CN109241636B - Finite element-based road surface structure multi-physical field coupling numerical simulation method - Google Patents
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Abstract
The invention discloses a finite element-based road surface structure multi-physical field coupling numerical simulation method, which comprises the following steps of: defining mechanical, thermodynamic and hydraulic parameters; defining vehicle load and meteorological functions; adding a solid mechanical module, applying load and setting boundary conditions; adding a porous medium heat transfer module, referring to a meteorological function and setting boundary conditions; adding a Darcy law module, quoting a meteorological function and setting boundary conditions; adding a multi-physical field coupling module to couple the multi-physical field; and calculating and performing post-processing analysis. The invention couples the stress field, the temperature field and the hydraulic field, and comprehensively studies the influence of a plurality of physical fields on the road performance. The method has good guiding significance for the selection and analysis of the road surface structure.
Description
Technical Field
The invention relates to numerical simulation of a pavement structure, in particular to a finite element-based pavement structure multi-physical-field coupling numerical simulation method.
Background
In the past, the pavement performance of asphalt pavements is one of research hotspots in the field of road engineering, and researchers can conveniently analyze the pavement structure by means of finite element software, so that manpower and material resources are saved.
The change of the pavement performance of the pavement structure is often the result of the combined action of a plurality of physical fields, including a stress field, a temperature field, a hydraulic field and the like, and the analysis of the pavement structure coupling the stress field, the temperature field and the hydraulic field cannot be comprehensively considered in the prior art, so that the analysis result inevitably has deviation.
Disclosure of Invention
The invention aims to overcome the defects in the prior art and provides a finite element-based road surface structure multi-physical-field coupling numerical simulation method, which utilizes meteorological data to establish a road surface structure transient temperature field and a hydraulic field and applies vehicle moving load to realize the multi-physical-field coupling numerical simulation of the road surface structure so as to more accurately analyze the road performance of the road surface structure and provide guidance for selecting road surface materials and structures.
The invention adopts the following technical scheme for solving the technical problems:
the invention relates to a finite element-based road surface structure multi-physical field coupling numerical simulation method which is characterized by being carried out in multi-physical field coupling finite element software according to the following steps:
step 1: defining mechanical parameters, thermodynamic parameters and hydraulic parameters of the road material;
the mechanical parameters comprise Young modulus, poisson's ratio and density, and for the viscoelastic material, the mechanical parameters also comprise viscoelastic parameters;
the thermodynamic parameters include thermal conductivity, specific heat capacity, and thermal expansion coefficient;
the hydraulic parameters include hydraulic conductivity, porosity, and Biot elasticity parameters;
step 2: defining a vehicle load function, and defining a meteorological function based on local meteorological data;
the vehicle load function F (t) is characterized by equation (1), the vehicle load includes a static load and a dynamic load, the dynamic load is a half-sinusoidal load:
in the formula (1), A is the load amplitude, t is the time, t 0 The load acting duration in a single period is shown, T is the time interval between two adjacent loads, k =0,1,2 \ 8230;
the meteorological functions comprise a solar radiation daily variation function q (T) represented by an equation (2), and an atmospheric temperature daily variation function T represented by an equation (3) a And a rainfall day variation function set according to the meteorological data;
wherein:
q 0 maximum daily radiation intensity, q 0 =0.131mq, m =12/c; q is the total daily solar radiation; c is the actual sunshine duration; omega is angular frequency;
is the daily average air temperature->
T m The change range of the daily air temperature is,
the highest temperature of the day is selected>
The daily lowest temperature; t is 0 Is an initial phase;
and step 3: adding a solid mechanical module, specifying the material properties of each structural layer aiming at the solid mechanical module, and adding boundary conditions;
the governing equation of the solid mechanics module is characterized by equation (4):
wherein:
s is total stress, F is external force vector, rho s Is the solid material density, u is the displacement vector, S is the divergence of S,
is the second time derivative of the displacement vector;
the specifying material properties of the structural layers includes: appointing each structural layer road material to be an elastic or visco-elastic material, and setting the thermal expansion property of each structural layer road material, wherein the thermal expansion property is the thermal expansion coefficient and the strain reference temperature;
the boundary conditions include: fixed constraint that all direction displacements are 0, specified displacement that makes a certain direction displacement be 0, and boundary load;
and 4, step 4: adding a porous medium heat transfer module, specifying material properties for the porous medium heat transfer module, and defining a heat flux of a road surface;
the governing equation of the porous medium heat transfer module is characterized by equation (5):
