CN113111415A - Cable-stayed bridge cable force reliability assessment method considering partial cable failure - Google Patents
Cable-stayed bridge cable force reliability assessment method considering partial cable failure Download PDFInfo
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Abstract
The invention relates to the technical field of bridge design, in particular to a cable-stayed bridge cable force reliability assessment method considering partial cable failure. The evaluation method comprises the following steps: determining the designed cable force amplification coefficient of the residual cable after the partial cable fails according to the maximum strain value of the residual cable after the partial cable fails in each position in the dynamic response stage; acquiring a cable force limit state of the strength of the stay cable based on the strength of the steel wire; and calculating the cable force reliability index of the rest cables based on the cable force extreme state according to the cable force amplification factor and the designed cable force extreme state. The assessment method can solve the problem that the risk of damage of the cable-stayed bridge under the condition of partial cable failure cannot be effectively estimated in the prior art.
Description
Technical Field
The invention relates to the technical field of bridge design, in particular to a cable-stayed bridge cable force reliability assessment method considering partial cable failure.
Background
Although current specifications dictate that incidental design considerations be taken into account in cable-stayed bridge design, design considerations of partial cable failure are not appreciated in design practice. The residual guy cable has a larger failure risk after the partial guy cable fails, and the failure of the residual guy cable can cause the continuous damage of the guy cable, however, the failure of the partial guy cable is not considered in the design of the guy cable at the present stage.
Although the cable-stayed bridge is an statically indeterminate structure, the cable-stayed bridge cannot collapse due to the failure of a small amount of cables, the cable is used as an important component of a stress system of the cable-stayed bridge, and the stress and the design condition of the cable are different due to the redistribution of cable force after the cable is failed. If the condition that a part of the guys possibly fail is ignored in the design, the design value of the guy force is smaller, and potential safety hazards are brought to the use of the cable-stayed bridge.
The unified design standard for the reliability of the highway engineering structure has relevant regulations on the reliability index of the bridge, however, a mature method for calculating the reliability index after cable force amplification is not available at the present stage, so that the risk of damage of the cable-stayed bridge under the condition of partial cable failure cannot be estimated.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to provide a cable-stayed bridge cable force reliability assessment method considering partial cable failure, which can solve the problem that the risk of damage of a cable-stayed bridge under partial cable failure cannot be effectively estimated in the prior art.
In order to achieve the above purposes, the technical scheme adopted by the invention is as follows:
the invention provides a cable-stayed bridge cable force reliability assessment method considering partial cable failure, which comprises the following steps:
determining the designed cable force amplification coefficient of the residual cable after the partial cable fails according to the maximum strain value of the residual cable after the partial cable fails in each position in the dynamic response stage;
acquiring a cable force limit state of the strength of the stay cable based on the strength of the steel wire;
and calculating the cable force reliability index of the rest cables based on the cable force extreme state according to the cable force amplification factor and the designed cable force extreme state.
In some optional schemes, the determining the cable force amplification factor of the remaining cables after the failure of the partial cables according to the maximum strain value of the remaining cables after the failure of the partial cables at each position in the dynamic response stage comprises the following steps:
one or more broken cables are processed for all the stay cables one by one, and the self cable force amplification coefficients of the rest stay cables corresponding to the broken cables are calculated respectively;
and determining a specific quantile as the design cable force amplification coefficient of one or more broken cables according to the design requirement of one or more broken cables based on the probability distribution type obeyed by the cable force amplification coefficient of the remaining cables corresponding to the one or more broken cables.
In some alternatives, the method is based on a formula
Calculating the self cable force amplification coefficient of the residual cables corresponding to one or more broken cables, wherein epsilonmaxThe maximum strain of the inhaul cable in the dynamic response stage after the cable is broken; epsilonaIs the allowable dynamic strain of the cable.
In some optional schemes, the self cable force amplification factor of the remaining cables corresponding to one or more broken cables is subject to a normal distribution type.
