CN105956753A - Street tree wind-caused damage rapid evaluation method - Google Patents

Abstract

The invention discloses a street tree wind-caused damage rapid evaluation method. A simplified model of street tree wind-caused damage is established, and according to finite element theory, tree materials are hypothesized to be isotropic and uniform, and then material physical parameters of dynamic behaviors affect tree individuals are abstracted. By giving consideration to the different types and the growth conditions of the trees, and the individual shape and character differences of the trees are great, and the material physical parameters of the street tree wind-caused damage model are regarded as the random variables. Davenport spectrum is used to represent input fluctuating wind speed, and a pseudo excitation method is used for street tree wind-caused response fast calculation. A street tree wind-caused damage criterion is defined based on bending strength, and by adopting Monte Carlo simulation, fast evaluation of street tree damage probability under a condition of different wind load levels. The street tree wind-caused damage rapid evaluation method is advantageous in that wind disaster damages on the street trees in the city areas are accurately and effectively predicted, and practical meaning is provided during making of corresponding defense measures.

Description

A kind of fast evaluation method of urban path tree wind-induced damage

Technical field

The invention belongs to field of engineering technology, relate to the fast evaluation method of a kind of urban path tree wind-induced damage.

Background technology

Disaster caused by a windstorm is a kind of serious natural disaster.As one of main hazard-affected body, the disaster caused by a windstorm damage study of trees the most more comes More receive publicity.In urban area, normally behave as losing or lodging of shade tree.Urban path tree destroys and often results in vehicle Impaired with house, power supply and communication line interrupt, traffic jam, have a strong impact on resident produce and life, endanger urban safety. Therefore, the disaster caused by a windstorm destructive characteristics of research shade tree has important practice significance.

In the world, about the existing many decades history of disaster caused by a windstorm damage study of trees；And in China, the disaster caused by a windstorm damage study of trees Start late, and mainly consider rarely have the research about trees dynamic behavior from management layer.Trees be a class by trunk, Bough, the labyrinth system of sprig composition.Owing to tree families is different with growth conditions, cause individual trees form and character Differ greatly, bring extreme difficulties to the modeling that becomes more meticulous of trees.Therefore, it is necessary when modeling to make the physical parameter of timber Considered for stochastic variable, particularly typhoon season, the disaster caused by a windstorm of urban area shade tree is destroyed make rapid evaluation time；But, Existing work not yet relates to this research.

Summary of the invention

It is an object of the invention to provide the fast evaluation method of a kind of urban path tree wind-induced damage, for urban path tree disaster caused by a windstorm work Journey defence provides reference.

For reaching object above, solution of the present invention is:

The fast evaluation method of a kind of urban path tree wind-induced damage, it is for the wind of typhoon prone areas urban path tree in recent years Calamity destroys problem, establishes the simplified model of shade tree wind-induced damage, according to finite element theory hypothesis tree wood material isotropic And uniformly, take out the Material Physics parameter affecting individual trees dynamic behavior；Simultaneously, it is considered to due to tree families and growth Condition is different, individual trees form and Traits change relatively big, the Material Physics parameter in shade tree wind-induced damage model is considered as with Machine variable；Input fluctuating wind speed is taken as Davenport spectrum, and (basic parameter is terrain rough factor and and the wind load of urban environment 10 minutes mean wind speeds that grade is corresponding), use pseudo-excitation method to carry out the quick calculating of shade tree wind-excited responese.Basis at this On, define shade tree wind-induced damage criterion based on bending strength, use Monte Carlo simulation, carry out different wind load grade bar The rapid evaluation of shade tree failure probability under part.

Concrete, the fast evaluation method of a kind of urban path tree wind-induced damage, it comprises the following steps:

1) according to the motion morphology of trees under wind action, the simplified model of shade tree wind-induced damage, i.e. trunk-branch are set up Y word model；

2) trunk, branch are considered as Euler-Bernoulli beam element, utilize finite element theory, build shade tree kinetics equation；

3) the stock physical parameter of shade tree wind-induced damage model is taken out: density of wood and Deflection Modulus of Elasticity, by them It is considered as stochastic variable, to consider the individual trees form and the Traits change that cause owing to tree families is different with growth conditions；

4) input fluctuating wind speed be taken as Davenport spectrum, basic parameter be urban environment terrain rough factor and with wind load etc. 10 minutes mean wind speeds that level is corresponding；

5) pseudo-excitation method is used to carry out the quick calculating of shade tree wind-excited responese；

6) shade tree wind-induced damage criterion based on bending strength is defined: with shade tree maximum trunk unit under random wind Root-mean-square bending strength characterizes the overall destruction of shade tree to limit values (bending strength) more than it；

7) use Monte Carlo simulation, carry out the rapid evaluation of urban path tree failure probability under different wind load rating conditions.

