CN1880576A - System identification technique for structural mechanics characteristic of pavement - Google Patents

Abstract

The invention relates to a road structure physic character system recognize technique, which is based on the system recognize theory and the sensitivity analyze theory, to build the reverse analysis of road structure. Based on the physic properties of different road structures, it researches the road model of several sheet cement concrete roads, as well as adhesive power model, and non-liner model, to build the cement concrete road physic character system recognize, road adhesive power character system recognize technique and stress non-liner character system recognize technique, based on the interaction of several sheets. The invention can be used to check and control the road quality.

Description

System identification technique for structural mechanics characteristic of pavement

Technical field

The invention belongs to subgrade and pavement nondestructive testing assessment technique, relate in particular to a kind of system identification technique for structural mechanics characteristic of pavement.

Background technology

Since the eighties in 20th century, particularly along with the enforcement of the strategic highway research program of the U.S. (SHRP) highly visible, the research and development of highway Dynamic Non-Destruction Measurement are subjected to increasingly extensive attention in the world with being applied in.But utility theory research and software kit exploitation lag behind the development of high-tech checkout equipment all the time generally, and wherein subgrade and pavement material behavior inversion problem hampers the development of Dynamic Non-Destruction Measurements such as Falling Weight Deflectometer always.

Because China's expressway construction is started late, subgrade and pavement detects the assessment technique slower development.The subgrade and pavement bearing capacity detects and continues to use the conventional method based on manually-operated that the fifties is introduced always.Though many units have successively introduced highway non-destructive detecting devices such as Falling Weight Deflectometer, owing to lack supporting technology and software, cause large number quipments not play one's part to the full.

Pavement deflection is one of important technology index in pavement construction quality examination, evaluation on bearing capacity and the reinforcement design.So far, the pavement deflection detection technique detects the dynaflector detection-phase that develops into the effect of simulation traffic load from the static(al) flexure, developing into the pavement deflection basin from the detection of single-point flexure detects, correspondingly, road structure performance evaluation also develops into road surface structare layer mechanical characteristic inverse and stress-strain state analysis from road surface bulk strength evaluation, and will pass by only to be confined to the flexure index of asphalt concrete pavement structure, be applied among the assay of cement concrete pavement structure.

Therefore, further investigation subgrade and pavement material behavior inversion theory has great impetus to the development and the application of highway Dynamic Non-Destruction Measurement, and is not only significant, and meets pressing for of China's expressway construction and maintenance.

Carried out the research of two more than ten years in the world according to Falling Weight Deflectometer testing result inverse road surface structare layer modulus.Existing achievement in research is broadly divided into two classes: database method and iterative method.

(1) database method

Database method basic principle: at first set up a deflection basin database according to road structure layer thickness and modulus approximate range, utilize Lagrange interpolation and pattern search data fitting method to determine one group of modulus then, target is to make the error of calculating between deflection basin and the Falling Weight Deflectometer measured result reach minimum.

Database method is a target with the data fitting, finds the solution more stablely, but does not reflect the essence of indirect problem in theory, on using certain limitation is arranged also.Database does not have versatility on the one hand, is not suitable for power back analysis and non-linear back analysis on the other hand.

(2) iterative method

The achievement in research of iterative method is than horn of plenty, and common in the world more influential modular inverse calculation software mostly adopts iterative method at present.The key of iterative method is how to guarantee the stability of computational process.On going result requires harsh to choosing of initial value.Initial value choose improper may cause refutation process not restrain or inversion result not unique, its basic reason is to fail to solve " morbid state " problem that refutation process exists.

As can be seen,, still have many problems not obtain fine solution so far, having a strong impact on the development of drop hammer type benkelman beams deflectometer application technology though obtained achievement around the research of structural mechanics characteristic of pavement inversion problem in the world than horn of plenty.Existing subject matter has:

(1) inversion method

The subject matter that existing road structure inversion method exists is not consider " morbid state " problem of inversion equation, causes refutation process instability or inversion result not unique.Iterative method inverse software usually to initial value choose the comparison sensitivity, initial value is chosen improper, and refutation process is not restrained, or inversion result is relevant with initial value, its basic reason is to fail to handle effectively " morbid state " problem of inversion equation.

(2) cement concrete pavement inverting

Achievement in research about structural mechanics characteristic of pavement inverting aspect is primarily aimed at asphalt concrete pavement at present, generally adopts the elastic multilayer theory.Because the difficulty of cement concrete pavement mechanical model aspect is less about the achievement in research of cement concrete pavement mechanical characteristic inverting aspect, particularly the power inversion problem of polylith plate has not yet to see relevant achievement on the multilayer system.

