Calculation method for permanent deformation of subgrade structure based on subgrade soil viscoelastic-plastic mechanics model

Abstract

The application discloses a kind of based on roadbed soil viscoelastic plastic mechanics model roadbed structure permanent deformation calculation method, the calculation method includes the following steps: determining cycle loading times N, state variable, load characteristic, road surface property;Based on cycle loading times N, state variable, load characteristic, road surface property, using roadbed structure permanent deformation maximum value calculation formula, roadbed structure permanent deformation maximum value calculation is carried out.The fitting process of roadbed structure permanent deformation maximum value calculation formula is: determining the size of calculation condition and road finite element simulation model;Based on the viscoelastic plastic mechanics model of roadbed soil, the finite element calculation of roadbed structure permanent deformation is carried out;Based on the finite element calculation result of roadbed structure permanent deformation under different conditions, determine the influence factor of roadbed structure permanent deformation and corresponding roadbed structure permanent deformation evolution law;Based on the evolution law, the roadbed structure permanent deformation maximum value calculation formula is fitted.The calculation efficiency and accuracy are improved.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of road engineering and relates to a method for calculating permanent deformation of a subgrade structure based on a subgrade soil viscoelastic-plastic mechanics model. BACKGROUND

[0002] Traffic infrastructure develops rapidly, the demand for road transportation grows, the tonnage of passenger and freight vehicles increases, and the design and construction standards of roads are constantly improved, all of which have put strict requirements on the service level of road systems. As the foundation of the pavement, the subgrade directly bears the large number of cyclic shear actions transmitted from the upper part to produce permanent deformation. Due to the permanent deformation of the subgrade, a certain depth of void area appears between the top of the subgrade and the bottom of the pavement structure, which hinders the transmission of the driving load from the pavement structure to the subgrade, causes the bending tensile stress and bending tensile strain of each structure layer of the pavement, and further causes various diseases such as fatigue cracking of the pavement structure, which will greatly restrict the road system to play the functions of safety, comfort and durability. However, the construction of the subgrade engineering in China lacks comprehensive consideration of the permanent deformation of the subgrade in the design, construction and acceptance stages, that is, the influence of the climate conditions on the resilience modulus of the subgrade soil is considered in the form of dry-wet / frozen-thaw reduction coefficient in the design stage, and the influence is taken as the design index of the subgrade. In the construction stage, the optimum water content and compaction degree of the subgrade soil obtained by the compaction test are taken as the control index of the compaction quality of the subgrade, and the deflection value of the top surface of the subgrade is taken as the acceptance index after the filling is completed. This whole set of procedures does not involve the permanent deformation of the subgrade under long-term cyclic load. Therefore, accurately calculating the permanent deformation of the subgrade under long-term cyclic load has important scientific value and engineering significance for supplementing the technical requirements of the subgrade design specification, building durable subgrade and constructing long-life road structure technology system.

[0003] Different types of permanent deformation calculation models of subgrade soil determine the calculation method selected when calculating the permanent deformation of the subgrade structure. At present, the calculation methods for the permanent deformation of the subgrade structure are divided into two categories: numerical calculation method and layered summation method.

[0004] The basic idea of numerical calculation method is to set a certain number of incremental steps, and to analyze each loading into multiple incremental steps. The core of this method is the soil constitutive model based on classical soil mechanics, which can accurately simulate the deformation behavior of subgrade structure under cyclic loading, and can change the parameter assignment to reveal the influence law of different factors on the permanent deformation of subgrade structure. Although some studies have tried this way, the consistent fact is that a large amount of computing resources is consumed. Specifically, the calculation model established by the geometric size of the soil sample, although the number of grid elements is small, only the deformation results of several tens of loadings are obtained. It can be imagined that if the calculation model is expanded to the large size of the actual subgrade, the numerical calculation method based on the constitutive model of classical soil mechanics cannot meet the analysis needs of the permanent deformation of subgrade structure under the loading of ten thousand times. The reason is that when tracking the stress path of each cyclic loading, the constitutive model of classical soil mechanics must remember the shape of all the nested surfaces and their relative position with the initial yield surface. Once the dimension of constitutive equation and the grid element of calculation model are too much, a large amount of computing resources and iteration time is needed, the efficiency and convergence of calculation will be greatly reduced, and some parameters of constitutive model are difficult to be calibrated by test. For example, the document "Dynamic Constitutive Model of Saturated Loess and Deformation Analysis of Soil Layer around Metro Tunnel[D]. Doctoral Dissertation of Xi'an University of Architecture and Technology, 2015" once tried to calculate the permanent deformation of Xi'an subway subgrade structure according to the dynamic constitutive model of saturated loess, and the calculation was stopped passively due to computer crash and insufficient storage disk space during the calculation process.