Grasp, in the shade tree wind-induced damage model set up, the timberphysics parameter caused owing to tree families is different with growth conditions Variability.

Furthermore, step (1) uses the Y word model of trunk-branch, and carry out kinetics according to finite element theory and build Mould.

Trunk, branch are considered as Euler-Bernoulli beam element, utilize finite element theory, build shade tree kinetics equation.

Step (2) use density of wood and Deflection Modulus of Elasticity as stock physical parameter.

In step (4), basic parameter is the terrain rough factor of urban environment and corresponding with wind load grade 10 minutes average winds Speed.

Step (6) is come to limit values more than it with shade tree maximum trunk unit root-mean-square bending strength under random wind Characterize the overall destructiveness of shade tree.

Described boundary value is bending strength.

Step (3) considers density of wood and Deflection Modulus of Elasticity are stochastic variable simultaneously.

Grasp, in the shade tree wind-induced damage model set up, the timberphysics parameter caused owing to tree families is different with growth conditions Variability.

Destroy by using frequency analysis method accurate, efficient to greatly reduce shade tree disaster caused by a windstorm based on Monte Carlo simulation Probability solve workload.

Owing to have employed such scheme, the method have the advantages that the present invention passes through considering of timber parameter stochastic property, The shade tree disaster caused by a windstorm damage model of tree families and growth conditions is grasped in constructing；Use pseudo-excitation method so that Monte Carlo Simulation solution is the most accurate, efficient, thus realizes the rapid evaluation of urban path tree failure probability under different wind load rating conditions.This Invention can be that the defence of urban path tree disaster caused by a windstorm engineering provides reference.

Accompanying drawing explanation

Fig. 1 is that shade tree disaster caused by a windstorm destroys simplified model figure.

Fig. 2 is the frequency histogram of shade tree density.

Fig. 3 is the frequency histogram of shade tree Deflection Modulus of Elasticity.

Fig. 4 is the disaster caused by a windstorm failure probability curve chart of shade tree.

Fig. 5 is technology path (method flow) figure.

Detailed description of the invention

Below in conjunction with accompanying drawing illustrated embodiment, the present invention is further illustrated.

1. shade tree disaster caused by a windstorm destroys simplified model

Owing under wind action, trees will move along prevailing wind direction, therefore the disaster caused by a windstorm destruction problem of shade tree can be considered plane problem. Meanwhile, trees are the labyrinth systems that a class is made up of trunk, bough, sprig, and individual trees form and Traits change are relatively big, The real material parameter of trees is used to have difficulties the most completely, it is necessary to reasonably to simplify.

According to correlation theory, shade tree by curved, can be reduced to mechanical model as shown in Figure 1 under wind load effect.Whole model Being positioned at XOY plane, beam S is trunk in X direction and consolidates with ground D；B is branching system, two symmetries divide Beam B1, B2 composition of cloth；Leaves uniform quality is distributed on beam B1 and B2；The distribution that model bears along Y-direction encourages F (x) [1+q (t)] acts on.Wherein, F (x) is amplitude, and q (t) is the stationary random process of zero-mean.Amplitude F (x) is in X direction Change:

$F\left(x\right)=\frac{1}{2}{C}_D{\mathrm{\ρ}}_a{\mathrm{AU}}^2\left(x\right)---\left(1\right)$

Wherein, C_DIt it is wind load coefficient；ρ_aIt is atmospheric density；A is front face area；U (x) is the mean wind speed at height x rice.Flat All wind speed is along the most exponentially change:

$U\left(x\right)=U_h{\left(\frac{x}{h}\right)}^{1/7}---\left(2\right)$

Wherein, U_hBeing the mean wind speed in treetop portion, h is the height of tree.

From the figure, it can be seen that the physical dimension of structure is determined by 6 parameters, it is trunk S bottom radius R (0) respectively, trunk The radius reduction parameter beta of S and sprig B1, B2, branch length (L, L_B1、L_B2) and its bottom radius (R (0), R_B1(0)、 R_B2(0) Relation Parameters k), sectional shrinkage λ, angle 2 α between cross section property factor κ and sprig.

