CN113849991A - Roadbed top surface equivalent resilience modulus determination method considering roadbed soil viscoelasticity and wet-force coupling - Google Patents
Roadbed top surface equivalent resilience modulus determination method considering roadbed soil viscoelasticity and wet-force coupling Download PDFInfo
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Abstract
The invention discloses a method for determining equivalent resilience modulus of a roadbed top surface by considering the viscoelastic property and the wet-force coupling of roadbed soil, which specifically comprises the following steps: establishing a two-dimensional finite element model of the pavement structure through numerical software; determining basic parameters in a solid mechanics module of numerical software, and determining boundary conditions; defining the driving dynamic load as a weak form partial differential equation and endowing the driving dynamic load with an initial value; inputting dynamic resilience modulus and viscous coefficient equations of the roadbed related to compactness, humidity and pressure; completing finite element calculation, and acquiring the change relation of the deflection of the top surface of the roadbed at the intersection position of the roadbed surface and the load central line along with the loading time, wherein the peak value is the maximum deflection of the top surface of the roadbed under the action of dynamic load; and establishing an elastic half-space estimation model, and obtaining the corresponding dynamic resilience modulus, namely the equivalent resilience modulus of the top surface of the roadbed. The method is closer to the real situation of the roadbed, improves the accuracy of predicting the performance of the active roadbed, provides reliable basis for road maintenance decision, and has simple and reliable determination process.
Description
Technical Field
The invention belongs to the technical field of road engineering, and relates to a method for determining equivalent resilience modulus of a roadbed top surface by considering the viscoelastic property of roadbed soil and wet-force coupling.
Background
The roadbed structure bears the traffic dynamic load effect transmitted by the road surface, the dynamic load that the roadbed soil received under different depths is different in size, and the different dynamic load size is different to the resilience modulus influence degree of roadbed soil. Under the action of the moving load, the action time of the moving load in the roadbed is different, and the resilience modulus of the roadbed soil is different under different loading time. Meanwhile, the different overburden pressures borne by the roadbed soil at different depths lead to different magnitudes of the confined pressure, and the different confined pressures also influence the modulus of resilience of the roadbed soil. The roadbed structure also bears the influence of complex environmental factors, under the environmental action, the water content in the roadbed changes along with time, and in the operation period, the roadbed is humidified gradually. Therefore, the vertical dynamic load, the dynamic load loading time, the confining pressure state and the humidity of each point in the roadbed are different, so that the resilience modulus of each point in the roadbed is different, the resilience modulus can influence the propagation of the dynamic load, the dynamic load adversely influences the distribution of the resilience modulus, and the modulus-stress-humidity mutual coupling relation exists in the roadbed.
The resilience modulus of the roadbed soil can only represent the resilience modulus value of a certain point of the top surface of the roadbed, and the equivalent resilience modulus of the top surface of the roadbed is the equivalent value of the resilience modulus of the roadbed structure; at present, the research on the equivalent resilience modulus of the roadbed top surface considering the viscoelastic property of roadbed soil and the wet-force coupling under the action of the dynamic load of a traveling crane is rare, the determination on the equivalent resilience modulus of the roadbed top surface is inaccurate, and preventive measures are not taken timely, so that the problems of the wetting deformation of a roadbed structure and the shortening of the service life are caused.
Disclosure of Invention
In order to solve the problems, the invention provides a method for determining the equivalent resilience modulus of the top surface of the roadbed by considering the viscoelastic property of the roadbed soil and the wet-force coupling, which is closer to the real situation of the roadbed, improves the accuracy of the prediction of the performance of the active roadbed, provides a reliable basis for road maintenance decision, has a simple and reliable determination process and solves the problems in the prior art.