[0005] Although numerical calculation method has made certain progress, the layered summation method is still the most commonly used method to determine the permanent deformation of subgrade structure. The basic idea of the layered summation method is to regard the subgrade as a linear elastic semi-infinite space body, to calculate the internal dynamic stress distribution level of the subgrade caused by traffic load in one time according to the elastic system theory, to divide the subgrade in the dynamic influence area into a plurality of thin layers, and to calculate the permanent deformation of each thin layer by using the pre-established mechanical-empirical prediction model and to accumulate to obtain the permanent deformation of the entire subgrade structure. However, the permanent deformation of the subgrade is the cumulative plastic deformation of the subgrade under long-term cyclic load, and it can be seen that there is an essential contradiction in the basic theory of the layered summation method that the internal stress field obtained based on the linear elastic assumption of the subgrade is used for the calculation of the plastic deformation of the subgrade. Although some scholars point out that even if the thickness of each thin layer is small, the phenomenon that the dynamic stress gradually decreases along the depth direction of the subgrade cannot be reflected, that is, the stress level of each point in each thin layer is considered to be the same in the calculation, and then the permanent deformation expression of the unit body under any small thickness in the subgrade is constructed by using the “micro-element” idea, and the permanent deformation of the entire subgrade is obtained by integrating the being-integral function along the depth of the dynamic influence area of the subgrade. Although the integral method is more reasonable in considering the nonlinear distribution of the dynamic stress in the subgrade, the essence is still the layered summation method, and there is still the contradiction that the elastic assumption is used for the calculation of the plastic deformation. In addition, the existing research analyzes the evolution law of the permanent deformation of the subgrade with different factors according to the calculation results of the layered summation method, but the setting of the influencing factors is not comprehensive, far from comprehensively considering the influence of the state variables, load characteristics and pavement properties on the permanent deformation of the subgrade, and the established prediction model of the permanent deformation of the subgrade is set by experience, and lacks reasonable logical support. SUMMARY

[0006] The embodiment of the present application aims to provide a subgrade structure permanent deformation calculation method based on a subgrade soil viscoelastic-plastic mechanics model, to solve the problems of the existing numerical calculation method for subgrade permanent deformation calculation, such as difficult to obtain parameters of the classical soil mechanics constitutive model, low calculation efficiency, large consumption of calculation resources, long calculation time, and difficult to converge, the layered summation method uses the stress distribution under the elastic assumption of the subgrade for the calculation of the plastic deformation, the basic theory has an essential contradiction, and the calculation result is inaccurate, and the prediction model of the permanent deformation of the subgrade does not comprehensively consider the factors, lacks theoretical support, and has limited engineering application significance.

[0007] The technical scheme adopted by the embodiment of the present application is: a subgrade structure permanent deformation calculation method based on a subgrade soil viscoelastic-plastic mechanics model, comprising the following steps:

[0008] Determine the number of cyclic loads N, the state variable, the load characteristic, and the pavement property;

[0009] Based on the cycle loading times N, state variables, load characteristics, pavement properties, the maximum permanent deformation of subgrade structure is calculated by the maximum permanent deformation calculation formula of subgrade structure.

[0010] Further, the state variable is the humidity of subgrade w, the load characteristics are the driving speed v and the single tire pressure M, and the pavement properties are the surface layer thickness H pave , the base layer thickness H base , and the subbase layer thickness H subb .