In some optional schemes, the obtaining the cable force limit state of the cable strength based on the steel wire strength specifically includes:
performing parameter estimation according to the experimental data sample of the steel wire strength to obtain a strength probability model of the steel wire;
based on a strength probability model, sampling an experimental data sample of the steel wire strength, and considering the influence of Daniels effect and strain rate effect on the strength of the stay cable to obtain a stay cable strength sample obeying Weibull distribution;
and carrying out parameter estimation on the inhaul cable strength sample which obeys Weibull distribution to obtain the cable force limit state of the inhaul cable strength.
In some optional schemes, the parameter estimation of the cable strength sample obeying Weibull distribution is performed to obtain the cable force limit state of the cable strength, and the method specifically includes:
according to the formula
And determining the cable force limit state of the cable strength, wherein z is the strength of the cable, lambda is a proportion parameter of Weibull distribution, k is a shape parameter of Weibull distribution, and R is the cable force limit state based on the cable strength.
In some optional schemes, the calculating the cable force reliability index of the remaining cables based on the cable force limit state according to the cable force amplification factor and the designed cable force limit state specifically includes:
sampling different structural parameters of the bridge to obtain a plurality of groups of structural parameter samples of the bridge;
determining cable force demand value samples corresponding to a plurality of groups of structural parameter samples based on each design cable force amplification coefficient;
and obtaining a corresponding cable force reliability index by a reliability calculation method according to the cable force limit state based on the probability distribution types obeyed by the multiple groups of cable force demand value samples.
In some alternatives, the determined sample of the force demand values are subjected to a lognormal distribution based on the respective design force amplification factors.
In some optional schemes, the obtaining of the corresponding cable force reliability index by a reliability calculation method according to the cable force limit state based on the probability distribution types obeyed by the multiple groups of cable force demand value samples specifically includes:
according to the formula β ═ Φ-1[P(D>R)]And determining a cable force reliability index beta, wherein D is a cable force demand value, R is a cable force limit state based on the strength of the stay cable, P is the probability that the cable force demand value is greater than the cable force limit state, and phi is a cumulative distribution function of standard normal distribution.
In some optional schemes, a Latin hypercube sampling method is adopted to sample different structural parameters of the bridge, and a Monte-Carlo simulation method is adopted to determine cable force demand value samples corresponding to multiple groups of structural parameter samples based on each design cable force amplification coefficient.
Compared with the prior art, the invention has the advantages that: according to the method, the designed cable force amplification coefficient is obtained through the maximum strain value of the residual cable in the dynamic response stage after the partial cable in each position fails, and the cable force reliability index of the residual cable based on the cable force limit state is calculated by combining the cable force limit state, so that the cable force reliability evaluation method of the cable-stayed bridge based on the cable strength considering the partial cable failure is provided, and the risk of damage of the cable-stayed bridge under the partial cable failure can be estimated. In addition, the method provided by the invention has certain flexibility and can be applied to cable force reliability evaluation of cable-stayed bridges of different forms.
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In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings needed to be used in the description of the embodiments are briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present application, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.
FIG. 1 is a general flowchart of a cable-stayed bridge cable force reliability evaluation method considering partial cable failure in the embodiment of the invention;
fig. 2 is a flowchart of a cable-stayed bridge cable force reliability evaluation method considering partial cable failure according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application, and it is obvious that the described embodiments are some embodiments of the present application, but not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present application.
FIG. 1 is a general flowchart of a cable-stayed bridge cable force reliability evaluation method considering partial cable failure in the embodiment of the invention; fig. 2 is a flowchart of a cable-stayed bridge cable force reliability evaluation method considering partial cable failure according to an embodiment of the present invention. As shown in fig. 1 and 2:
embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.
The invention provides a cable-stayed bridge cable force reliability assessment method considering partial cable failure, which comprises the following steps:
s1: and determining the designed cable force amplification coefficient of the residual cables after the partial cables fail according to the maximum strain value of the residual cables after the partial cables fail in each position in the dynamic response stage.