2. shade tree kinetics equation

The kinetics equation of shade tree wind-induced vibration is:

$M\left(\mathrm{\Θ}\right)\stackrel{\·\·}{Y}\left(t\right)+C\left(\mathrm{\Θ}\right)\stackrel{\·}{Y}\left(t\right)+K\left(\mathrm{\Θ}\right)Y\left(t\right)=F\left(t\right)---\left(3\right)$

In formula, Μ (Θ), C (Θ), K (Θ), Y (t), F (t) represent the quality of structural system, damping, rigidity, displacement, moment of face respectively Battle array；Θ is the random vector representing shade tree structural parameters randomness.Use Rayleigh damping

C (Θ)=aM (Θ)+bK (Θ) (4)

In formula, a, b are Rayleigh Damping Scale Coefficient.

Using Euler-Bernoulli beam element, the unit number of trunk and branch is respectively defined as 10 and 5, and total unit number is 20, Owing to model bottom is clamped, 20 nodes altogether.The cross section of definition beam element is circular cross-section.According to finite element theory, i-th The stiffness matrix k of individual beam element_eiWith element mass matrix m_eiFormula (5) and (6) are shown in definition.

$k_{ei}=\left[\begin{array}{cccccc}\frac{{\mathrm{EA}}_i}{L_i}& 0& 0& -\frac{{\mathrm{EA}}_i}{L_i}& 0& 0\\ 0& \frac{12{\mathrm{EI}}_i}{{L_i}^3}& \frac{6{\mathrm{EI}}_i}{{L_i}^2}& 0& -\frac{12{\mathrm{EI}}_i}{{L_i}^3}& \frac{6{\mathrm{EI}}_i}{{L_i}^2}\\ 0& \frac{6{\mathrm{EI}}_i}{{L_i}^2}& \frac{4{\mathrm{EI}}_i}{L_i}& 0& -\frac{6{\mathrm{EI}}_i}{{L_i}^2}& \frac{2{\mathrm{EI}}_i}{L_i}\\ -\frac{{\mathrm{EA}}_i}{L_i}& 0& 0& \frac{{\mathrm{EA}}_i}{L_i}& 0& 0\\ 0& -\frac{12{\mathrm{EI}}_i}{{L_i}^3}& -\frac{6{\mathrm{EI}}_i}{{L_i}^2}& 0& \frac{12{\mathrm{EI}}_i}{{L_i}^3}& -\frac{6{\mathrm{EI}}_i}{{L_i}^2}\\ 0& \frac{6{\mathrm{EI}}_i}{{L_i}^2}& \frac{2{\mathrm{EI}}_i}{L_i}& 0& -\frac{6{\mathrm{EI}}_i}{{L_i}^2}& \frac{4{\mathrm{EI}}_i}{L_i}\end{array}\right]---\left(5\right)$

$m_{ei}=\left[\begin{array}{cccccc}\frac{1}{3}& 0& 0& \frac{1}{6}& 0& 0\\ 0& \frac{13}{35}& \frac{11}{210}{L}_i& 0& \frac{9}{70}& -\frac{13}{420}{L}_i\\ 0& \frac{11}{210}{L}_i& \frac{{L_i}^2}{105}& 0& \frac{13}{420}{L}_i& -\frac{{L_i}^2}{140}\\ \frac{1}{6}& 0& 0& \frac{1}{3}& 0& 0\\ 0& \frac{9}{70}& \frac{13}{420}{L}_i& 0& \frac{13}{35}& -\frac{11}{210}{L}_i\\ 0& -\frac{13}{420}{L}_i& -\frac{{L_i}^2}{140}& 0& -\frac{11}{210}{L}_i& \frac{{L_i}^2}{105}\end{array}\right]{\mathrm{\ρA}}_i{L}_i---\left(6\right)$

In formula, A_iIt it is the area of section of unit；L_iIt it is element length；I_iCross section second order away from；E is Deflection Modulus of Elasticity；ρ is material Density.

Consider owing to tree families is different with growth conditions, individual trees form and Traits change relatively greatly, by shade tree wind-induced damage Stock physical parameter in model, i.e. density of material and Deflection Modulus of Elasticity, be considered as stochastic variable.

3. shade tree failure probability fast evaluation method based on Monte Carlo simulation

Solve the shade tree kinetics equation (3) under given structural parameters sample conditions, class frequency accurate, efficient can be used to divide Analysis method, i.e. pseudo-excitation method carry out the rapid solving of structural response

S_Y(ω)=H^*(ω)S_F(ω)H^T(ω) (7)

In formula, S_F(ω) it is wind load spectral density matrix；H (ω) is frequency response function；H^*(ω) it is its complex conjugate matrix.

