CN103761348A - Asphalt pavement structure optimization design method based on finite element - Google Patents

Abstract

The invention discloses an asphalt pavement structure optimization design method based on a finite element. The method includes the steps: building a pavement structure optimization mathematical model; compiling and initializing parameters in the pavement structure optimization mathematical model by the aid of an ANSYS command stream mode, and building a pavement structure simulation model; extracting pavement structure design indicators to serve as boundary conditions of pavement structure optimization design; optimally calculating a pavement structure, and entering /opt to set value ranges of design variables and state variables; reviewing the parameters according to optimization results, and amending and verifying asphalt pavement structure parameters. The asphalt pavement structure parameters have better practical operability. Compared with the prior art, by the aid of the designed pavement structure scheme, road performance requirements are met, and engineering construction cost is the lowest.

Description

Asphalt pavement structure Optimization Design based on finite element

Technical field

The present invention relates to belong to the asphalt pavement structure optimization method of technical field of civil engineering, relating in particular to a kind of is basic based on finite element theory and application ANSYS optimization tool, the asphalt pavement structure optimization method take construction cost as optimization aim.

Background technology

Bituminous pavement is the version that a kind of formation is very complicated, the acting in conjunction that it need to bear driving vehicle load and environment simultaneously.The pavement structure scheme that designer recommends, except meeting certain pavement performance requires, also should make every effort to accomplish that engineering construction cost is minimum.

Pavement structure is especially during Structure of Expressway Asphalt Pavement, needs value arbitrarily in certain scope such as In-put design parameter such as each Laminate construction thickness, modulus etc., makes so the selectable pavement structure scheme of designer a lot.How in numerous pavement structures, to select optimization design scheme, be a very difficult problem.During Asphalt Pavement Structure Design, relate to multiple design variables, asphalt pavement structure also must meet multiple design objective simultaneously, and this makes existing Asphalt Pavement Structure Design software be difficult to implementation structure optimization.In current existing optimization of pavement structure method, be all to utilize Optimization Design in mathematics, pavement structure Mechanics Calculation and optimal design decouples computation.This method is exactly that optimization of pavement structure has departed from pavement structure mechanical analysis category, and requires designer to have higher mathematical knowledge.Be not easy to be applied in engineering reality.

Summary of the invention

Based on problems of the prior art, the present invention proposes a kind of asphalt pavement structure Optimization Design based on finite element, especially by the structure optimization module in ANSYS software, take pavement structure network minimal as objective function, each Laminate construction thickness, material bending tensile strength and compression rebound modulu are constraint condition, built optimization of pavement structure model, thereby simulation, calculating, the optimization of road pavement structure structure have been realized, and carry out simulation calculation by case history, result has shown feasibility and the validity of the method.

The present invention proposes a kind of asphalt pavement structure Optimization Design based on finite element, the method comprises the following steps:

An asphalt pavement structure Optimization Design based on finite element, the method comprises the following steps:

Step 1, set up optimization of pavement structure mathematical model

$F=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{k}_i{c}_i{b}_i{h}_i$

Wherein, n represents the number of plies of asphalt pavement structure combination; C _irepresent to build the expense that each different structure layer different materials of road surface of unit length consumes, K _iwhat represent material takes mould ratio, the modulus of resilience of asphalt pavement structural layer material by E increase to E ' afterwards corresponding expense by C, be increased to C ', material coefficient C '=C*K _i* (E '-E), b _irepresent each structural sheet width of pavement structure; h _irepresent pavement structure layer thickness;

Step 2, utilize parameter in ANSYS command stream mode road pavement structural mathematics Optimized model to compile and initialization, set up transversal section, road surface overall with model, i.e. formula in above-mentioned steps (1) in, by width of roadway b _ior Width is scaled, road surface top layer width is got 2000mm, other each layer of width computing formula

set up width b _ior bb _i, thickness h _ipavement structure and to soil matrix below, extend 2000mm as pavement structure realistic model; , wherein, i=1,2 ... n, n is pavement structure number of layers;

The boundary condition that step 3, extraction Pavement Structure Design index design as optimization of pavement structure, concrete operations are: choice structure is end nodes of locations layer by layer, show node stress, and node is sorted according to first principal stress, extract maximum tension stress;

Step 4, optimization of pavement structure calculate, and enter/opt sets design variable, the span of state variable, concrete operations are: set i layer thickness maximal value MAX, minimum value MIN, determines objective function and precision thereof, select optimization method, select optimization method, set corresponding Optimal Parameters;

Step 5, according to step 4 optimum results, parameters is checked, revise asphalt pavement structure parameter and verified and make it have better actual operation.