In some optional embodiments, determining the cable force amplification factor of the remaining cables after the failure of the part of the cables comprises the following steps:
s11: and one or more broken cables are processed for all the stay cables one by one, and the self cable force amplification coefficients of the rest stay cables corresponding to the broken cables are respectively calculated.
In some alternative embodiments, the formula is based on
Calculating the cable force amplification coefficient of the residual cables corresponding to one or more broken cables, wherein epsilonmaxThe maximum strain of the inhaul cable in the dynamic response stage after the cable is broken; epsilonaIs the allowable dynamic strain of the cable.
In this embodiment, one broken cable is sequentially performed on all the cables, for example, 10 cables, and in the case of one broken cable, each cable is sequentially disconnected, and the self-cable-force amplification coefficients of the remaining cables are calculated, so that 90 sets of self-cable-force amplification coefficients of one broken cable can be obtained. Similarly, in the subsequent steps, the corresponding calculated design cable force amplification factor is also the reliability of the broken cable, and the reliability calculated by the reliability evaluation method is also the reliability of the broken cable. For example, in the case of two broken cables, two cables are sequentially disconnected, and the self-cable-force amplification factor of the remaining cable is calculated, so that 8 × 9 × 10/2 of the two broken cables is obtained as 360 sets of self-cable-force amplification factors, and accordingly, the designed cable-force amplification factor of the two broken cables is calculated, and the reliability calculated by the reliability evaluation method is also the reliability of the two broken cables.
S12: and determining a specific quantile as the design cable force amplification coefficient of one or more broken cables according to the design requirement of one or more broken cables based on the probability distribution type obeyed by the cable force amplification coefficient of the remaining cables corresponding to the one or more broken cables.
In this embodiment, the self-cable-force amplification factor of the remaining cables corresponding to one or more broken cables follows a normal distribution type.
The following explanation is made for solving the design cable force amplification factor.
Because the cable force redundancy rates of the stay cables at different positions are different when the stay cables at the same position normally work, the cable force amplification coefficients of the rest stay cables are different after the stay cables at the same position fail; in addition, the cable failure at different positions can also cause different values of the self cable force amplification coefficients of the same cable. Therefore, the self-cable force amplification factor calculated by the single-position cable is not representative, and the envelope value of each case is taken as the value of the design cable force amplification factor, which causes material waste. The uncertainty of the failure position of the stay cable and the strain of the residual stay cable is counted by adopting an enumeration method, the amplification coefficients of a plurality of self cable forces are assumed to obey normal distribution, and the average value and the variation coefficient are calculated according to the numerical simulation result.
S2: and acquiring the cable force limit state of the cable strength based on the steel wire strength.
In some optional embodiments, the obtaining the cable force limit state of the cable strength based on the steel wire strength specifically includes:
s21: and performing parameter estimation according to the experimental data sample of the steel wire strength to obtain a strength probability model of the steel wire.
S22: based on the strength probability model, the experimental data samples of the steel wire strength are sampled, the influence of Daniels effect and strain rate effect on the cable strength is considered, and the cable strength samples obeying Weibull distribution are obtained.
In this embodiment, according to Daniels (denier) effect, in the parallel system, the average strength of each wire is reduced due to the increase of the number of wires in the cable, and when calculating the total strength of the cable, the strength of the cable needs to be reduced according to the number of wires. Meanwhile, the high-speed strain rate has a reinforcing effect on the strength of the inhaul cable, and the ultimate stress of the steel wire under the power is greater than the static ultimate strength of the steel wire under the consideration of the influence of the strain rate. Therefore, in the example, the strength sample of the cable obtained is reduced according to Daniels effect, and the strength sample of the cable is amplified by 1.2 times according to strain rate effect to be used as the ultimate strength of the cable under power.