(3) power inverting

Existing structural mechanics characteristic of pavement inverse software is forward model with the elastic multilayer theory mostly, adopts the pavement deflection basin data of Falling Weight Deflectometer test to intend the static(al) inverting.How to consider the dynamic characteristics of road structure and the viscous-elastic behaviour of ground surface material, utilizing the time-histories information of Falling Weight Deflectometer collection to come inverting road surface structare layer dynamic parameter is a still unsolved problem.

(4) non-linear inversion

At present all suppose generally that about the research of road surface structare layer modulus inversion problem the subgrade and pavement material meets the linear elasticity model, do not consider the nonlinear characteristic of material.How to set up rational road structure nonlinear model, present research is deep not enough.Particularly the achievement in research of power non-linear inversion aspect is more rare.

Summary of the invention

The present invention is directed to the problems referred to above that the structural mechanics characteristic of pavement inverting exists, created system identification technique for structural mechanics characteristic of pavement, studied polylith plate cement concrete pavement model, viscoplasticity dynamic model and nonlinear model on the multistrata foundation, set up based on the interactional cement concrete pavement mechanical characteristic of polylith plate system identification technique, road surface viscoelastic dynamic characteristics system identification technique and stress nonlinear characteristic system identification technique.

Solution of the present invention is:

A kind of system identification technique for structural mechanics characteristic of pavement,

(1) utilize Falling Weight Deflectometer detection system road pavement to carry out field trial, the deflection basin information of observation road structure under known load action;

(2) set up the mechanical model of reflection road structure material behavior, calculated under identical load action flexure corresponding to Falling Weight Deflectometer sensing station place;

(3) set up road structure inversion equation, utilized the singular value decomposition technology to solve " morbid state " problem of inversion equation based on sensitivity analysis;

Implementation method is as follows:

If the road structure mechanical model can be expressed as:

W ^c＝f(E ₁，E ₂，……E _n；x) (1)

Wherein x is a space variable, is used for representing the distance of sensor apart from the load center here, W ^cFlexure vector, E are calculated in expression ₁E _nThe mechanics parameters of n need inverse of expression;

The deflection value W of k sensor _kCan be expressed as:

W _k＝f _k(E) (2)

E represents vector { E in the formula ₁E _n} ^T

With the following formula Taylor series expansion, and get its single order approximate quantity, then have:

f _k(E+ΔE)＝f _k(E)+f _kΔE (3)

Following formula can be written as:

$e_k=f_k(E+\mathrm{\ΔE})-f_k\left(E\right)$

$={\▿f}_k\·\mathrm{\ΔE}=\frac{{\∂f}_k}{{\∂E}_1}{\mathrm{\ΔE}}_1+\frac{{\∂f}_k}{{\∂E}_2}\mathrm{\Δ}{E}_2+\·\·\·\·\·\·+\frac{{\∂f}_k}{\∂E_n}{\mathrm{\ΔE}}_n$ (4)

If use f _k(E) representative actual measurement flexure, f _kThe calculating flexure after the mechanics parameters is adjusted in (E+ Δ E) representative, and Δ E represents the adjustment amount of mechanics parameters, then e _kCalculate the margin of error between flexure and the actual measurement flexure after the adjustment of expression mechanics parameters;

The different sensors place is set up above-mentioned equation, then has:

$e_1=\frac{\∂f_1}{{\∂E}_1}{\mathrm{\ΔE}}_1+\frac{\∂f_1}{{\∂E}_2}{\mathrm{\ΔE}}_2+\·\·\·\·\·\·\frac{\∂f_1}{{\∂E}_n}{\mathrm{\ΔE}}_n$

$e_2=\frac{\∂f_2}{{\∂E}_1}{\mathrm{\ΔE}}_1+\frac{\∂f_2}{{\∂E}_2}{\mathrm{\ΔE}}_2+\·\·\·\·\·\·\frac{\∂f_2}{{\∂E}_n}{\mathrm{\ΔE}}_n---\left(5\right)$

………………

$e_m=\frac{\∂f_m}{{\∂E}_1}{\mathrm{\ΔE}}_1+\frac{\∂f_m}{{\∂E}_2}{\mathrm{\ΔE}}_2+\·\·\·\·\·\·\frac{\∂f_m}{{\∂E}_n}{\mathrm{\ΔE}}_n$

With above-mentioned equation group both sides divided by f _k, make equation become nondimensional equation group, then have:

$\frac{e_1}{f_1}=\frac{\∂f_1}{{\∂E}_1}\·\frac{E_1}{f_1}\·\frac{{\mathrm{\ΔE}}_1}{E_1}+\frac{{\∂f}_1}{{\∂E}_2}\·\frac{E_2}{f_1}\·\frac{{\mathrm{\ΔE}}_2}{E_2}+\·\·\·\·\·\·+\frac{{\∂f}_1}{\∂E_n}\·\frac{E_n}{f_1}\·\frac{{\mathrm{\ΔE}}_n}{E_n}$