Described expense mould ratio all gets 1.0 when the modulus of resilience of not carrying out material is optimized; When carrying out modulus of resilience optimization, test is determined, concrete grammar is: by changing material mixture ratio, make the test specimen of different modulus, detect the modulus of resilience of each test specimen, then utilize least square method estimation

wherein $S_{\mathrm{xx}}=\underset{j=i}{\overset{m}{\mathrm{\Σ}}}{E}_j(E_j-\stackrel{\‾}{E}).$

The pavement structure scheme designing by the present invention, except having met pavement performance requires, also should make every effort to accomplish that engineering construction cost is minimum.

Accompanying drawing explanation

Fig. 1 is the optimization of pavement structure process flow diagram based on ANSYS of the present invention

Fig. 2 is parametrization pavement structure model;

Fig. 3 is the model calculation tension cloud charts of the present invention;

Fig. 4 is that each pavement structure layer thickness of the present invention is along with optimizing number of times change curve;

Fig. 5 is that different pavement expense of the present invention is with optimizing number of times change curve.

Embodiment

The method mainly comprises the following steps:

Step 1, set up optimization of pavement structure mathematical model: mainly comprise:

Determine objective function and the parameter thereof of optimization of pavement structure mathematical model: " asphalt pavement structure cost ", as objective function F, mathematical model is

wherein relate to parameter and physical meaning comprises:

The number of plies of n-asphalt pavement structure combination; K _ithe-the i structural material take mould ratio, expense mould ratio all gets 1.0 when the modulus of resilience of not carrying out material is optimized; When carrying out modulus of resilience optimization, test is determined, concrete grammar is: by changing material mixture ratio, make the test specimen of different modulus, detect the modulus of resilience of each test specimen, then utilize least square method estimation $K=S_{\mathrm{xy}}/S_{\mathrm{xx}},$ Wherein $S_{\mathrm{xy}}=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{E}_i(c_j-\stackrel{\‾}{c}),$ $S_{\mathrm{xx}}=\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{E}_j(E_j-\stackrel{\‾}{E});$ C _i-build the expense that the road surface i structural material of unit length (as m, km etc.) consumes, the modulus of resilience of asphalt pavement structural layer material by E increase to E ' afterwards corresponding expense by C, be increased to C ', Master Cost C '=C+K _i* (E '-E);

B _ieach structural sheet width of-pavement structure;

H _i-pavement structure layer thickness (i=1,2 ..., n, n is the road surface structare layer number of plies).

In above-mentioned optimization of pavement structure mathematical model boundary condition, using asphalt pavement structure changeable material parameter as design variable, as (pavement structure layer thickness, the modulus of resilience), bar structure layer design objective (as flexure, tension) is as state variable.

Step 2, set up the parameterized simulation model of pavement structure: mainly comprise:

(2-1) utilize the parameter in ANSYS command stream mode road pavement structural mathematics Optimized model to compile and initialization, initial method for inputting respectively successively k in ANSYS command window _i=k, c _i=c, b _i=b, h _i=h, (i=1,2 ..., n, n is the road surface structare layer number of plies, k, c, b, h is the concrete numerical value of road surface structare layer i, implication and definite method are the same);

(2-2) set up pavement structure realistic model.While considering that between ground subsoil layer, basic unit, surface layer, width is different, set up transversal section, road surface overall with model, each Laminate construction thickness of pavement structure h _irepresent width of roadway b _i(i=1,2 ... n, n is pavement structure number of layers) or Width scaled, each Laminate construction thickness of pavement structure h _irepresent, road surface top layer width is got 2000mm, other each layer of width computing formula

(i=1,2 ... n, n is pavement structure number of layers), set up width b _ior bb _i, thickness h _ipavement structure and to soil matrix below, extend 2000mm as pavement structure realistic model.

