, fcThe strength of the concrete is the strength of the concrete,ais the height of the pier, d is the effective height of the section of the pier, P is the axial force of the pier, AgIs the cross-sectional area of a pier, AsTotal area of stirrups parallel to the direction of loading, fyThe yield strength of the stirrups and s the distance between the stirrups.
Step three: constructing a bridge numerical analysis model in OpenSees based on the bridge basic information;
as shown in fig. 2, in the third step, the concrete bridge pier is simulated by using a displacement-based beam-column unit in openses, specifically, an element dispbeeamccolumn unit;
the concrete pier adopts a unit division method that a unit is divided every 1 m in height;
a spring unit with zero length is arranged at the bottom of the pier and used for simulating shear response, and particularly an element zeroLength unit in OpenSees.
Setting the initial stiffness of a shear spring of the pier to be infinite;
the bridge deck is longitudinally simulated by adopting an elastic unit, in particular to an element elastic Beam column unit in OpenSees;
the bridge deck is simulated by rigid units in the constant direction, specifically, the element elastic Beam column units in OpenSees, and the rigidity is set to be infinite.
Step four: determining the water flow depth, further applying uniform load at the corresponding depth of the bridge, and performing push-coating analysis until the bridge pier reaches the maximum bearing capacity;
as shown in fig. 2, in the fourth step, when the water flow depth does not reach the bottom of the bridge deck, only the acting force of the water flow on the bridge pier is considered, and the water flow force applied on the bridge pier is assumed to be pressure p uniformly distributed along the height;
as shown in fig. 2, when the water flow depth exceeds the height of the bridge pier in the fourth step, in addition to the acting force of the water flow on the bridge pier, the water flow force applied to the bridge deck needs to be considered;
the water flow force applied on the bridge deck is buoyancy, the direction of the water flow force acts on the center line of the bridge deck vertically and upwards, and the calculation method of the buoyancy comprises the following steps:
Ff＝ρsgdhwd
wherein, FfFor buoyancy forces exerted on the deck of the bridge, psIs the density of the water flow, g is the acceleration of gravity, dhDepth of water flow on the bridge deck, wdIs the deck width of the bridge.
As shown in fig. 3, the method for defining the maximum bearing capacity of the pier in the fourth step includes: if maximum base shear FcBefore the displacement of 5 percent of the bridge pier occurs, the maximum bearing capacity of the bridge pier is directly taken as the maximum base shearing force F at the momentc(ii) a If maximum base shear FcWhen the maximum bearing capacity of the bridge pier is 5 percent of the base shearing force F after the displacement of the bridge pier is 5 percentc-5。
Step five: determining the water flow acting force when the bridge pier reaches the maximum bearing capacity, and calculating the water flow speed at the moment;
in the fifth step, the method for determining the water flow acting force when the bridge pier reaches the maximum bearing capacity comprises the following steps: according to the maximum bearing capacity of the bridge pier determined in the fourth step, assuming that the corresponding water flow pressure applied to the bridge pier at the moment is p, the corresponding water flow acting force is as follows:
Fflood＝ph
wherein, FfloodH is the water flow depth applied to the pier at this time.
In the fifth step, the method for determining the water flow speed when the bridge pier reaches the maximum bearing capacity comprises the following steps:
where ρ issIs the density of the water stream, deltaDAnd B is the water flow impact coefficient, B is the section width of the pier facing the water flow, and v is the water flow velocity.
In the fifth step, in the method for determining the water flow speed when the middle pier reaches the maximum bearing capacity, the water flow density rhosCoefficient of water flow impact deltaDTaking into account the effect of the uncertainty,
wherein, the density of the water flow accords with the uniform distribution, and the distribution function is as follows:
wherein, a is 1000kg/m3，b＝1250kg/m3。
aThe value of b can be determined by surveying the water area data of the bridge or by field test.
Wherein, the water flow impact coefficient accords with the even distribution, and its distribution function is:
wherein c is 1.0 and d is 2.
The values of c and d can be determined by investigation according to the water area data of the bridge or by field test.
Flow force F applied to bridge pier when determined that bridge pier fails or collapsesfloodThereafter, the water flow rate was determined using 10000 Monte Carlo simulations.
And specifically, 10000 water flow density values and 10000 water flow impact coefficient values are sampled, and then water flow velocity values under each water flow density and water flow impact coefficient are respectively calculated according to the formula in the step five.
Step six: and obtaining the water flow velocity of the pier at different depths when the pier collapses, and fitting to obtain a bridge flood vulnerability curve.
In the sixth step, the calculation formula of the bridge flood vulnerability curve at different depths is as follows:
where Φ is the cumulative distribution function.
Wherein,
the median value of 10000 water flow velocities, beta, causing pier collapse under a certain water flow depth in the step fivevIs the standard deviation of the water velocity.
And repeating the fourth step, the fifth step and the sixth step to obtain the vulnerability curves of the bridge collapse under different water flow depths.
The embodiments of the present invention are described in detail with reference to the drawings and the specific embodiments, but the present invention is not limited to the described embodiments. It will be apparent to those skilled in the art that various changes, modifications, substitutions and alterations can be made on the embodiments without departing from the spirit and scope of the inventive concept.