wherein: rho l Is the density of the fluid, C p Is the constant pressure heat capacity of fluid (rho) l C p ) eff For effective volumetric constant pressure heat capacity, T tem Is the temperature of the liquid to be treated,
as first time derivative of temperature, u l Is the fluid velocity field, # T tem For temperature gradient, q is the conducted heat flux, q = -k eff ▽T tem ，k eff Is the effective coefficient of thermal conductivity,. Q is the divergence of Q, Q h Is a heat source;
the specified material properties refer to imparting the thermodynamic parameters defined in step 1 into the material;
the step 2 of defining the heat flux of the road surface is to add a heat flux interface in the porous medium heat transfer module and input a solar radiation daily variation function q (T) and an atmospheric temperature daily variation function T defined in the step a Wherein the heat flux type of the solar radiation daily variation function q (T) is generalized inward heat flux, and the atmospheric temperature daily variation function T a The type of heat flux of (1) is convective heat flux, which is a function of the daily variation of the atmospheric temperature T a The associated convective heat flux defines the heat transfer coefficient h c ：h c ＝3.7v w +9.4，v w Is the wind speed;
and 5: adding a Darcy law module, specifying material properties aiming at the Darcy law module, and adding boundary conditions;
the control equation of the Darcy's law module is characterized by equation (6):
in the formula (6), S p To store coefficients, p l In order to obtain the pore water pressure,
is p l First time derivative of ∑ ρ l Is rho l K is the hydraulic conductivity, g is the acceleration of gravity,. V.p l Is the fluid pressure gradient, [ D ] unit vector in the direction of gravity, Q m Is a quality source item;
the specified material properties refer to the hydraulic conductivity and porosity in the hydraulic parameters defined in the step 1 are endowed to the material;
the boundary conditions include pore water pressure and normal rainwater inflow speed on the boundary;
step 6: adding a multi-physical-field coupling module, and inputting Biot elastic parameters into the multi-physical-field coupling module;
the governing equation of the multi-physics coupling module is characterized by equation (7):
wherein: alpha is alpha B Is the Biot-Willis coefficient, I is the identity matrix, ε vol In order to be a volume strain,
is epsilon vol First time derivative of (S- α + B p l I) Is S-alpha B p l Divergence of I · (ρ) l u l ) Is rho l u l Divergence of (d);
and 7: calculating and post-processing analysis
The calculation refers to dividing finite element grids aiming at the constructed pavement structure body, and performing coupling solution on control equations of all modules by using a finite element method;
the post-processing analysis comprises stress field analysis, displacement field analysis, temperature field analysis and pore water pressure field analysis of the pavement structure, and a stress cloud picture, a displacement cloud picture, a temperature cloud picture, a pore water pressure cloud picture and the like are obtained, so that the multi-physical field coupling analysis of the pavement structure is completed.
Compared with the prior art, the invention has the beneficial effects that:
1. the method couples the pavement structure with the stress field, the temperature field and the hydraulic field, and realizes multi-field coupling numerical simulation of the pavement structure, so that the pavement performance of the pavement structure is accurately analyzed, and the method has good guiding significance for selection of pavement materials and structures;
2. the influence of a temperature field on the pavement structure is considered, the temperature stress is introduced, and the method has good guiding significance for researching the performances of the pavement structure, such as track resistance and the like;
3. the influence of a hydraulic field on the pavement structure is considered, so that the influence of the pore water pressure on the asphalt peeling degree can be analyzed;
4. the method for analyzing the pavement structure based on the finite elements enriches the application of the finite elements in the field of road engineering.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a model of a parameterized roadway structure in an embodiment of the present invention;
FIG. 3 is a graph of temperature versus time at the midpoint of the load region for the results of the calculations in an embodiment of the present invention;
FIG. 4 is a graph of vertical displacement at the midpoint of the load region as a function of time for the results of the calculations in an embodiment of the present invention;
fig. 5 is a graph of pore water pressure at the midpoint of the load region as a function of time, calculated in an example of the invention.
Reference numbers in the figures: 1 surface layer, 2 base layer, 3 cushion layer and 4 soil base;
Detailed Description
Referring to fig. 1, the method for simulating the multi-physical-field coupling numerical value of the road surface structure based on the finite elements in the embodiment is performed in the multi-physical-field coupling finite element software according to the following steps:
step 1: defining mechanical, thermodynamic and hydraulic parameters of the road material: the mechanical parameters comprise Young modulus, poisson's ratio and density, and for the viscoelastic material, the viscoelastic parameters are also included; the thermodynamic parameters include thermal conductivity, specific heat capacity, and thermal expansion coefficient; the hydraulic parameters include hydraulic conductivity, porosity and Biot elasticity parameters. In addition, a variable α is defined T ，α T For describing the relationship between relaxation time and temperature, a displacement factor of time-temperature equivalent principle can be defined by adopting the form of WLF equation: log (log) 10 α T ＝c 1 T 2 +c 2 T+c 3 Wherein c is 1 、c 2 And c 3 Respectively, are constants, and T is the temperature of the surface layer. The parameters and variables are shown in Table 2.