According to the achievement in research of Davenport, the element S of wind load spectral density matrix_F(ω) can be expressed as

S_F(ω)=χ ' (ω) S_u(ω) (8)

In formula, ω is circular frequency；χ ' (ω) is aerodynamic admittance function；S_u(ω) it is fluctuating wind speed spectral density function.Fluctuation wind speed spectrum takes Davenport composes

$S_u\left(f\right)=4K{\stackrel{\‾}{U}}_{10}\frac{z_0^2}{f{\[1+z_0^2\]}^{\frac{4}{3}}}---\left(9\right)$

$K={\[\frac{\stackrel{\‾}{k}}{ln\left(\frac{10}{{\stackrel{\‾}{z}}_0}\right)}\]}^2---\left(10\right)$

$z_0=\frac{1200f}{{\stackrel{\‾}{U}}_{10}}---\left(11\right)$

The expression formula of aerodynamic admittance is

${\mathrm{\χ}}^{\′}\left(f\right)=\frac{1}{(1+3.5fh/U_h)(1+4fB/U_h)}---\left(12\right)$

In formula, K is surface damp coefficient, with von Karman constantAnd terrain rough factorRelevant；High for 10m standard Mean wind speed at degree；F is natural frequency；B is the effective width of shade tree windward side.

Consider structural parameters randomness, then the power spectral density matrix of structural response is

$S_Y\left(\mathrm{\ω}\right)={\∫}_{{\mathrm{\Ω}}_{\mathrm{\Θ}}}{S}_Y\left(\mathrm{\ω}\right|\mathrm{\θ})f_{\mathrm{\Θ}}\left(\mathrm{\θ}\right)d\mathrm{\θ}---\left(13\right)$

In formula, S_Y(ω) element of spectral density matrix it is in response to；S_YResponse spectral density entry of a matrix element when (ω | θ) is structural parameters sample θ； f_Θ(θ) it is the probability density function of Θ.Solving of integration type (10) typically uses numerical method, uses Monte Carlo random here Simulation method.

4. shade tree wind-induced damage criterion based on bending strength

Use single failure criteria, give demarcation with shade tree maximum trunk unit root-mean-square bending strength under wind action more than it Limit value(bending strength) characterizes the overall destruction of shade tree, i.e. indicative function

$I=H\left\{\max \right\{\left|X_i\right|\}-\hat{X}\},i=\[1,N_e\]---\left(14\right)$

Wherein, X_iIt it is the root-mean-square bending strength of i-th trunk unit；H{ } represent Heaviside function, whenTime, H=1, represents that trunk lost efficacy, whenTime, H=0, represent that trunk did not lost efficacy；N_eFor trunk unit number.

5. application example

Being modeled with main cities, Shanghai shade tree for object, the geometric parameter of model is: highly h=6m, bottom trunk partly Footpath R (0)=0.05m, height and Relation Parameters k=76 of its bottom radius, sectional shrinkage λ=0.6, the cross section property factor κ=0.25, radius reduction parameter beta=0.8 of trunk S and sprig B1, B2, angle 2 α=60 ° between branch.von Karman Constant k takes 0.4, terrain rough factorTake 1.6.

With the density of main cities, Shanghai City street tree species and Deflection Modulus of Elasticity as stochastic variable, obtain density through data statistics With the frequency histogram of Deflection Modulus of Elasticity, as shown in Figure 2,3.It can be seen that the density approximation of shade tree is just being obeyed State is distributed, and its average is 468.1kg/m³, the coefficient of variation is 0.22；Deflection Modulus of Elasticity approximation is obeyed uniformly, and its average is 9.65 GPa, coboundary is 13.1GPa, and lower boundary is 6.2GPa, and the coefficient of variation is 0.21.Use Deflection Modulus of Elasticity average, main The bending strength of dry each unit is respectively defined as to top successively from bottom: 3.65kNm, 3.49kNm, 3.33kNm, 3.17 kNm、3.02kNm、2.87kNm、2.73kNm、2.58kNm、2.44kNm、2.31kNm.Use Monte Carlo Analogy method, sampling number 10000 times, obtain shade tree disaster caused by a windstorm failure probability curve as shown in Figure 4.As can be seen from Figure 4, from Understanding in figure, when mean wind speed is less than 18m/s, shade tree has no (failure probability during mean wind speed 18m/s that substantially lost efficacy It is only 0.0045)；When mean wind speed is 19m/s, failure probability is 0.0136；When mean wind speed is more than 20m/s, trade Tree failure probability increases rapidly, when reaching mean wind speed 24m/s 0.9988, this (storm power that is consistent with the phenomenon observed Interval [24.5 28.4] m/s is the wind load scope that shade tree is likely to occur lodging).If with failure probability 5 ‰ for boundary definitions shade tree Inefficacy wind speed, it is believed that in this example, the inefficacy wind speed of shade tree is 19m/s.