After the failure of part of the guy cables, the rest guy cables are in a high-speed strain state. Under the high-speed strain rate, the ultimate stress and the yield stress of the inhaul cable are improved, but the ultimate strain and the yield strain are reduced to a certain extent. In addition, with the increase of the strain rate, the wire breaking tendency of the inhaul cable steel wire before reaching the limit state is increased to a certain extent. The high rate of strain results in a decrease in the ductility of the cable, increased brittleness and a more adverse dynamic response phase to the remaining cable. The mechanical property of the stay cable under power is greatly different from that of the stay cable under static state, and the strain rate effect needs to be considered. The strain rate effect is considered by adopting the Cowper-Symonds constitutive equation:
in the formula, σequIs equivalent dynamic yield stress; sigma0Is the equivalent static yield stress;
is the strain rate;
is an effective plastic strain; epIs the plastic hardening modulus; e and EtanRespectively is the elastic modulus of a random reinforced model of the inhaul cable in an online elastic stage and the tangent elastic modulus of the inhaul cable in an elastic-plastic stage; d and q are strain parameters.
S23: and carrying out parameter estimation on the inhaul cable strength sample which obeys Weibull distribution to obtain the inhaul cable force limit state of the inhaul cable strength.
The Weibull distribution is widely applied to reliability engineering, and is particularly suitable for the distribution form of wear cumulative failure of electromechanical products. The method is widely applied to data processing of various life tests because the distribution parameters of the method can be easily deduced by using the probability value.
In some optional embodiments, the parameter estimation on the cable strength sample complying with the Weibull distribution to obtain the cable force limit state of the cable strength specifically includes:
according to the formula
And determining the cable force limit state of the cable strength, wherein z is the strength of the cable, lambda is a proportion parameter of Weibull distribution, k is a shape parameter of Weibull distribution, and R is the cable force limit state based on the cable strength.
S3: and calculating the cable force reliability index of the rest cables based on the cable force extreme state according to the cable force amplification factor and the designed cable force extreme state.
In some optional embodiments, the calculating the cable force reliability index of the remaining cables based on the cable force limit state according to the cable force amplification factor and the designed cable force limit state specifically includes:
s31: sampling different structural parameters of the bridge to obtain multiple groups of structural parameter samples of the bridge.
In this embodiment, a Latin hypercube sampling method is adopted to sample different structural parameters of the bridge.
In the reliability evaluation process, the uncertainty of load, material property and construction error is considered by adopting a Latin hypercube sampling method. The corresponding probability model is derived from probability statistics of original data measured by experiment or equal precision; uncertainties in material properties include uncertainties in material modulus of elasticity, strength; uncertainty in construction errors includes uncertainty in structural member dimensions, position. Due to the uncertainty of these material properties and the uncertainty of construction errors, different structural parameters are generated.
S32: and determining cable force required value samples corresponding to the multiple groups of structural parameter samples based on each design cable force amplification coefficient.
In this embodiment, the cable force demand value samples corresponding to a plurality of sets of structural parameter samples are determined based on each design cable force amplification factor by using a Monte-Carlo simulation method.
Monte Carlo (Monte Carlo) simulation is a method for researching the distribution characteristics of a time sequence by setting a random process, repeatedly generating the time sequence, calculating parameter estimators and statistics and further researching the distribution characteristics of the time sequence.
In this embodiment, the determined sample of the cable force demand value is subjected to log-normal distribution based on each design cable force amplification factor.
S33: and obtaining a corresponding cable force reliability index by a reliability calculation method according to the cable force limit state based on the probability distribution types obeyed by the multiple groups of cable force demand value samples.
In this embodiment, the obtaining of the corresponding cable force reliability index through the reliability calculation method in S33 specifically includes:
according to the formula β ═ Φ-1[P(D>R)]And determining a cable force reliability index beta, wherein D is a cable force demand value, R is a cable force limit state based on the strength of the stay cable, P is the probability that the cable force demand value is greater than the cable force limit state, and phi is a cumulative distribution function of standard normal distribution.