And 2, step: defining a vehicle load function, and defining a meteorological function based on local meteorological data:
the vehicle load function F (t) is characterized by equation (1), the vehicle load includes a static load and a dynamic load, and the dynamic load may be a half-sine load:
in the formula (1), A is the load amplitude, t is the time, t 0 The load acting duration in a single period is shown, T is the time interval between two adjacent loads, k =0,1,2 \ 8230, and k is a non-negative integer.
The meteorological functions comprise a solar radiation daily variation function q (T) represented by an equation (2), and an atmospheric temperature daily variation function T represented by an equation (3) a And a rainfall day variation function set according to the meteorological data;
wherein:
q 0 maximum daily radiation intensity, q 0 =0.131mq, m =12/c; q is the total daily solar radiation; c is the actual sunshine duration; omega is angular frequency;
is the daily average air temperature>
T m For the magnitude of the change in the daily air temperature, in combination with>
The highest temperature of the day is selected>
The daily minimum temperature; t is 0 Is the initial phase.
Because the road surface has limited solar radiation absorbing capacity, the solar radiation daily variation function q (t) needs to be multiplied by a reduction coefficient, and the reduction coefficient is generally taken as 0.85; initial phase T in formula (3) 0 And may be 9, such that equation (3) is calculated from the beginning of the morning hours, consistent with the time of day start, for ease of understanding.
And step 3: adding a solid mechanics module, specifying material properties of each structural layer for the solid mechanics module, and adding boundary conditions:
the governing equation of the solid mechanics module is characterized by equation (4):
wherein:
s is total stress, F is external force vector, rho s Is the solid material density, u is the displacement vector, S is the divergence of S,
the second time derivative of the displacement vector.
Specifying material properties for each structural layer includes: newly building a viscoelastic interface in the surface layer, selecting a generalized Maxwell model, inputting Young modulus and relaxation time, namely, designating the surface layer as a viscoelastic material, and simultaneously, all the other layers are made of elastic materials; a thermal expansion interface is newly built in each layer, the temperature, the thermal expansion coefficient and the strain reference temperature are input, and the initial temperature of the pavement structure is generally taken as the strain reference temperature.
The boundary conditions include: setting the bottom surface to a fixed constraint that the displacement in each direction is 0, setting the right side surface to a specified displacement that the displacement in the x direction is 0, setting the front and rear surfaces to a specified displacement that the displacement in the y direction is 0, and setting a boundary load in the loading region, it is also possible to add a symmetric boundary condition on the left side surface for simplification of the calculation.
And 4, step 4: adding a porous media heat transfer module, specifying material properties for the porous media heat transfer module, and defining a heat flux for a road surface:
the governing equation of the porous medium heat transfer module is characterized by equation (5):
wherein: ρ is a unit of a gradient l Is the density of the fluid, C p Is constant pressure heat capacity of fluid (rho) l C p ) eff For effective volumetric constant pressure heat capacity, T tem It is the temperature that is set for the purpose,
as first time derivative of temperature, u l Is the fluid velocity field, # T tem Is temperature gradient, q is conduction heat flux, q = -k eff ▽T tem ，k eff Is the effective coefficient of thermal conductivity, and Q is the divergence of Q, Q h Is a heat source.
Specifying a material property refers to imparting a thermodynamic parameter defined in step 1 into the material.
Defining the heat flux of the road surface means adding a heat flux interface in the porous medium heat transfer module and inputting the solar radiation daily change function q (T) and the atmospheric temperature daily change function T defined in the step 2 a Wherein the heat flux type of the solar radiation daily variation function q (T) is generalized inward heat flux and the atmospheric temperature daily variation function T a The type of heat flux of (1) is convective heat flux, which is a function of the daily variation of the atmospheric temperature T a The heat transfer coefficient h is defined by the related convection heat flux c ：h c ＝3.7v w +9.4，v w Is the wind speed.
Generalized inward heat flux and atmospheric temperature daily variation function T to which solar radiation daily variation function q (T) belongs a The convection heat flux is defined on the top surface of the pavement structure, and a symmetrical boundary condition can be added on the left side surface for simplifying calculation.