[0011] The maximum permanent deformation of subgrade structure is calculated by the maximum permanent deformation calculation formula of subgrade structure shown in formula (14):

[0012]

[0013] In the formula, ε pmax is the maximum permanent deformation of subgrade structure, N is the cycle loading times, OMC is the optimum moisture content, and w / OMC is the moisture degree of subgrade.

[0014] Further, the state variable is the humidity of subgrade w, the load characteristics are the driving speed v and the single tire pressure M, and the pavement properties are the surface layer thickness H pave , the base layer thickness H base , and the subbase layer thickness H subb .

[0015] The maximum permanent deformation of subgrade structure is calculated by the maximum permanent deformation calculation formula of subgrade structure shown in formula (13):

[0016] ε pmax = f(N)·f(w)·f(v)·f(M)·f(H pave )·f(H base )·f(H subb ) (13)

[0017] In the formula, ε pmax is the maximum permanent deformation of subgrade structure, f(N) is the influence function of cycle loading times, f(w) is the influence function of the humidity of subgrade w, f(v) is the influence function of the driving speed v, f(M) is the influence function of the single tire pressure M, f(H pave ) is the influence function of the surface layer thickness H pave , f(H base ) is the influence function of the base layer thickness H base , and f(H subb ) is the influence function of the subbase layer thickness H subb , which is calculated according to the following table:

[0018]

[0019] Further, the state variable is subgrade humidity w, the load characteristic is vehicle speed v and single tire pressure M, and the pavement property is surface layer material modulus E pave , base layer material modulus E base , base material modulus E subb , surface layer thickness H pave , base layer thickness H base , base thickness H subb ;

[0020] The maximum permanent deformation of the subgrade structure is calculated by using the maximum permanent deformation calculation formula of the subgrade structure shown in formula (12):

[0021] ε pmax =f(N)·f(w)·f(v)·f(M)·f(E pave )·f(E base )·f(E subb )·f(H pave )·f(H base )·f(H subb ) (12)

[0022] Wherein, ε pmax is the maximum permanent deformation of the subgrade structure, f(N) is the influence function of the number of cyclic loading, f(w) is the influence function of the subgrade humidity w, f(v) is the influence function of the vehicle speed v, f(M) is the influence function of the single tire pressure M, f(E pave ) is the influence function of the surface layer material modulus E pave , f(E base ) is the influence function of the base layer material modulus E base , f(E subb ) is the influence function of the base material modulus E subb , f(H pave ) is the influence function of the surface layer thickness H pave , f(H base ) is the influence function of the base layer thickness H base , f(H subb ) is the influence function of the base thickness H subb , and is calculated according to the following table:

[0023]

[0024] Further, the maximum permanent deformation calculation formula of the subgrade structure is fitted according to the following process:

[0025] Step S1, determine the calculation condition and the size of the road finite element simulation model;

[0026] Step S2, based on the viscoelastic-plastic mechanics model of subgrade soil, performing finite element calculation of permanent deformation of the subgrade structure;

[0027] Step S3, based on the finite element calculation results of permanent deformation of the subgrade structure under different working conditions, determining the influencing factors of permanent deformation of the subgrade structure and the corresponding evolution law of permanent deformation of the subgrade structure;

[0028] Step S4, based on the influencing factors of permanent deformation of the subgrade structure and the corresponding evolution law of permanent deformation of the subgrade structure, fitting the maximum value calculation formula of permanent deformation of the subgrade structure.