Claims (7)
1. A concrete bridge flood vulnerability analysis method considering bridge pier failure modes is characterized by comprising the following steps:
(1) determining basic information of a bridge to be researched, wherein the basic information comprises bridge deck size, pier structure and reinforcement information;
(2) calculating the shearing resistance bearing capacity of the bridge pier based on the basic information of the bridge pier;
(3) constructing a bridge numerical analysis model in OpenSees based on the bridge basic information;
(4) determining the water flow depth, further applying uniform load at the corresponding depth of the bridge, and performing push-coating analysis until the bridge pier reaches the maximum bearing capacity;
(5) determining the water flow acting force when the bridge pier reaches the maximum bearing capacity, and calculating the water flow speed at the moment;
(6) and (5) repeating the steps (4) and (5), obtaining the water flow velocity when the piers collapse under different depths, and fitting to obtain a bridge flood vulnerability curve.
2. The method for analyzing the flood vulnerability of the concrete bridge girder considering the bridge pier failure mode according to claim 1, wherein the basic information of the bridge girder in the step (1) mainly comprises: the bridge span L, the bridge deck width Wd, the bridge deck height Dh, the concrete strength fc, the steel bar yield strength fy, the pier height ColH, the pier section width Cb, the pier section height Ch, the longitudinal bar reinforcement ratio pl, the stirrup reinforcement ratio pt, the bridge abutment foundation pile number Pn, the support number Bn, the support friction coefficient Cof, the bridge deck and bridge abutment gap Agap and the bridge deck and shear key gap Sgap.
3. The method for analyzing the flood vulnerability of the concrete bridge considering the bridge pier failure mode according to claim 1, wherein the formula for calculating the shear-resistant bearing capacity of the bridge pier in the step (2) is as follows:
wherein VshearFor bridge pier shear-resisting bearing capacity, fcThe strength of the concrete is the strength of the concrete,ais the height of the pier, d is the effective height of the section of the pier, P is the axial force of the pier, AgIs the cross-sectional area of a pier, AsTotal area of stirrups parallel to the direction of loading, fyIn order to obtain the yield strength of the stirrup,sthe stirrup spacing.
4. The method for analyzing the flood vulnerability of the concrete bridge girders based on the pier failure mode of claim 1, wherein the initial stiffness of the pier shear response in the step (3) is assumed to be infinite, that is, the influence of the shear bearing capacity is considered without considering the pier shear deformation.
5. The method for analyzing a concrete bridge pier flood vulnerability according to a pier failure mode, according to claim 1, wherein the water flow force exerted on the pier in the step (4) is assumed to be a pressure p uniformly distributed along the height;
in the step (4), when the water flow depth exceeds the height of the pier, the water flow force applied to the bridge deck is buoyancy, and the calculation method comprises the following steps:
Ff＝ρsgdhwd
wherein, FfFor buoyancy forces exerted on the deck of the bridge, psIs the density of the water flow, g is the acceleration of gravity, dhDepth of water flow on the bridge deck, wdIs the bridge deck width;
the method for defining the maximum bearing capacity of the pier in the step (4) comprises the following steps: if maximum base shear FcBefore the displacement of 5 percent of the bridge pier occurs, the maximum bearing capacity of the bridge pier is directly taken as the maximum base shearing force F at the momentc(ii) a If maximum base shear FcWhen the displacement of the bridge pier is 5 percent, the maximum bearing capacity of the bridge pier is the corresponding base shear force F when the displacement of the bridge pier is 5 percentc-5。
6. The method for analyzing the flood vulnerability of the concrete bridge girder considering the bridge pier failure mode according to claim 1, wherein the method for determining the water flow acting force when the maximum bearing capacity of the bridge pier is reached in the step (5) comprises: according to the maximum bearing capacity of the bridge pier determined in the step (4), assuming that the corresponding water flow pressure applied to the bridge pier at the moment is p, the corresponding water flow acting force is as follows:
Fflood＝ph
wherein, FfloodThe water flow force is applied to the bridge pier, and h is the water flow depth applied to the bridge pier at the moment;
the method for determining the water flow speed when the bridge pier reaches the maximum bearing capacity in the step (5) comprises the following steps:
where ρ issIs the density of the water stream, deltaDThe water flow impact coefficient is shown, B is the section width of the pier facing the water flow, and v is the water flow velocity;
in the method for determining the water flow speed when the maximum bearing capacity of the pier is achieved in the step (5), the water flow density rhosCoefficient of water flow impact deltaDTaking into account the effect of the uncertainty,
wherein, the density of the water flow accords with the uniform distribution, and the distribution function is as follows:
wherein, a is 1000kg/m3，b＝1250kg/m3Or according to the water area data of the bridge or the field test;
wherein, the water flow impact coefficient accords with the even distribution, and its distribution function is:
wherein c is 1.0, d is 2, or determined according to the data of the water area where the bridge is located or field test;
adopting a Monte-La-Luo simulation method to determine the water flow speed when the bridge pier reaches the maximum bearing capacity in the step (5), specifically, sampling 10000 water flow density values and 10000 water flow impact coefficient values, and further according to the formula in the step (5)
And respectively calculating the water flow speed value under each water flow density and water flow impact coefficient.
7. The method for analyzing the flood vulnerability of the concrete bridge girder considering the bridge pier failure mode according to claim 1, wherein the calculation formula of the flood vulnerability curve of the bridge girder at different depths in the step (6) is as follows:
wherein Φ is a cumulative distribution function;
for inducing bridge pier under corresponding heightMedian of 10000 water velocities collapsed, βvIs the standard deviation of the water velocity.
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