The invention adopts the technical scheme that a method for determining the equivalent resilience modulus of the top surface of the roadbed by considering the viscoelastic property and the wet-force coupling of the roadbed soil is specifically carried out according to the following steps:
step S1: establishing a two-dimensional finite element model of the pavement structure through numerical software;
step S2: determining basic parameters in a solid mechanics module of numerical software, wherein the basic parameters are Young modulus, Poisson ratio, density, boundary load and viscosity; wherein, the surface layer and the foundation are taken as linear elastic bodies, and the corresponding Young modulus, Poisson ratio and density are input; the roadbed is regarded as a viscoelastic body related to compactness, stress and humidity;
determining boundary conditions, setting the y-direction displacement as 0 on the boundary of the bottom of the roadbed, setting the x-direction displacement as 0 on the boundaries of the left side and the right side, and simulating the moving load, wherein the boundary load is the moving load of the vehicle under the action of front and rear double shafts;
step S3: defining the driving dynamic load as a weak form partial differential equation and endowing the driving dynamic load with an initial value;
step S4: inputting dynamic resilience modulus and viscous coefficient equations of the roadbed related to compactness, humidity and pressure;
step S5: running finite element software to complete finite element calculation, and acquiring the change relation of the deflection of the top surface of the roadbed at the intersection position of the roadbed surface and the load central line along with the loading time, wherein the peak value is the maximum deflection of the top surface of the roadbed under the action of dynamic load;
step S6: and (4) establishing an elastic half-space estimation model, obtaining the maximum deflection of the top surface of the roadbed under different dynamic resilience moduli of the roadbed soil by adopting the same roadbed pavement structure model and the same dynamic load loading mode, and according to a deflection equivalence principle, enabling the calculation result of the elastic half-space numerical value to be equal to the maximum deflection of the top surface of the roadbed obtained in the step S5, wherein the corresponding dynamic resilience modulus is the equivalent resilience modulus of the top surface of the roadbed.
Further, in the step S3, the running load, i.e., the boundary load FA-LoadIntensity (Pulse (x-LoadSpeed t) + Pulse (x +2.7-LoadSpeed t)), where LoadIntensity is numerically equal to the load amplitude; LoadSpeed is numerically equal to the vehicle speed; pulse is a square wave function; x represents a position coordinate of a traveling direction; along with the increase of the time t, the load acting area is changed continuously, and the moving load is simulated.
Further, the step S4 is specifically performed according to the following steps:
step S41: establishing a dynamic resilience modulus and a viscosity coefficient equation related to compactness, humidity and pressure, see formulas (1) to (3);
wherein: mRTThe dynamic resilience modulus under the loading duration T; ω is the circle frequency, ω 2 π/T; t is loading duration; e is Young's modulus; eta is viscosity coefficient; k is the degree of compaction; w is the water content; w is aoptThe water content is optimal; thetamFor minimum body stress, τcotIs octahedral shear stress, paAtmospheric pressure, a is reference viscosity; k is a radical of0～k4、α1～α4Is a model parameter; fitting the formulas (1) to (3) according to the dynamic triaxial test result to obtain a model parameter k0～k4、α1～α4；
Step S42: creating a new physical field v in the weak form partial differential equation module of COMSOL Multiphysics numerical software, wherein the independent variable of the physical field v is v1, and v1 is numerically equal to the octahedral shear stress taucot；
Step S43: setting the Young modulus of the roadbed as a function related to compactness, stress and humidity, and recording the function as Ez, wherein the expression of Ez corresponds to the formula (2); the viscosity coefficient of the roadbed is a function related to compactness, stress and humidity, and is recorded as nz, and the expression of the nz corresponds to the formula (3).
Further, in step S42, v1 ═ v1-sqrt (abs (solid.ii2s) × 2/3)) × test (v 1);
wherein test () represents a trial function, solid. II2s is a stress offset second invariant,
σ1to overburden stress, σ2Is equal to sigma3，σ3Is confining pressure; test () and solid. II2s are both predefined variables in COMSOL Multiphysics.