$\frac{e_2}{f_2}=\frac{\∂f_2}{{\∂E}_1}\·\frac{E_1}{f_2}\·\frac{{\mathrm{\ΔE}}_1}{E_1}+\frac{{\∂f}_2}{{\∂E}_2}\·\frac{E_2}{f_2}\·\frac{{\mathrm{\ΔE}}_2}{E_2}+\·\·\·\·\·\·+\frac{{\∂f}_2}{\∂E_n}\·\frac{E_n}{f_2}\·\frac{{\mathrm{\ΔE}}_n}{E_n}---\left(6\right)$

………………

$\frac{e_m}{f_m}=\frac{\∂f_m}{{\∂E}_1}\·\frac{E_1}{f_m}\·\frac{{\mathrm{\ΔE}}_1}{E_1}+\frac{{\∂f}_m}{{\∂E}_2}\·\frac{E_2}{f_m}\·\frac{{\mathrm{\ΔE}}_2}{E_2}+\·\·\·\·\·\·+\frac{{\∂f}_m}{\∂E_n}\·\frac{E_n}{f_m}\·\frac{\mathrm{\ΔE}}{E_n}$

Following formula is expressed as matrix or vector form, that is:

$r={[\frac{e_1}{f_1},\frac{e_2}{f_2},\frac{e_3}{f_3}\·\·\·\·\·\·\frac{e_m}{f_m}]}^T$

F＝[F _ki]

$F_{\mathrm{ki}}=\frac{\∂f_k}{{\∂E}_i}\·\frac{E_i}{f_k}$ k＝1，2……m；i＝1，2……n

$\mathrm{\α}={[\frac{\mathrm{\Δ}{E}_1}{E_1},\frac{{\mathrm{\ΔE}}_2}{E_2},\·\·\·\·\·\·\frac{{\mathrm{\ΔE}}_n}{E_n}]}^T$

Then equation (6) can be expressed as: become:

r＝Fα (7)

It is definite fully with the actual measurement flexure that error vector r can calculate flexure by model, and matrix F is a sensitivity matrix, element F wherein _KiRepresent the sensitiveness of the flexure at k sensor place, can adopt numerical computation method to set up i mechanics parameters;

Equation (7) adopts the singular value decomposition technology to find the solution, wherein any one m * n rank matrix A (m 〉=n) can be decomposed into m * n rank orthogonal matrix U, transposition V of n * n rank diagonal matrix w and n * n rank orthogonal matrix v ^TProduct, that is:

A＝U·W·V ^T (8)

Wherein

U ^TU＝V ^TV＝E

w _i≥0 (i＝1，2，…，n)

The conditional number r=w of matrix F _Max/ w _MinThe singularity that has reflected matrix.As r infinity, i.e. w _Min=0 o'clock, matrix was unusual, and when r is bigger but non-when infinite, matrix is an ill-condition matrix; Therefore, the singular value decomposition theory not only can diagnostic equation morbid state whether, and can provide the stable answer of equation by the cancellation minimum singular value.

Set up based on the interactional cement concrete pavement mechanical characteristic of polylith plate system identification technique, the road structure mechanical model of described foundation is the mechanical model of polylith plate, suppose that getting in touch by the shearing of seam crossing between plate and the plate realize, represent seam transmission form with load transfer efficient e=w '/w, set up the interactional cement pavement computation model of polylith plate on the multi-form ground; In the Viscoelastic Multi-layered Soil model, introduce complex damping theory, found the solution the dynamic stiffness matrix of viscoplasticity ground, and it has been coupled in the kinetic equation of plate; Use this model and Falling Weight Deflectometer time-histories information respectively frequency domain and time domain inverting the dynamic characteristics parameter of cement concrete pavement.

Set up asphalt concrete pavement viscoelastic dynamic characteristics system identification technique, the road surface mechanical model of described foundation is that asphalt surface course adopts two-parameter creep compliance model: E (t)=E ₁t ^-m, basic unit and roadbed adopt complex damping model: E ^*(ω)=E (1+i2 β); In frequency domain, the single-frequency response curve as the match target, has been finished the inverting of viscous-elastic behaviour power; In time domain, adopt the Rayleigh damper model, flexure Dynamic time history curve as the match target, has been finished the inverting of viscous-elastic behaviour power.