The final cable force reliability index beta needs to meet relevant regulations in 'unified design standard for reliability of highway engineering structure'; if not, the structural design needs to be adjusted, the design cable force amplification factor AF needs to be calculated again, and the steps S2 and S3 are repeated until the obtained cable force reliability index beta meets the specification requirement.
In conclusion, the design cable force amplification coefficient of the residual cable after the failure of the partial cable is determined according to the maximum strain value of the residual cable after the failure of the partial cable at each position in the dynamic response stage. Then based on the strength of the steel wire, acquiring the ultimate state of the cable force of the strength of the stay cable; and calculating the cable force reliability index of the rest cables based on the cable force extreme state according to the cable force amplification factor and the designed cable force extreme state. According to the method, the designed cable force amplification coefficient is obtained through the maximum strain value of the residual cable in the dynamic response stage after the partial cable in each position fails, and the cable force reliability index of the residual cable based on the cable force limit state is calculated by combining the cable force limit state, so that the cable force reliability evaluation method of the cable-stayed bridge based on the cable strength considering the partial cable failure is provided, and the risk of damage of the cable-stayed bridge under the partial cable failure can be estimated. In addition, the method provided by the invention has certain flexibility and can be applied to cable force reliability evaluation of cable-stayed bridges of different forms.
In addition, when the power amplification coefficient of the stay cable is calculated, the basic combination of load and cable breakage failure is adopted, and the uncertainty of the load is not considered; and when the reliability of the cable force based on the cable strength is evaluated, the standard combination of the load is adopted, and the uncertainty of the load is considered. The loading modes of the constant load and the live load are all full-bridge uniform distribution. The method assumes that the permanent load of the bridge obeys normal distribution, the automobile load obeys log-normal distribution, the crowd load obeys extreme value I-type distribution, and the average value and the variation coefficient are determined by a mathematical statistical method according to observation data, so that a more accurate evaluation result can be obtained.
In the description of the present application, it should be noted that the terms "upper", "lower", and the like indicate orientations or positional relationships based on the orientations or positional relationships shown in the drawings, which are only for convenience in describing the present application and simplifying the description, and do not indicate or imply that the referred device or element must have a specific orientation, be constructed in a specific orientation, and operate, and thus, should not be construed as limiting the present application. Unless expressly stated or limited otherwise, the terms "mounted," "connected," and "connected" are intended to be inclusive and mean, for example, that they may be fixedly connected, detachably connected, or integrally connected; can be mechanically or electrically connected; they may be connected directly or indirectly through intervening media, or they may be interconnected between two elements. The specific meaning of the above terms in the present application can be understood by those of ordinary skill in the art as appropriate.
It is noted that, in the present application, relational terms such as "first" and "second", and the like, are used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Also, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other identical elements in a process, method, article, or apparatus that comprises the element.
The above description is merely exemplary of the present application and is presented to enable those skilled in the art to understand and practice the present application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the application. Thus, the present application is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims (10)
1. A cable-stayed bridge cable force reliability assessment method considering partial cable failure is characterized by comprising the following steps:
determining the designed cable force amplification coefficient of the residual cable after the partial cable fails according to the maximum strain value of the residual cable after the partial cable fails in each position in the dynamic response stage;
acquiring a cable force limit state of the strength of the stay cable based on the strength of the steel wire;
and calculating the cable force reliability index of the rest cables based on the cable force extreme state according to the cable force amplification factor and the designed cable force extreme state.