Further, in the step S43,
Ez＝k0*Pa*(K1/100)^k1*(W/W0)^k2*(P2/Pa+eps)^k3*(abs(v1)/Pa+1)^k4，
wherein k0, k1, k2, k3 and k4 are model parameters and are respectively equal to the model parameter k in the formula (2) in terms of value0～k4(ii) a Pa is numerically equal to atmospheric pressure, K1 represents the compaction of the different horizons, W is numerically equal to the moisture content W, W0 is numerically equal to the optimal moisture content WoptP2 is numerically equal to the minimum body stress θmEps represents the minimum calculation accuracy, being a positive number close to 0; abs () represents an absolute value function;
nz＝(a0*(K1/100)^a1*(W/W0)^a2*(P2/Pa+eps)^a3*(abs(v1)/Pa+1)^a4)，
wherein a0, a1, a2, a3 and a4 are model parameters and are respectively equal to the model parameter alpha in the formula (3) in value1～α4。
Further, the minimum body stress θmIs equal to σ under no dynamic stress1+σ2+σ3Confining pressure σ3Is numerically equal to P1 × nu0/(1-nu0), nu0 is the Poisson's ratio of the roadbed soil; thus, P2 is equal to (2 × nu0/(1-nu0) +1) × P1, P1 is numerically equal to σ1P1 is the overburden pressure at each point in the subgrade, and is the wet density at each point multiplied by the vertical indeterminate integral of the gravitational acceleration, and the integral is converted to a positive value using the abs () function.
Further, K1 is numerically equal to RC1(y), and RC1(y) is a piecewise function of compaction, scaled according to the actual dry density of the horizon.
Further, W0 is a distribution function of the water content in the y direction, and is represented as W0(y), and is obtained by an actual test.
Further, in step S5, finite element software is run to complete finite element calculation, specifically, the method includes the following steps:
step S51: acquiring initial dynamic load of each node;
step S52: calculating initial values of initial dynamic resilience modulus and viscosity coefficient of each grid unit generated in finite element modeling;
step S53: applying a moving load;
step S54: updating stress field distribution of each node, and updating dynamic resilience modulus and viscous coefficient of the unit;
step S55: checking whether the finite element model is converged, if not, adjusting the dynamic resilience modulus and the viscous coefficient, and repeating the steps S53-S54; and if the finite element is converged, carrying out the next time step until the finite element calculation is completed.
Further, the error of the calculation results of the two times before and after the single time step is within 0.5% -1%, and the overall error is within 5% -10%, so that the calculation accuracy of the modulus field in the roadbed is considered to meet the requirement.
The invention has the beneficial effects that:
according to the method, the viscoelasticity and the wet-force coupling effect of the roadbed soil are considered at the same time, multiple physical fields are coupled, the equivalent resilience modulus of the top surface of the roadbed at different driving speeds is obtained through COMSOL Multiphysics, the method is closer to the real condition of the roadbed, the accuracy is higher, the realization process is simpler, the effective estimation of the stiffness of the roadbed in service under the wet and hot environment is realized, the performance prediction accuracy of the roadbed in service is improved, and a reliable basis is provided for road maintenance decisions.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a flow chart of an embodiment of the present invention.
Fig. 2 is a humidity field diagram of the subgrade.
Fig. 3 is a graph of the deflection of the top surface of the roadbed along with the change of loading time under different driving speeds.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
In the case of the example 1, the following examples are given,
a roadbed top equivalent resilience modulus determination method considering roadbed soil viscoelasticity and wet-force coupling specifically comprises the following steps:
step S1: establishing a two-dimensional finite element model of the pavement structure through COMSOL Multiphysics numerical software; the surface layer adopts 0.20m asphalt concrete, the base layer adopts 0.40m cement stabilized macadam, the subbase layer adopts 0.20m cement stabilized macadam, the roadbed adopts 7.0m road foundation soil, the foundation is 2.0m, and the pavement structure parameters are shown in table 1.
TABLE 1 road surface structural parameters
| Horizon | Structural layer material type | Thickness (m) | Modulus of restitution (MPa) | Density (g/cm)3) | Poisson ratio |
| Surface layer | Asphalt concrete | 0.20 | 11000 | 2.35 | 0.3 |
| Base layer | Cement stabilized macadam | 0.40 | 9000 | 2.10 | 0.25 |
| Sub-base layer | Cement stabilized macadam | 0.20 | 7000 | 2.10 | 0.25 |
| Road bed | Road foundation soil | 7.0 | 100 | 1.85 | 0.35 |
| Foundation | Foundation soil | 2.0 | 40 | 1.8 | 0.35 |
Step S2: determining basic parameters in a solid mechanics module of numerical software, wherein the basic parameters are Young modulus, Poisson ratio, density, boundary load and viscosity; wherein, the surface layer and the foundation are taken as linear elastic bodies, and the corresponding Young modulus, Poisson ratio and density are input; the roadbed is regarded as a viscoelastic body related to compactness, stress and humidity;
determining boundary conditions, setting the y-direction displacement as 0 on the boundary of the bottom of the roadbed, setting the x-direction displacement as 0 on the boundary of the left side and the right side, setting boundary load as the driving dynamic load with front and rear double-axis action, loading by adopting the moving load with standard axle weight, setting the axle base as 2.7m, setting the pressure of each tire as 0.7MPa, setting the acting diameter of each tire as 0.213m and setting the moving speed as 20-120 km/h.