Set up road structure ply stress nonlinear characteristic system identification technique, the road structure mechanical model of described foundation is at the nonlinear actual features of ground surface material, selects for use body stress model and bilinear model to carry out back analysis respectively, that is:

The body stress model: $E_r=k_1{\left(\mathrm{\θ}\right)}^{k_2}$

Wherein: E _r---the modulus of resilience

θ---body stress θ=(σ ₁+ σ ₂+ σ ₃)

k ₁, k ₂---parameter, be on the occasion of

Bilinear model: work as σ _d＜k ₂E _r=k ₁+ k ₃(k ₂-σ _d)

Work as σ _d＞k ₂E _r=k ₁-k ₄(σ _d-k ₂)

Wherein: k ₁, k ₂, k ₃, k ₄Be parameter;

Utilize certain actual basic unit test deflection basin, basic unit is made as body stress is non-linear, ground layer is made as linear elasticity, roadbed is made as bilinear model.

The present invention has solved the problem that the structural mechanics characteristic of pavement inverting exists by above technical scheme, has created system identification technique for structural mechanics characteristic of pavement.The present invention is academicly abundant and developed the road structure inversion theory, on using, for detecting and control subgrade and pavement construction quality, scientific evaluation bearing capacity of pavement structure have great practical value, will play strong impetus for the development of Falling Weight Deflectometer Dynamic Non-Destruction Measurement.Current, the highway construction of China Higher level is in the stage of developing rapidly, and the highway construction quality is subjected to the great attention of governments at all levels and the extensive concern of the whole society.Existing subgrade and pavement detects with the assessment technique level overall also relatively backward, is difficult to satisfy the actual needs of highway construction and maintenance management.Therefore, highway in China detects and the assessment technique level has important function for improving in the present invention, has the remarkable economical social benefit at aspects such as ensureing workmanship, formulation Maintenance Decision making.

Description of drawings

Fig. 1 is the system identification technique for structural mechanics characteristic of pavement flow chart;

Fig. 2 is the mechanical model figure of polylith plate.

The specific embodiment

Embodiment: the specific embodiment of the present invention comprises following particular content:

1, system identification technique for structural mechanics characteristic of pavement

The present invention has created system identification technique for structural mechanics characteristic of pavement based on system identification principle and sensitivity analysis theory, utilizes the singular value decomposition technology to solve " morbid state " problem of inversion equation.The basic implementation process of this technology as shown in Figure 1.

(1) utilize Falling Weight Deflectometer detection system road pavement to carry out field trial, the deflection basin information of observation road structure under known load action;

(2) set up the mechanical model of reflection road structure material behavior, calculated under identical load action flexure corresponding to Falling Weight Deflectometer sensing station place;

(3) set up road structure inversion equation, utilized the singular value decomposition technology to solve " morbid state " problem of inversion equation based on sensitivity analysis;

Implementation method is as follows:

If the road structure mechanical model can be expressed as:

W ^c＝f(E ₁，E ₂，……E _n；x) (1)

Wherein x is a space variable, is used for representing the distance of sensor apart from the load center here, W ^cFlexure vector, E are calculated in expression ₁E _nThe mechanics parameters of n need inverse of expression;

The deflection value W of k sensor _kCan be expressed as:

W _k＝f _k(E) (2)

E represents vector { E in the formula ₁E _n} ^T

With the following formula Taylor series expansion, and get its single order approximate quantity, then have:

f _k(E+ΔE)＝f _k(E)+f _kΔE (3)

Following formula can be written as:

$e_k=f_k(E+\mathrm{\ΔE})-f_k\left(E\right)$

$={\▿f}_k\·\mathrm{\ΔE}=\frac{{\∂f}_k}{{\∂E}_1}{\mathrm{\ΔE}}_1+\frac{{\∂f}_k}{{\∂E}_2}\mathrm{\Δ}{E}_2+\·\·\·\·\·\·+\frac{{\∂f}_k}{\∂E_n}{\mathrm{\ΔE}}_n---\left(4\right)$

If use f _k(E) representative actual measurement flexure, f _kThe calculating flexure after the mechanics parameters is adjusted in (E+ Δ E) representative, and Δ E represents the adjustment amount of mechanics parameters, then e _kCalculate the margin of error between flexure and the actual measurement flexure after the adjustment of expression mechanics parameters;

The different sensors place is set up above-mentioned equation, then has:

$e_1=\frac{\∂f_1}{{\∂E}_1}{\mathrm{\ΔE}}_1+\frac{\∂f_1}{{\∂E}_2}{\mathrm{\ΔE}}_2+\·\·\·\·\·\·\frac{\∂f_1}{{\∂E}_n}{\mathrm{\ΔE}}_n$