2. The cable-stayed bridge cable force reliability evaluation method considering the failure of the partial cable as set forth in claim 1, wherein: the method for determining the cable force amplification factor of the residual cables after the partial cables fail according to the maximum strain value of the residual cables after the partial cables fail in each position in the dynamic response stage comprises the following steps:
one or more broken cables are processed for all the stay cables one by one, and the self cable force amplification coefficients of the rest stay cables corresponding to the broken cables are calculated respectively;
and determining a specific quantile as the design cable force amplification coefficient of one or more broken cables according to the design requirement of one or more broken cables based on the probability distribution type obeyed by the cable force amplification coefficient of the remaining cables corresponding to the one or more broken cables.
3. The cable-stayed bridge cable force reliability evaluation method considering the failure of the partial cable as set forth in claim 2, wherein: according to the formula
Calculating the self cable force amplification coefficient of the residual cables corresponding to one or more broken cables, wherein epsilonmaxThe maximum strain of the inhaul cable in the dynamic response stage after the cable is broken; epsilonaIs the allowable dynamic strain of the cable.
4. The cable-stayed bridge cable force reliability evaluation method considering the failure of the partial cable as set forth in claim 2, wherein: and the self cable force amplification coefficient of the rest cables corresponding to one or more broken cables obeys a normal distribution type.
5. The cable-stayed bridge cable force reliability assessment method considering the failure of the partial cable according to claim 1, wherein the obtaining of the cable force limit state of the cable strength based on the strength of the steel wire specifically comprises:
performing parameter estimation according to the experimental data sample of the steel wire strength to obtain a strength probability model of the steel wire;
based on a strength probability model, sampling an experimental data sample of the steel wire strength, and considering the influence of Daniels effect and strain rate effect on the strength of the stay cable to obtain a stay cable strength sample obeying Weibull distribution;
and carrying out parameter estimation on the inhaul cable strength sample which obeys Weibull distribution to obtain the cable force limit state of the inhaul cable strength.
6. The method for evaluating cable-stayed bridge cable force reliability considering partial cable failure according to claim 5, wherein the parameter estimation is performed on cable strength samples which obey Weibull distribution to obtain the cable force limit state of the cable strength, and specifically comprises the following steps:
according to the formula
And determining the cable force limit state of the cable strength, wherein z is the strength of the cable, lambda is a proportion parameter of Weibull distribution, k is a shape parameter of Weibull distribution, and R is the cable force limit state based on the cable strength.
7. The cable-stayed bridge cable force reliability assessment method considering the failure of the partial cables as claimed in claim 1, wherein the calculating of the cable force reliability index of the remaining cables based on the cable force limit state according to the cable force amplification factor and the design cable force limit state specifically comprises:
sampling different structural parameters of the bridge to obtain a plurality of groups of structural parameter samples of the bridge;
determining cable force demand value samples corresponding to a plurality of groups of structural parameter samples based on each design cable force amplification coefficient;
and obtaining a corresponding cable force reliability index by a reliability calculation method according to the cable force limit state based on the probability distribution types obeyed by the multiple groups of cable force demand value samples.
8. The cable-stay bridge cable-force reliability assessment method considering partial cable failure according to claim 7, wherein the determined cable-force demand value samples are subjected to log-normal distribution based on each design cable-force amplification factor.
9. The cable-stayed bridge cable force reliability assessment method considering the partial cable failure as claimed in claim 8, wherein the obtaining of the corresponding cable force reliability index by the reliability calculation method according to the cable force limit state based on the probability distribution type obeyed by the multiple sets of cable force demand value samples specifically comprises:
according to the formula β ═ Φ-1[P(D>R)]And determining a cable force reliability index beta, wherein D is a cable force demand value, R is a cable force limit state based on the strength of the stay cable, P is the probability that the cable force demand value is greater than the cable force limit state, and phi is a cumulative distribution function of standard normal distribution.
10. The cable-stayed bridge cable force reliability evaluation method considering the failure of the partial cable according to claim 8, wherein: different structural parameters of the bridge are sampled by adopting a Latin hypercube sampling method, and cable force required value samples corresponding to a plurality of groups of structural parameter samples are determined by adopting a Monte-Carlo simulation method based on each design cable force amplification coefficient.
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