Step S3: defining the driving dynamic load as a weak form partial differential equation and endowing the driving dynamic load with an initial value; dynamic loads of the vehicle, i.e. boundary loads FA-LoadIntensity (Pulse (x-LoadSpeed t) + Pulse (x +2.7-LoadSpeed t)), where LoadIntensity is numerically equal to the load amplitude, taking 113.6 kPa; the LoadSpeed is numerically equal to the driving speed and is selected according to the actual situation; pulse is a square wave function, the lower limit is-0.1065 m, the upper limit is 0.1065m, the minimum value of the function is 0, and the maximum value is 1; x represents a position coordinate of a traveling direction; along with the increase of the time t, the load acting area is continuously changed and is used for simulating the moving load.
Step S4: inputting dynamic resilience modulus and viscous coefficient equations of the roadbed related to compactness, humidity and pressure in COMSOL Multiphysics numerical software;
step S41: establishing a dynamic resilience modulus and a viscosity coefficient equation related to compactness, humidity and pressure, see formulas (1) to (3);
wherein: mRTIs the dynamic modulus of resilience (MPa) for a loading time period T; ω is the circle frequency, ω 2 π/T; t is loading duration(s); e is young's modulus (modulus of resilience of roadbed soil); eta is viscosity coefficient; k is the degree of compaction; w is the water content; w is aoptThe water content is optimal; thetamFor minimum body stress, τcotIs the shear stress of an octahedron,
for the three-axis test, θm＝θ-σd＝3σ3Theta is the bulk stress, sigmadTo cyclically bias stress, σ3To confining pressure, σ1、σ2、σ3Respectively, a first principal stress, a second principal stress, and a third principal stress, specifically, σ1To overburden stress, σ2Is equal to sigma3；paAt atmospheric pressure, pa101.3 kPa; a is reference viscosity, and A is 1MPa · s; k is a radical of0～k4、α1～α4Are model parameters.
In the test, the value of the resilience modulus of the roadbed soil is gradually reduced to be stable along with the increase of the loading time, the value of the resilience modulus when the resilience modulus is stable along with the change of the loading time is taken as the Young modulus E, and the resilience modulus under the loading time of 4.2s is taken as the Young modulus E in the embodiment; fitting the formulas (1) to (3) according to the dynamic triaxial test result to obtain a model parameter k0～k4、α1～α4As shown in table 2; if the viscosity coefficient is set, the obtained result is not matched with the actual roadbed condition.
TABLE 2 prediction model parameters of viscoelasticity modulus of resilience of high liquid limit silt
Step S42: in COMSOL Multiphysics valuesCreating a new physical field v in a weak form partial differential equation module of software, wherein the independent variable of the physical field v is v1, and v1 is equal to the octahedral shear stress tau in valuecot；
v1＝-(v1-sqrt(abs(solid.II2s)*2/3))*test(v1)；
Wherein test () represents a trial function, solid. II2s is a stress offset second invariant,
test () and solid.II2s are predefined variables in COMSOL Multiphysics and can be directly called;
step S43: setting the Young modulus of the roadbed as a function related to compactness, stress and humidity, and recording the function as Ez, wherein the expression of Ez corresponds to the formula (2); the viscosity coefficient of the roadbed is a function related to compactness, stress and humidity, and is recorded as nz, and the expression of the nz corresponds to the formula (3).