$e_2=\frac{\∂f_2}{{\∂E}_1}{\mathrm{\ΔE}}_1+\frac{\∂f_2}{{\∂E}_2}{\mathrm{\ΔE}}_2+\·\·\·\·\·\·\frac{\∂f_2}{{\∂E}_n}{\mathrm{\ΔE}}_n---\left(5\right)$

………………

$e_m=\frac{\∂f_m}{{\∂E}_1}{\mathrm{\ΔE}}_1+\frac{\∂f_m}{{\∂E}_2}{\mathrm{\ΔE}}_2+\·\·\·\·\·\·\frac{\∂f_m}{{\∂E}_n}{\mathrm{\ΔE}}_n$

With above-mentioned equation group both sides divided by f _k, make equation become nondimensional equation group, then have:

$\frac{e_1}{f_1}=\frac{\∂f_1}{{\∂E}_1}\·\frac{E_1}{f_1}\·\frac{{\mathrm{\ΔE}}_1}{E_1}+\frac{{\∂f}_1}{{\∂E}_2}\·\frac{E_2}{f_1}\·\frac{{\mathrm{\ΔE}}_2}{E_2}+\·\·\·\·\·\·+\frac{{\∂f}_1}{\∂E_n}\·\frac{E_n}{f_1}\·\frac{{\mathrm{\ΔE}}_n}{E_n}$

$\frac{e_2}{f_2}=\frac{\∂f_2}{{\∂E}_1}\·\frac{E_1}{f_2}\·\frac{{\mathrm{\ΔE}}_1}{E_1}+\frac{{\∂f}_2}{{\∂E}_2}\·\frac{E_2}{f_2}\·\frac{{\mathrm{\ΔE}}_2}{E_2}+\·\·\·\·\·\·+\frac{{\∂f}_2}{\∂E_n}\·\frac{E_n}{f_2}\·\frac{{\mathrm{\ΔE}}_n}{E_n}---\left(6\right)$

………………

$\frac{e_m}{f_m}=\frac{\∂f_m}{{\∂E}_1}\·\frac{E_1}{f_m}\·\frac{{\mathrm{\ΔE}}_1}{E_1}+\frac{{\∂f}_m}{{\∂E}_2}\·\frac{E_2}{f_m}\·\frac{{\mathrm{\ΔE}}_2}{E_2}+\·\·\·\·\·\·+\frac{{\∂f}_m}{\∂E_n}\·\frac{E_n}{f_m}\·\frac{\mathrm{\ΔE}}{E_n}$

Following formula is expressed as matrix or vector form, that is:

$r={[\frac{e_1}{f_1},\frac{e_2}{f_2},\frac{e_3}{f_3}\·\·\·\·\·\·\frac{e_m}{f_m}]}^T$

F＝[F _ki]

$F_{\mathrm{ki}}=\frac{\∂f_k}{{\∂E}_i}\·\frac{E_i}{f_k}$ k＝1，2……m；i＝1，2……n

$\mathrm{\α}={[\frac{{\mathrm{\ΔE}}_1}{E_1},\frac{{\mathrm{\ΔE}}_2}{E_2},\·\·\·\·\·\·\frac{{\mathrm{\ΔE}}_n}{E_n}]}^T$

Then equation (6) can be expressed as: become:

r＝Fα (7)

It is definite fully with the actual measurement flexure that error vector r can calculate flexure by model, and matrix F is a sensitivity matrix, element F wherein _KiRepresent the sensitiveness of the flexure at k sensor place, can adopt numerical computation method to set up i mechanics parameters;

Equation (7) adopts the singular value decomposition technology to find the solution, wherein any one m * n rank matrix A (m 〉=n) can be decomposed into m * n rank orthogonal matrix U, transposition V of n * n rank diagonal matrix w and n * n rank orthogonal matrix v ^TProduct, that is:

A＝U·W·V ^T (8)

Wherein

U ^TU＝V ^TV＝E

w _i≥0 (i＝1，2，…，n)

The conditional number r=w of matrix F _Max/ w _MinThe singularity that has reflected matrix.As r infinity, i.e. w _Min=0 o'clock, matrix was unusual, and when r is bigger but non-when infinite, matrix is an ill-condition matrix; Therefore, the singular value decomposition theory not only can diagnostic equation morbid state whether, and can provide the stable answer of equation by the cancellation minimum singular value.

2, based on the interactional cement concrete pavement mechanical characteristic of polylith plate system identification technique

The present invention has set up based on the interactional cement concrete pavement mechanical characteristic of polylith plate system identification technique.In the Viscoelastic Multi-layered Soil model, introduce complex damping theory, found the solution the dynamic stiffness matrix of viscoplasticity ground, and it has been coupled in the kinetic equation of plate.Use this model and Falling Weight Deflectometer time-histories information respectively in frequency domain and time domain in inverting the dynamic characteristics parameter of cement concrete pavement.