Step 3, extraction Pavement Structure Design index are as design variable so that it meets the boundary condition of optimization of pavement structure design, and key extracted statement is as follows:

Step 4, optimization of pavement structure calculate, and enter/opt sets design variable, the span of state variable.And select optimization method in ANSYS optimization tool to be optimized.Key order is as follows:

Step 5, according to step 4 optimum results, parameters is checked, revise asphalt pavement structure parameter and verified and make it have better actual operation.

Example

Optimization of pavement structure design has 3 key elements, i.e. design variable, constraint condition and objective function.The appropriate design of objective function is the key of optimal design work.

(1) take pavement structure expense as objective function, set up Optimized model:

$\begin{array}{c}\min F=c_1{h}_1{\mathrm{<figure-callout\; id="1"\; label="b"\; filenames="DEST\_PATH\_HDA0000388113370000021.png,DEST\_PATH\_HDA0000388113370000031.png"\; state="\{\{state\}\}">b</figure-callout>}}_1+c_2{h}_2{b}_2+c_3{h}_3{b}_3+c_4{h}_4{\mathrm{<figure-callout\; id="4"\; label="b"\; filenames="DEST\_PATH\_HDA0000388113370000031.png"\; state="\{\{state\}\}">b</figure-callout>}}_4+c_5{h}_5{b}_5\\ s.t.\begin{array}{c}\end{array}\left\{\begin{array}{c}{l}_s\&le;30\left(0.01\mathrm{mm}\right)\\ \begin{array}{cc}{\mathrm{\&sigma;}}_{1\max }\&le;0.2\mathrm{<figure-callout\; id="4"\; label="MPa"\; filenames="DEST\_PATH\_HDA0000388113370000031.png"\; state="\{\{state\}\}">MPa</figure-callout>}& 4\mathrm{c\; m}\&le;{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="DEST\_PATH\_HDA0000388113370000021.png,DEST\_PATH\_HDA0000388113370000031.png"\; state="\{\{state\}\}">h</figure-callout>}}_1\&le;10\mathrm{cm}\\ {\mathrm{\&sigma;}}_{2\max }\&le;0.33\mathrm{<figure-callout\; id="4"\; label="M\; Pa"\; filenames="DEST\_PATH\_HDA0000388113370000031.png"\; state="\{\{state\}\}">M\; Pa</figure-callout>}& 4\mathrm{cm}\&le;h_2\&le;10\mathrm{cm}\\ {\mathrm{\&sigma;}}_{3\max }\&le;0.18\mathrm{MPa}& 5\mathrm{cm}\&le;h_3\&le;20\mathrm{cm}\\ {\mathrm{\&sigma;}}_{4\max }\&le;0.26\mathrm{<figure-callout\; id="15"\; label="MPa"\; filenames="DEST\_PATH\_HDA0000388113370000031.png"\; state="\{\{state\}\}">MPa</figure-callout>}& 15\mathrm{cm}\&le;{\mathrm{<figure-callout\; id="4"\; label="h"\; filenames="DEST\_PATH\_HDA0000388113370000031.png"\; state="\{\{state\}\}">h</figure-callout>}}_4\&le;40\mathrm{cm}\\ {\mathrm{\&sigma;}}_{5\max }\&le;0.12\mathrm{<figure-callout\; id="15"\; label="M\; Pa"\; filenames="DEST\_PATH\_HDA0000388113370000031.png"\; state="\{\{state\}\}">M\; Pa</figure-callout>}& 15\mathrm{cm}\&le;h_5\&le;40\mathrm{cm}\end{array}\end{array}\right.\end{array}$

In formula: the objective function of F-pavement structure expense, represents to build the required expense of highway unit length;

-represent to build the expense (unit can be unit, Wan Yuan etc.) that each different structure layer different materials of road surface of unit length (as m, km etc.) consumes;

Each structural sheet width (cm) of-expression road surface;

Design variable, represents respectively in particulate formula bituminous concrete upper layer, middle grain formula bituminous concrete the thickness of surface layer, cement stabilized macadam base, two grey stabilization gravel subbases under surface layer, Coarse Graded Bituminous Concrete;

For state variable, represent road table design flexure and corresponding construction floor the maximal bend stress at the bottom.