Ez is K0 Pa (K1/100) K1 (W/W0) K2 (P2/Pa + eps) K3 (abs (v1)/Pa +1) K4, and Ez has a unit of N/m2；
nz＝(a0*(K1/100)^a1*(W/W0)^a2*(P2/Pa+eps)^a3*(abs(v1)/Pa+1)^a4)；
Wherein k0, k1, k2, k3 and k4 are model parameters and are respectively equal to the model parameter k in the formula (2) in terms of value0～k4(ii) a a0, a1, a2, a3 and a4 are model parameters which are respectively equal to the model parameter alpha in the formula (3) in value1～α4. Pa is numerically equal to atmospheric pressure, K1 represents the compaction of the different horizons, W is numerically equal to the moisture content W, W0 is numerically equal to the optimal moisture content WoptP2 is numerically equal to the minimum body stress θm(unit Pa), eps represents the minimum calculation accuracy, and is a positive number close to 0, and the term is guaranteed to be not 0; abs () represents an absolute value function to avoid misconvergence due to negative values during the calculation.
Minimum body stress thetamIs equal to σ under no dynamic stress1+σ2+σ3Confining pressure σ3Is numerically equal to P1 × nu0/(1-nu0), nu0 is the Poisson's ratio of the roadbed soil; thus, P2 is equal to (2 × nu0/(1-nu0) +1) × P1, P1 is numerically equal to σ1The unit Pa, P1 is the overlying pressure at each point in the subgrade, and the unit Pa is the moisture density at each point multiplied by the indeterminate integral of the gravity acceleration in the vertical direction, and the integral is converted into a positive value by adopting an abs () function.
P1 abs (integral (rho1 g _ const, y, H +2+0.78, y)) is the indefinite integral of the top of the pavement in the y direction, rho1 is the total density of the material (in kg/m)3) G _ const is numerically equal to the gravitational acceleration, H is the subgrade height, integration is the integration function, rho1 g _ const is the expression of the integration function, y is the integration variable and is the upper bound, and H +2+0.78 is the lower bound.
rho1 is equal to rho0 (W +1) and rho0 is the dry density (in kg/m)3). rho0 is rho2 (K1/100), rho2 is the maximum dry density of the roadbed soil, and the value of rho2 is 1.62g/cm according to the actual requirement3。
K1 is numerically equal to RC1(y), RC1(y) is a piecewise function of compaction, scaled according to the actual dry density of the horizon, the scaling method: for example, the maximum dry density of soil is 1.6g/cm3And the actual compaction degree of the roadbed soil is 96%, the K1 is 96. The density of the pavement layer is 2.2g/cm3Then K1 takes 2.2/1.6 x 100 — 137.5.
W0 is the distribution function of water cut in the y direction, and is recorded as W0(y), and is obtained by actual test, as shown in FIG. 2.
Step S5: running finite element software to complete finite element calculation;
step S51: acquiring initial dynamic load of each node;
step S52: calculating initial values of initial dynamic resilience modulus and viscosity coefficient of each grid unit generated in finite element modeling;
step S53: applying a moving load;
step S54: updating stress field distribution of each node, and updating dynamic resilience modulus and viscous coefficient of the unit;
step S55: checking whether the finite element model is converged, if not, adjusting the dynamic resilience modulus and the viscous coefficient, and repeating the steps S53-S54; if the time is converged, carrying out the next time step length until the finite element calculation is completed; when the roadbed modulus field numerical value calculation considering the viscoelastic properties is carried out, the solving precision is set by adjusting the tolerance of a solver, the relative tolerance is 0.005-0.01, the absolute tolerance is 0.05-0.1, namely the error of the calculation result of two times before and after a single time step is within 0.5-1%, and the integral error is within 5-10%, the calculation precision of the roadbed modulus field is considered to meet the requirement.
And acquiring the change relation of the deflection of the top surface of the roadbed at the intersection position of the roadbed surface and the load central line along with the loading time, wherein the peak value is the maximum deflection of the top surface of the roadbed under the action of dynamic load as shown in figure 3.
Step S6: establishing an elastic half-space estimation model, obtaining the maximum deflection of the top surface of the roadbed under different dynamic resilience moduli of the roadbed soil by adopting the same roadbed pavement structure model and the same dynamic load loading mode, and according to a deflection equivalence principle, enabling the calculation result of the elastic half-space numerical value to be equal to the maximum deflection of the top surface of the roadbed obtained in the step S5, wherein the corresponding dynamic resilience modulus is the equivalent resilience modulus of the top surface of the roadbed, and the equivalent resilience modulus of the top surface of the roadbed obtained in the embodiment of the invention is shown in Table 3.