Suppose that getting in touch by the shearing of seam crossing between plate and the plate realize, represent that with load transfer efficient e=w '/w seam transmits form, set up the interactional cement concrete pavement computation model of polylith plate on the multi-form ground.The mechanical model of the polylith plate of setting up as shown in Figure 2.

Based on the system identification principle, the present invention has finished polylith plate interact Winkler, the semi-infinite half-space, multilayer elastomeric ground Concrete Pavement Materials characteristic power, static(al) inverting down respectively, and partial results sees Table 1 and table 2.

Table 1 Winkler grade slab inversion result

Initial value	Theoretical value	Inverting value	Error (%)
				E＝2.7×10 2MPa k＝4.0×10 2kN/m 3	E＝2.6×10 4MPa k＝5.0×10 4kN/m 3	E＝2.5999×10 4MPa k＝5.0000×10 4kN/m 3	0.004 0.000
E＝3.0×10 5MPa k＝5.5×10 5kN/m 3	E＝2.5999×10 4MPa k＝5.0000×10 4kN/m 3	0.004 0.000
			E＝9.0×10 5MPa k＝9.0×10 5kN/m 3	E＝2.5999×10 4MPa k＝5.0000×10 4kN/m 3		0.004 0.000

Table 2 is the substrate inversion result layeredly

Initial value (MPa)	Theoretical value (MPa)	Inverting value (MPa)	Error (%)
				E 0＝3.6×10 3 E 1＝3.0×10 2 E 2＝2.0×10 1	E 0＝3.6×10 4 E 1＝3.0×10 3 E 2＝2.0×10 2	E 0＝3.6034×10 4 E 1＝2.971×10 3 E 2＝2.0×10 2	0.09 0.97 0.00
E 0＝3.6×10 5 E 1＝3.0×10 5 E 2＝2.0×10 4	E 0＝3.6040×10 4 E 1＝2.971×10 3 E 2＝2.0×10 2	0.11 0.97 0.00

3, asphalt concrete pavement viscoelastic dynamic characteristics system identification technique

The present invention is directed to the viscous-elastic behaviour of actual asphalt concrete pavement, set up the viscoplasticity dynamic model of asphalt concrete pavement, and set up asphalt concrete pavement viscoelastic dynamic characteristics system identification technique.Asphalt surface course adopts two-parameter creep compliance model: E (t)=E ₁t ^-m, basic unit and roadbed adopt complex damping model: E ^*(ω)=E (1+i2 β).In frequency domain, the single-frequency response curve as the match target, has been finished the inverting of viscous-elastic behaviour power, result such as table 3; In time domain, adopt the Rayleigh damper model, flexure Dynamic time history curve as the match target, has been finished the inverting of time domain viscoelastic power.

Table 3 ground surface material viscous-elastic behaviour parametric inversion result

4, road structure ply stress nonlinear characteristic system identification technique

The present invention is directed to the nonlinear actual features of ground surface material, select body stress model and bilinear model respectively for use, set up road surface structare layer nonlinear characteristic system recognition technology; That is:

The body stress model: $E_r=k_1{\left(\mathrm{\θ}\right)}^{k_2}$

Wherein: E _r---the modulus of resilience

θ---body stress θ=(σ ₁+ σ ₂+ σ ₃)

k ₁, k ₂---parameter, be on the occasion of

Bilinear model: work as σ _d＜k ₂E _r=k ₁+ k ₃(k ₂-σ _d)

Work as σ _d＞k ₂E ₁=k ₁-k ₄(σ _d-k ₂)

Wherein: k ₁, k ₂, k ₃, k ₄Be parameter.

Utilize certain actual basic unit test deflection basin, basic unit is made as body stress is non-linear, ground layer is made as linear elasticity, roadbed is made as bilinear model, the nonlinear modulus that obtains after the inverting distributes as table 4.

Table 4 multilayered nonlinear inverse modulus (MPa) is along the variation of the degree of depth and radial distance

Apart from basic unit's end face distance (m)		Apart from load center radial distance (mm)
												30	60	120	180	205	309	450	609	914	1219
		Basic unit	0.013	1053	1036	819
0.09	606											548	398	233
			0.168	439	409	332	242	180
0.245	359											345	305	252	208	101
			0.297	326	318	294	262	230	127
Subbase	0.31-0.546											382	382	382	382	382.	382	382	382	382			382
		Soil matrix	0.60	131	132	132	132	133	139	149	160										172	173
0.84	145											145	146	147	148	151	156	162	170	173
			1.19	160	161	161	161	161	163	165	167										171	173
2.03	173											173	173	173	173	173	173	173	173	173
			19.0	173	173	173	173	173	173	173	173										173	173