Certain each design parameter of Class II highway pavement structure, index are as shown in table 1.

Each design parameter of table 1 Highway Pavement Structures

(2) in optimization of pavement structure model each calculating parameter determine

According to < < bituminous pavement design for highway standard > > (JTGD50-2006), determine Pavement Structure Design index.Design flexure computing formula suc as formula:

$l_d=600N_e^{-0.2}{A}_c{A}_s{A}_b$

In formula: l _d-design deflection value (0.01mm);

N _ea track accumulative equivalent axles in-design period;

A _c-road quality classification coefficient, highway, Class I highway are 1.0, Class II highway is 1.1, three, Class IV highway is 1.2;

A _s-surface layer genre modulus, asphalt concrete pavement is 1.0; Heat mix and stir cold-mix asphalt rubble, on mix down and pass through or penetration type road surface, bituminous surface treatment are 1.1; In, low class pavement is 1.2.

A _b-basic unit genre modulus, to semi-rigid type base A _b=1.0; Flexbile base A _b=1.6; For composite base, adopt linear interpolation to determine that basic unit's genre modulus is: A _b=(H _f+ 2) in/20 formulas: H _f-be flexible structure layer gross thickness (cm) on semi-rigid type base or subbase.

Asphalt concrete pavement, semi-rigid material basic unit, subbase be during take flexural tensile stress as design objective, the allowable tensile stress σ of material _rshould calculate by following formula:

${\mathrm{\&sigma;}}_R=\frac{{\mathrm{\&sigma;}}_S}{K_S}$

In formula: σ _rthe allowable tensile stress (MPa) of-pavement structure layer material;

σ _sthe ultimate tensile strength (UTS) (MPa) of-bituminous concrete or semi-rigid material;

K _s-tensile strength construction coefficient.

Calculate according to the method described above certain each design objective of Class II highway pavement structure as shown in table 2.

Certain each design objective of Class II highway pavement structure of table 2

In plan employing particulate formula bituminous concrete upper layer, middle grain formula bituminous concrete, under surface layer, Coarse Graded Bituminous Concrete, surface layer, cement stabilized macadam base, two grey stabilization gravel subbases are as pavement structure form, and existing each Laminate construction thickness of road pavement carries out optimization of pavement structure design as design variable.

The mathematical model of optimization of pavement structure is:

$F=\underset{i=1}{\overset{5}{\mathrm{\&Sigma;}}}{k}_i{c}_i{b}_i{h}_i,(k_i=1.0,{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="DEST\_PATH\_HDA0000388113370000021.png,DEST\_PATH\_HDA0000388113370000031.png"\; state="\{\{state\}\}">c</figure-callout>}}_1=2=5.8,c_2=5.8,c_3=5.7,{\mathrm{<figure-callout\; id="4"\; label="c"\; filenames="DEST\_PATH\_HDA0000388113370000031.png"\; state="\{\{state\}\}">c</figure-callout>}}_4=1.3,c_5=1.1).$

(3) parametrization structure simulation model is set up and is solved

Choose PLANE82 cell type, adopt ANSYS command stream mode to extract each structural sheet tensile stress at the bottom of layer result of calculation, and be assigned to corresponding state variable, the mathematical model of input optimization of pavement structure.

Parameterized model

Parametric modeling result is as Fig. 2, and load application also solves rear structural sheet tension cloud charts as Fig. 3.

Modeling result is as shown in Figure 2 sequentially from top to bottom: surface layer, cement stabilized macadam base, two grey stabilization gravel subbases, soil matrix under surface layer, Coarse Graded Bituminous Concrete in particulate formula bituminous concrete upper layer, middle grain formula bituminous concrete.