TABLE 3 equivalent modulus of restitution of the subgrade top surface
The data from table 3 can show that the equivalent modulus of resilience of the roadbed top surface of different driving speeds is different, can reflect the difference of equivalent modulus of resilience of the roadbed top surface under the different driving speeds, can more reflect the actual conditions, and the modulus of the roadbed can be more accurately determined, so that when the pavement structure is designed, the stress and strain distribution in the roadbed can be more accurately obtained, and further the actual service life of the pavement can be more accurately obtained, the design is more accurate, and the practical application value is important.
The above description is only for the preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention shall fall within the protection scope of the present invention.
Claims (10)
1. A roadbed top equivalent resilience modulus determination method considering roadbed soil viscoelasticity and wet-force coupling is characterized by comprising the following steps:
step S1: establishing a two-dimensional finite element model of the pavement structure through numerical software;
step S2: determining basic parameters in a solid mechanics module of numerical software, wherein the basic parameters are Young modulus, Poisson ratio, density, boundary load and viscosity; wherein, the surface layer and the foundation are taken as linear elastic bodies, and the corresponding Young modulus, Poisson ratio and density are input; the roadbed is regarded as a viscoelastic body related to compactness, stress and humidity;
determining boundary conditions, setting the y-direction displacement as 0 on the boundary of the bottom of the roadbed, setting the x-direction displacement as 0 on the boundaries of the left side and the right side, and simulating the moving load, wherein the boundary load is the moving load of the vehicle under the action of front and rear double shafts;
step S3: defining the driving dynamic load as a weak form partial differential equation and endowing the driving dynamic load with an initial value;
step S4: inputting dynamic resilience modulus and viscous coefficient equations of the roadbed related to compactness, humidity and pressure;
step S5: running finite element software to complete finite element calculation, and acquiring the change relation of the deflection of the top surface of the roadbed at the intersection position of the roadbed surface and the load central line along with the loading time, wherein the peak value is the maximum deflection of the top surface of the roadbed under the action of dynamic load;
step S6: and (4) establishing an elastic half-space estimation model, obtaining the maximum deflection of the top surface of the roadbed under different dynamic resilience moduli of the roadbed soil by adopting the same roadbed pavement structure model and the same dynamic load loading mode, and according to a deflection equivalence principle, enabling the calculation result of the elastic half-space numerical value to be equal to the maximum deflection of the top surface of the roadbed obtained in the step S5, wherein the corresponding dynamic resilience modulus is the equivalent resilience modulus of the top surface of the roadbed.
2. The method for determining the equivalent resilience modulus of the topsides of the roadbed according to claim 1, wherein the viscoelastic properties and the wet-force coupling of the roadbed soil are taken into consideration, and in the step S3, the traveling crane dynamic load is appliedLoads, i.e. boundary loads FA-LoadIntensity (Pulse (x-LoadSpeed t) + Pulse (x +2.7-LoadSpeed t)), where LoadIntensity is numerically equal to the load amplitude; LoadSpeed is numerically equal to the vehicle speed; pulse is a square wave function; x represents a position coordinate of a traveling direction; along with the increase of the time t, the load acting area is changed continuously, and the moving load is simulated.
3. The method for determining the equivalent resilience modulus of the topsides of the roadbed according to claim 1, wherein the step S4 is performed according to the following steps:
step S41: establishing a dynamic resilience modulus and a viscosity coefficient equation related to compactness, humidity and pressure, see formulas (1) to (3);
wherein: mRTThe dynamic resilience modulus under the loading duration T; ω is the circle frequency, ω 2 π/T; t is loading duration; e is Young's modulus; eta is viscosity coefficient; k is the degree of compaction; w is the water content; w is aoptThe water content is optimal; thetamFor minimum body stress, τcotIs octahedral shear stress, paAtmospheric pressure, a is reference viscosity; k is a radical of0～k4、α1～α4Is a model parameter; fitting the formulas (1) to (3) according to the dynamic triaxial test result to obtain a model parameter k0～k4、α1～α4；
Step S42: in COMSOL MultA new physical field v is created in a weak form partial differential equation module of iphysics numerical software, the independent variable of the physical field v is v1, and v1 is equal to the octahedral shear stress tau in valuecot；
Step S43: setting the Young modulus of the roadbed as a function related to compactness, stress and humidity, and recording the function as Ez, wherein the expression of Ez corresponds to the formula (2); the viscosity coefficient of the roadbed is a function related to compactness, stress and humidity, and is recorded as nz, and the expression of the nz corresponds to the formula (3).