Claims (4)

1, a kind of system identification technique for structural mechanics characteristic of pavement is characterized in that:

(1) utilize Falling Weight Deflectometer detection system road pavement to carry out field trial, the deflection basin information of observation road structure under known load action;

(2) set up the mechanical model of reflection road structure material behavior, calculated under identical load action flexure corresponding to Falling Weight Deflectometer sensing station place;

(3) set up road structure inversion equation, utilized the singular value decomposition technology to solve " morbid state " problem of inversion equation based on sensitivity analysis;

Implementation method is as follows:

If the road structure mechanical model can be expressed as:

W ^c＝f(E ₁，E ₂，……E _n；x) (1)

Wherein x is a space variable, is used for representing the distance of sensor apart from the load center here, W ^cFlexure vector, E are calculated in expression ₁E _nThe mechanics parameters of n need inverse of expression;

The deflection value W of k sensor _kCan be expressed as:

W _k=f _k(E) E represents vector { E in (2) formula ₁E _n} ^T

With the following formula Taylor series expansion, and get its single order approximate quantity, then have:

f _k(E+ΔE)＝f _k(E)+f _kΔE (3)

Following formula can be written as:

$e_k=f_k(E+\mathrm{\ΔE})-f_k\left(E\right)$

$={\▿f}_k\·\mathrm{\ΔE}=\frac{{\∂f}_k}{{\∂E}_1}{\mathrm{\ΔE}}_1+\frac{\∂f_k}{{\∂E}_2}\mathrm{\Δ}{E}_2+\·\·\·\·\·\·+\frac{\∂f_k}{{\∂E}_n}\mathrm{\Δ}{E}_n---\left(4\right)$

If use f _k(E) representative actual measurement flexure, f _kThe calculating flexure after the mechanics parameters is adjusted in (E+ Δ E) representative, and Δ E represents the adjustment amount of mechanics parameters, then e _kCalculate the margin of error between flexure and the actual measurement flexure after the adjustment of expression mechanics parameters;

The different sensors place is set up above-mentioned equation, then has:

$e_1=\frac{{\∂f}_1}{{\∂E}_1}\mathrm{\Δ}{E}_1+\frac{{\∂f}_1}{{\∂E}_2}{\mathrm{\ΔE}}_2+\·\·\·\·\·\·\frac{{\∂f}_1}{{\∂E}_n}{\mathrm{\ΔE}}_n$

$e_2=\frac{{\∂f}_2}{{\∂E}_1}\mathrm{\Δ}{E}_1+\frac{{\∂f}_2}{{\∂E}_2}{\mathrm{\ΔE}}_2+\·\·\·\·\·\·\frac{\∂f_2}{{\∂E}_n}\mathrm{\Δ}{E}_n---\left(5\right)$

………………

$e_m=\frac{{\∂f}_m}{\∂E_1}\mathrm{\Δ}{E}_1+\frac{\∂f_m}{\∂E_2}\mathrm{\Δ}{E}_2+\·\·\·\·\·\·\frac{{\∂f}_m}{{\∂E}_n}{\mathrm{\ΔE}}_n$

With above-mentioned equation group both sides divided by f _k, make equation become nondimensional equation group, then have:

$\frac{e_1}{f_1}=\frac{{\∂f}_1}{{\∂E}_1}\·\frac{E_1}{f_1}\·\frac{{\mathrm{\ΔE}}_1}{E_1}+\frac{\∂f_1}{{\∂E}_2}\·\frac{E_2}{f_1}\·\frac{{\mathrm{\ΔE}}_2}{E_2}+\·\·\·\·\·\·+\frac{{\∂f}_1}{{\∂E}_n}\·\frac{E_n}{f_1}\·\frac{{\mathrm{\ΔE}}_n}{E_n}$

$\frac{e_2}{f_2}=\frac{{\∂f}_2}{{\∂E}_1}\·\frac{E_1}{f_2}\·\frac{{\mathrm{\ΔE}}_1}{E_1}+\frac{\∂f_2}{{\∂E}_2}\·\frac{E_2}{f_2}\·\frac{{\mathrm{\ΔE}}_2}{E_2}+\·\·\·\·\·\·+\frac{{\∂f}_2}{{\∂E}_n}\·\frac{E_n}{f_2}\·\frac{{\mathrm{\ΔE}}_n}{E_n}---\left(6\right)$