As seen from Figure 3, pavement structure interlayer tension mainly concentrates in basic unit and subbase, and surface layer interlayer tension almost can be ignored.Its part key order stream is as follows:

(4) optimization of pavement structure calculates

In OPT order, set the span of design variable, state variable, choose zeroth order optimization method and be optimized design.Its part key order stream is as follows:

(5) check optimum results

At ANSYS command window input OPEXE, carry out and optimize order, optimum results is along with optimization of pavement structure number of times changes as shown in Figure 4, Figure 5.Optimum results by Fig. 4, Fig. 5 can be found out, along with optimizing number of times, increases, and pavement structure expense is tending towards convergence, and convergence result approaches objective function minimum value.The optimum pavement structure form obtaining is thus: surface layer, 358.4mm cement stabilized macadam base, the grey stabilization gravel subbase of 321.4mm bis-under surface layer, 50.2mm Coarse Graded Bituminous Concrete in grain formula bituminous concrete in 40.2mm particulate formula bituminous concrete upper layer, 40.1mm.

In addition, can also check that each Laminate construction thickness changes each state variable impact in ANSYS, as Fig. 6, Fig. 7 is respectively tension impact in upper layer variation in thickness and subbase variation in thickness road pavement structural sheet.By Fig. 6, Fig. 7, can be found out, when increasing pavement structure layer thickness, between structural sheet more than this structural sheet, maximum tension stress can reduce, and between the structural sheet below this structural sheet, maximum tension stress increases.Therefore, visible pavement structure subbase, groundwork thickness are larger, and surface thickness can be suitably slightly little.

Claims (2)

1. the asphalt pavement structure Optimization Design based on finite element, is characterized in that, the method comprises the following steps:

Step (1), set up optimization of pavement structure mathematical model

$F=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{k}_i{c}_i{b}_i{h}_i$

Wherein, n represents the number of plies of asphalt pavement structure combination; C _irepresent to build the expense that each different structure layer different materials of road surface of unit length consumes, K _iwhat represent material takes mould ratio, the modulus of resilience of asphalt pavement structural layer material by E increase to E ' afterwards corresponding expense by C, be increased to C ', material coefficient C '=C*K _i* (E '-E), b _irepresent each structural sheet width of pavement structure; h _irepresent pavement structure layer thickness;

Step (2), utilize parameter in ANSYS command stream mode road pavement structural mathematics Optimized model to compile and initialization, set up transversal section, road surface overall with model, i.e. formula in above-mentioned steps (1)

in, by width of roadway b _ior Width is scaled, road surface top layer width is got 2000mm, other each layer of width computing formula set up width b _ior bb _i, thickness h _ipavement structure and to soil matrix below, extend 2000mm as pavement structure realistic model; , wherein, i=1,2 ... n, n is pavement structure number of layers;

The boundary condition that step (3), extraction Pavement Structure Design index design as optimization of pavement structure, concrete operations are: choice structure is end nodes of locations layer by layer, show node stress, and node is sorted according to first principal stress, extract maximum tension stress;

Step (4), optimization of pavement structure calculate, and enter/opt sets design variable, the span of state variable, concrete operations are: set i layer thickness maximal value MAX, minimum value MIN, determines objective function and precision thereof, select optimization method, select optimization method, set corresponding Optimal Parameters;

Step (5), according to step (4) optimum results, parameters is checked, revise asphalt pavement structure parameter and verified and make it have better actual operation.

2. the asphalt pavement structure Optimization Design based on finite element as claimed in claim 1, is characterized in that, described expense mould ratio all gets 1.0 when the modulus of resilience of not carrying out material is optimized; When carrying out modulus of resilience optimization, test is determined, concrete grammar is: by changing material mixture ratio, make the test specimen of different modulus, detect the modulus of resilience of each test specimen, then utilize least square method estimation K=S _xy/ S _xx, wherein

$S_{\mathrm{xx}}=\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}{E}_j(E_j-\stackrel{\&OverBar;}{E}).$

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