4. The method for determining the equivalent rebound modulus of the subgrade top surface in consideration of the viscoelastic properties and the wet-force coupling of the subgrade soil according to the claim 3, wherein in the step S42, v1 is- (v1-sqrt (abs (solid. II2s) 2/3))) test (v 1);
wherein test () represents a trial function, solid. II2s is a stress offset second invariant,
σ1to overburden stress, σ2Is equal to sigma3，σ3Is confining pressure; test () and solid. II2s are both predefined variables in COMSOL Multiphysics.
5. The method for determining equivalent resilience modulus of subgrade top surface according to claim 4, which takes account of the viscoelastic properties of subgrade soil and wet-force coupling, wherein in step S43,
Ez＝k0*Pa*(K1/100)^k1*(W/W0)^k2*(P2/Pa+eps)^k3*(abs(v1)/Pa+1)^k4，
wherein k0, k1, k2, k3 and k4 are model parameters and are respectively equal to the model parameter k in the formula (2) in terms of value0～k4(ii) a Pa is numerically equal to atmospheric pressure, K1 represents the compaction of the different horizons, W is numerically equal to the moisture content W, W0 is numerically equal to the optimal moisture content WoptP2 is numerically equal to the minimum body stress θmEps represents the minimum calculation accuracy, being a positive number close to 0; abs () represents an absolute value function;
nz＝(a0*(K1/100)^a1*(W/W0)^a2*(P2/Pa+eps)^a3*(abs(v1)/Pa+1)^a4)，
wherein a0, a1, a2, a3 and a4 are model parameters and are respectively equal to the model parameter alpha in the formula (3) in value1～α4。
6. The method of claim 5, wherein the minimum body stress θ is determined by considering viscoelastic properties of roadbed soil and wet-force coupling equivalent resilience modulusmIs equal to σ under no dynamic stress1+σ2+σ3Confining pressure σ3Is numerically equal to P1 × nu0/(1-nu0), nu0 is the Poisson's ratio of the roadbed soil; thus, P2 is equal to (2 × nu0/(1-nu0) +1) × P1, P1 is numerically equal to σ1P1 is the overburden pressure at each point in the subgrade, and is the wet density at each point multiplied by the vertical indeterminate integral of the gravitational acceleration, and the integral is converted to a positive value using the abs () function.
7. The method of claim 5, wherein K1 is numerically equal to RC1(y), and RC1(y) is a piecewise function of compaction, scaled according to the actual dry density of the horizon.
8. The method for determining the equivalent resilience modulus of the topsides of the roadbed according to claim 5, wherein W0 is a distribution function of the water content in the y direction, is recorded as W0(y), and is obtained through practical tests.
9. The method for determining the equivalent resilience modulus of the top surface of the roadbed considering the viscoelastic property and the wet-force coupling of the roadbed soil as claimed in claim 1, wherein the step S5 is executed with finite element software to complete finite element calculation, and the method is specifically performed according to the following steps:
step S51: acquiring initial dynamic load of each node;
step S52: calculating initial values of initial dynamic resilience modulus and viscosity coefficient of each grid unit generated in finite element modeling;
step S53: applying a moving load;
step S54: updating stress field distribution of each node, and updating dynamic resilience modulus and viscous coefficient of the unit;
step S55: checking whether the finite element model is converged, if not, adjusting the dynamic resilience modulus and the viscous coefficient, and repeating the steps S53-S54; and if the finite element is converged, carrying out the next time step until the finite element calculation is completed.
10. The method for determining the equivalent resilience modulus of the top surface of the roadbed considering the viscoelastic property and the wet-force coupling of the roadbed soil as claimed in claim 9, wherein the calculation result error of the two times before and after the single time step is within 0.5-1%, and the overall error is within 5-10%, and the calculation accuracy of the modulus field in the roadbed is considered to meet the requirement.
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