………………

$\frac{e_m}{f_m}=\frac{{\∂f}_m}{{\∂E}_1}\·\frac{E_1}{f_m}\·\frac{{\mathrm{\ΔE}}_1}{E_1}+\frac{\∂f_m}{{\∂E}_2}\·\frac{E_2}{f_m}\·\frac{{\mathrm{\ΔE}}_2}{E_2}+\·\·\·\·\·\·+\frac{{\∂f}_m}{{\∂E}_n}\·\frac{E_n}{f_m}\·\frac{{\mathrm{\ΔE}}_n}{E_n}$

Following formula is expressed as matrix or vector form, that is:

$r={[\frac{e_1}{f_1},\frac{e_2}{f_2},\frac{e_3}{f_3}\·\·\·\·\·\·\frac{e_m}{f_m}]}^T$

F＝[F _ki]

$F_{\mathrm{ki}}=\frac{{\∂f}_k}{{\∂E}_i}\·\frac{E_i}{f_k}k=\mathrm{1,2}\·\·\·\·\·\·m;i=\mathrm{1,2}\·\·\·\·\·\·n$

$\mathrm{\α}={[\frac{{\mathrm{\ΔE}}_1}{E_1},\frac{{\mathrm{\ΔE}}_2}{E_2},\·\·\·\·\·\·\frac{{\mathrm{\ΔE}}_n}{E_n}]}^T$

Then equation (6) can be expressed as: become:

r＝Fα (7)

It is definite fully with the actual measurement flexure that error vector r can calculate flexure by model, and matrix F is a sensitivity matrix, element F wherein _KiRepresent the sensitiveness of the flexure at k sensor place, can adopt numerical computation method to set up i mechanics parameters;

Equation (7) adopts the singular value decomposition technology to find the solution, wherein any one m * n rank matrix A (m 〉=n) can be decomposed into m * n rank orthogonal matrix U, transposition V of n * n rank diagonal matrix w and n * n rank orthogonal matrix v ^TProduct, that is:

A＝U·W·V ^T (8)

Wherein

U ^TU＝V ^TV＝E

The conditional number r=w of matrix F _Max/ w _MinThe singularity that has reflected matrix.As r infinity, i.e. w _Min=0 o'clock, matrix was unusual, and when r is bigger but non-when infinite, matrix is an ill-condition matrix; Therefore, the singular value decomposition theory not only can diagnostic equation morbid state whether, and can provide the stable answer of equation by the cancellation minimum singular value.

2, system identification technique for structural mechanics characteristic of pavement according to claim 1, it is characterized in that: set up based on the interactional cement concrete pavement mechanical characteristic of polylith plate system identification technique, the road structure mechanical model of described foundation is the mechanical model of polylith plate, suppose that getting in touch by the shearing of seam crossing between plate and the plate realize, represent seam transmission form with load transfer efficient e=w '/w, set up the interactional cement pavement computation model of polylith plate on the multi-form ground; In the Viscoelastic Multi-layered Soil model, introduce complex damping theory, found the solution the dynamic stiffness matrix of viscoplasticity ground, and it has been coupled in the kinetic equation of plate; Use this model and Falling Weight Deflectometer time-histories information respectively frequency domain and time domain inverting the dynamic characteristics parameter of cement concrete pavement.

3, system identification technique for structural mechanics characteristic of pavement according to claim 1, it is characterized in that: set up asphalt concrete pavement viscoelastic dynamic characteristics system identification technique, the road surface mechanical model of described foundation is that asphalt surface course adopts two-parameter creep compliance model: E (t)=E ₁t ^-m, basic unit and roadbed adopt complex damping model: E ^*(ω)=E (1+i2 β); In frequency domain, the single-frequency response curve as the match target, has been finished the inverting of viscous-elastic behaviour power; In time domain, adopt the Rayleigh damper model, flexure Dynamic time history curve as the match target, has been finished the inverting of viscous-elastic behaviour power.

4, system identification technique for structural mechanics characteristic of pavement according to claim 1, it is characterized in that: set up road structure ply stress nonlinear characteristic system identification technique, the road structure mechanical model of described foundation is at the nonlinear actual features of ground surface material, select for use body stress model and bilinear model to carry out back analysis respectively, that is:

The body stress model:

$E_r=k_1{\left(\mathrm{\θ}\right)}^{k_2}$

Wherein: E _r---the modulus of resilience

θ---body stress θ=(σ ₁+ σ ₂+ σ ₃)

k ₁, k ₂---parameter, be on the occasion of

Bilinear model: work as σ _d＜k ₂E _r=k ₁+ k ₃(k ₂-σ _d)

Work as σ _d＞k ₂E _r=k ₁-k ₄(σ _d-k ₂)

Wherein: k ₁, k ₂, k ₃, k ₄Be parameter;

Utilize certain actual basic unit test deflection basin, basic unit is made as body stress is non-linear, ground layer is made as linear elasticity, roadbed is made as bilinear model.