And 5: adding a Darcy law module, specifying material properties for the Darcy law module, and adding boundary conditions:
the governing equation of the Darcy's law module is characterized by equation (6):
in the formula (6), S p To store coefficients, p l In order to obtain the pore water pressure,
is p l First time derivative of ∑ ρ l Is rho l K is the hydraulic conductivity, g is the acceleration of gravity,. V.p l Is the fluid pressure gradient, [ D ] unit vector in the direction of gravity, Q m Are quality source terms.
Specifying material properties means imparting hydraulic conductivity and porosity in the hydraulic parameters defined in step 1 into the material.
The boundary conditions include pore water pressure and normal rainwater inflow velocity at the boundary. Where pore water pressure is defined on the right flank, the function p can be taken l (ii) = -15 × (Z + 2), Z being the structure depth, i.e. pore water pressure varies linearly with depth; the normal inflow speed of rainwater is the daily variation function of rainfall defined in step 2, and is defined on the top surface.
And 6: adding a multi-physical field coupling module, and inputting Biot elastic parameters into the multi-physical field coupling module:
the governing equation of the multi-physics coupling module is characterized by equation (7):
wherein: alpha is alpha B Is the Biot-Willis coefficient, I is the identity matrix, ε vol In order to be a volume strain,
is epsilon vol Is v (S- α) B p l I) Is S-alpha B p l Divergence of I · (ρ) l u l ) Is rho l u l Divergence of (d).
And 7: calculating and post-processing analysis
The calculation refers to dividing finite element grids aiming at the constructed pavement structure body, and performing coupling solution on control equations of all modules by using a finite element method; the post-processing analysis comprises the steps of carrying out stress field analysis, displacement field analysis, temperature field analysis and pore water pressure field analysis on the pavement structure to obtain a stress cloud picture, a displacement cloud picture, a temperature cloud picture, a pore water pressure cloud picture and the like, so that the multi-physical field coupling analysis of the pavement structure is completed.
And (3) simulation process:
step 1: the pavement structure geometry shown in table 1 was set:
TABLE 1 geometric dimensions (m)
The construction of the geometric model of the pavement structure is shown in fig. 2 and comprises the following steps from top to bottom: surface course 1, basic unit 2, bed course 3 and soil base 4.
Step 2: the mechanical, thermodynamic and hydraulic parameters defining each layer are shown in table 2:
TABLE 2 mechanical, thermodynamic and hydrodynamic parameters
(continuation table 2)
Defining a vehicle load function in multi-physics coupling finite element software according to the method, defining a meteorological function based on local meteorological data, adding a solid mechanics module, applying load and setting boundary conditions, adding a porous medium heat transfer module, adding a Darcy law module and adding the Darcy law module; a multi-physical-field coupling module is added, multi-physical fields are coupled, and through calculation and post-processing analysis, a change graph of the calculation result in the load region midpoint along with time in the embodiment shown in fig. 3, a change graph of the calculation result in the load region midpoint along with time in the embodiment shown in fig. 4, and a change graph of the calculation result in the load region midpoint along with time in the embodiment shown in fig. 5 are obtained, so that more data can be obtained according to demand analysis.
Fig. 3 shows that the road-surface temperature gradually decreases between 0 and 6 in the morning under the dual effect of the solar radiation and the heat exchange of the atmospheric temperature, because the solar radiation is almost 0 during this period and the air temperature is low; the road surface temperature gradually increases between 6 o 'clock and 12 o' clock due to the solar radiation and the increase of the air temperature.
Figure 4 shows that under vehicle load the vertical displacement at the midpoint of the load area increases gradually, reaching 0.17mm when the load reaches a peak.
FIG. 5 shows that under vehicle loading, when the load peaks, the pore water pressure rises to 223kPa; after unloading, the pore water pressure reached-50 kPa. It is this pumping action that causes a strong impact on the asphalt mixture, causing the asphalt to strip from the aggregate.