The technology path of application example of the present invention, i.e. method flow are as shown in Figure 5.Idiographic flow is as follows: (1) is according to wind load The motion morphology of the lower trees of effect, sets up the simplified model of shade tree wind-induced damage；(2) trunk, branch are considered as Euler-Bernoulli beam element, utilizes finite element theory to build shade tree kinetics equation；(3) definition trade trees material density and Deflection Modulus of Elasticity is basic random variables, and uses Monte Carlo simulation method to carry out sample of random variable, assignment；(4) Use Davenport stave levy input fluctuating wind speed, basic parameter be urban environment terrain rough factor and with wind load grade 10 minutes corresponding mean wind speeds；(5) pseudo-excitation method is used to carry out the quick calculating of shade tree wind-excited responese；(6) definition base Shade tree wind-induced damage criterion in bending strength；(7) based on Monte Carlo simulation, city under different wind load rating conditions is carried out The rapid evaluation of city's shade tree failure probability.

Owing to considering the randomness of street tree species and critical physical parameter, the present invention is conducive to predicting city more accurately and efficiently The disaster caused by a windstorm of region, city shade tree destroys, and has practice significance for formulating corresponding defensive measure.

The above-mentioned description to embodiment is to be understood that for ease of those skilled in the art and apply the present invention.It is familiar with These embodiments obviously easily can be made various amendment by the personnel of art technology, and should General Principle described herein Use in other embodiments without through performing creative labour.Therefore, the invention is not restricted to embodiment here, this area skill Art personnel should be within protection scope of the present invention according to the announcement of the present invention, the improvement made for the present invention and amendment.

Claims (10)

1. the fast evaluation method of a urban path tree wind-induced damage, it is characterised in that: it comprises the following steps:

(1) simplified model of shade tree wind-induced damage is set up；

(2) the stock physical parameter of shade tree wind-induced damage model is taken out；

(3) consider owing to tree families is different with growth conditions, individual trees form and character there are differences, by shade tree charming appearance and behaviour Material Physics parameter in damage model is considered as stochastic variable；

(4) input fluctuating wind speed is taken as Davenport spectrum；

(5) pseudo-excitation method is used to carry out the quick calculating of shade tree wind-excited responese；

(6) shade tree wind-induced damage criterion based on bending strength is defined；

(7) use Monte Carlo simulation, carry out the rapid evaluation of urban path tree failure probability under different wind load rating conditions.

2. the fast evaluation method of urban path tree wind-induced damage as claimed in claim 1, it is characterised in that: step (1) The Y word model of middle employing trunk-branch, and carry out Dynamic Modeling according to finite element theory.

3. the fast evaluation method of urban path tree wind-induced damage as claimed in claim 2, it is characterised in that: by trunk, branch Bar is considered as Euler-Bernoulli beam element, utilizes finite element theory, builds shade tree kinetics equation.

4. the fast evaluation method of urban path tree wind-induced damage as claimed in claim 1, it is characterised in that: step (2) Middle employing density of wood and Deflection Modulus of Elasticity are as stock physical parameter.

5. the fast evaluation method of urban path tree wind-induced damage as claimed in claim 1, it is characterised in that: step (4) Middle basic parameter is the terrain rough factor of urban environment and corresponding with wind load grade 10 minutes mean wind speeds.

6. the fast evaluation method of urban path tree wind-induced damage as claimed in claim 1, it is characterised in that: step (6) Shade tree is characterized more than it to limit values with shade tree maximum trunk unit root-mean-square bending strength under random wind Overall destructiveness.

7. the fast evaluation method of urban path tree wind-induced damage as claimed in claim 1, it is characterised in that: described boundary value For bending strength.

8. the fast evaluation method of urban path tree wind-induced damage as claimed in claim 1, it is characterised in that: step (3) Middle consideration density of wood and Deflection Modulus of Elasticity simultaneously are stochastic variable.

9. the fast evaluation method of urban path tree wind-induced damage as claimed in claim 1, it is characterised in that: the row set up The variability of the timberphysics parameter caused owing to tree families is different with growth conditions has been grasped in road tree wind-induced damage model.

10. the fast evaluation method of urban path tree wind-induced damage as claimed in claim 1, it is characterised in that: by using Accurately, efficient frequency analysis method reduce shade tree disaster caused by a windstorm failure probability based on Monte Carlo simulation solve workload.