Claims (1)
1. A road surface structure multi-physical field coupling numerical simulation method based on finite elements is characterized in that the simulation method is carried out in multi-physical field coupling finite element software according to the following steps:
step 1: defining mechanical parameters, thermodynamic parameters and hydraulic parameters of the road material;
the mechanical parameters comprise Young modulus, poisson's ratio and density, and for the viscoelastic material, the mechanical parameters also comprise viscoelastic parameters;
the thermodynamic parameters include thermal conductivity, specific heat capacity and thermal expansion coefficient;
the hydraulic parameters include hydraulic conductivity, porosity, and Biot elasticity parameters;
step 2: defining a vehicle load function, and defining a meteorological function based on local meteorological data;
the vehicle load function F (t) is characterized by equation (1), the vehicle load includes a static load and a dynamic load, the dynamic load is a half-sinusoidal load:
in the formula (1), A is the load amplitude, t is the time, t 0 The load acting duration in a single period is shown, T is the time interval between two adjacent loads, k =0,1,2 \ 8230;
the meteorological functions comprise a solar radiation daily variation function q (T) represented by an equation (2), and an atmospheric temperature daily variation function T represented by an equation (3) a And a rainfall day variation function set according to the meteorological data;
wherein:
q 0 maximum daily radiation intensity, q 0 =0.131mq, m =12/c; q is the total daily solar radiation; c is the actual sunshine duration; omega is angular frequency;
is the average daily air temperature of the air,
T m the change range of the daily air temperature is,
the temperature is the highest temperature of the day,
the daily minimum temperature; t is 0 Is an initial phase;
and step 3: adding a solid mechanical module, specifying the material properties of each structural layer aiming at the solid mechanical module, and adding boundary conditions;
the governing equation of the solid mechanics module is characterized by equation (4):
wherein:
s is total stress, F is external force vector, rho s Is the density of the solid material, u is the displacement vector,
is the divergence of the S and is,
is the second time derivative of the displacement vector;
the specifying material properties of the structural layers includes: appointing each structural layer road material to be an elastic or visco-elastic material, and setting the thermal expansion property of each structural layer road material, wherein the thermal expansion property is the thermal expansion coefficient and the strain reference temperature;
the boundary conditions include: fixed constraint that all direction displacements are 0, specified displacement that makes a certain direction displacement be 0, and boundary load;
and 4, step 4: adding a porous medium heat transfer module, specifying material properties for the porous medium heat transfer module, and defining a heat flux of a road surface;
the control equation of the porous medium heat transfer module is characterized by equation (5):
wherein: rho l Is the density of the fluid, C p Is constant pressure heat capacity of fluid (rho) l C p ) eff For effective volumetric constant pressure heat capacity, T tem Is the temperature of the liquid to be treated,
as first time derivative of temperature, u l In order to be a field of fluid velocity,
for temperature gradients, q is the conducted heat flux,
k eff in order to be an effective thermal conductivity coefficient,
is the divergence of Q, Q h Is a heat source;
the specified material properties refer to imparting thermodynamic parameters defined in step 1 into the material;
the step 2 of defining the heat flux of the road surface is to add a heat flux interface in the porous medium heat transfer module and input a solar radiation daily variation function q (T) and an atmospheric temperature daily variation function T defined in the step a Wherein the heat flux type of the solar radiation daily variation function q (T) is generalized inward heat flux, and the atmospheric temperature daily variation function T a The type of heat flux of (1) is convective heat flux, which is a function of the daily variation of the atmospheric temperature T a The associated convective heat flux defines the heat transfer coefficient h c ：h c ＝3.7v w +9.4，v w Is the wind speed;
and 5: adding a Darcy law module, specifying material properties aiming at the Darcy law module, and adding boundary conditions;
the control equation of the Darcy's law module is characterized by equation (6):
in the formula (6), S p To store coefficients, p l In order to obtain the pore water pressure,
is p l The first time derivative of (a) is,
is rho l The divergence of (A), K is the hydraulic conductivity, g is the acceleration of gravity,
in order to be a pressure gradient of the fluid,
unit vector in the direction of gravity, Q m Is a quality source item;
the specified material properties refer to the hydraulic conductivity and porosity in the hydraulic parameters defined in step 1 are imparted into the material;
the boundary conditions include pore water pressure and normal rainwater inflow speed on the boundary;
step 6: adding a multi-physical-field coupling module, and inputting Biot elastic parameters into the multi-physical-field coupling module;
the governing equation of the multi-physical field coupling module is characterized by equation (7):
wherein: alpha is alpha B Is the Biot-Willis coefficient, I is the identity matrix, ε vol In order to be a volume strain,
is epsilon vol The first time derivative of (a) is,
is S-alpha B p l The divergence of the beam of I is determined,
is rho l u l Divergence of (d);
and 7: calculating and post-processing analysis
The calculation refers to dividing finite element grids aiming at the constructed pavement structure body, and performing coupling solution on control equations of all modules by using a finite element method;
the post-processing analysis comprises stress field analysis, displacement field analysis, temperature field analysis and pore water pressure field analysis of the pavement structure, and a stress cloud picture, a displacement cloud picture, a temperature cloud picture, a pore water pressure cloud picture and the like are obtained, so that the multi-physical field coupling analysis of the pavement structure is completed.
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| 基于无网格法的沥青路面三维瞬态温度场和车辆荷载耦合;姚莉莉等;《公路交通科技》;20111115(第11期);全文 * |
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