[0029] Further, in the step S1, when designing the calculation conditions:

[0030] Pavement part: adjust the thickness range of the base course to 15-40 cm, determine the material modulus variation range of the base course to 7000-14000 MPa, the material modulus variation range of the base course to 5000-10000 MPa, and the material modulus variation range of the asphalt mixture surface course to 5000-13500 MPa, consider the surface course, the base course and the base course as linear elastic bodies, and take the Poisson's ratios of the surface course, the base course and the base course materials as 0.3, 0.25 and 0.25 respectively, and take the material densities as 2.35 g / cm 3 , 2.10 g / cm 3 , 2.10 g / cm 3 ;

[0031] Subgrade part: determine the required subgrade humidity variation range for calculation to 1.0 OMC-1.6 OMC, wherein OMC is the optimum moisture content;

[0032] Load part: determine the variation range of the driving speed to 40-140 km / h, the variation range of the single wheel ground pressure to 0.7-1.4 MPa, and the cycle loading number to 5x10 7 ;

[0033] The calculation conditions shown in the following table are designed, the factors investigated in each group of conditions are denoted as x, and other factors are controlled as "w-v-M-E pave -E base -E subb -H pave -H base -H subb ", wherein w is the subgrade humidity, v is the driving speed, M is the single tire pressure, E pave is the surface course material modulus, E base is the base course material modulus, E subb is the base course material modulus, H pave is the surface course thickness, H base is the base course thickness, and H subbFor the thickness of the base layer:

[0034]

[0035]

[0036] Further, the step S2 sub-grade soil viscoelastic plastic mechanics model is:

[0037]

[0038]

[0039]

[0040]

[0041]

[0042] In the formula: ε p is the permanent deformation of the subgrade soil, σ max is the cyclic stress amplitude, G1 is the viscoelastic shear modulus of the viscoelastic element in three-dimensional case, η1 is the viscous coefficient of the viscoelastic element, T is the cycle of cyclic load, t1 is the load acting time in each cycle, t2 is the load intermittent time in each cycle, T = t1 + t2, N is the number of cyclic load, β is the non-integer order of the viscoplastic element, c is the total cohesion of the soil, is the total internal friction angle of the soil, π is the circular constant, η2 is the viscous coefficient of the viscoplastic element, Γ is the Gamma function, w is the actual water content, OMC is the optimum water content, K is the compaction degree, σ3 is the confining pressure, and abs represents the calculation of absolute value.

[0043] Further, the step S2 uses the creep module formula (1)-(5) of COMSOL to carry out the finite element calculation of the permanent deformation of the subgrade structure, and uses the creep rate equation shown in formula (6) as the calculation control equation:

[0044]

[0045] Wherein, represents the derivative of formula (1) with respect to time.

[0046] Further, when the creep module formula (1)-(5) of COMSOL is used to carry out the finite element calculation of the permanent deformation of the subgrade structure:

[0047] For the number of cyclic loads N, it is realized by the expression floor(t / T)+1, where t is the total creep time, T is the cycle of cyclic load, and floor is the integer function in COMSOL;

[0048] For the water content w and the compaction degree K, the direct assignment call is made by predefining variables;

[0049] For the total cohesion c of the soil body and the total internal friction angle The total cohesion c of the soil body and the total internal friction angle The functional relationship with the water content and the compaction degree is written into COMSOL:

[0050] c = 32.18 (12.38K-10.38) (-18.52w+4.57) (7)

[0051]

[0052] For the confining pressure σ3, it is converted by the overburden stress;

[0053] For the cyclic load, it is applied by the expression LoadIntensity*(Pulse(x-a)+Pulse(x-b)), where LoadIntensity is the load amplitude, and a and b correspond to the positions of the center points of the left and right two-wheel groups;

[0054] For the load action time t1 and the load intermittent time t2, it is written according to the expressions (9) and (10):

[0055] t1 = 107.22[Ln(e+v)] -3.52 (h+1) 0.36 (9)

[0056] t2 = 0.50(h+1) -0.11 v 0.40 (10)

[0057] In the formula: v is the vehicle speed, and h is the depth of the subgrade top surface downward;

[0058] For the cyclic stress amplitude σ max The cyclic stress amplitude is converted into octahedral shear stress, an additional dependent variable is created in the weak form partial differential equation finite element method to define the octahedral shear stress and give the initial value, which is:

[0059] A new physical field V is created in the weak form partial differential equation module, and independent variables V1 are defined, V1 is the value of the octahedral shear stress, and the weak expression form of V1 is defined as -(V1-sqrt(abs(solid.II2s)*2 / 3))*test(V1), wherein: test() represents the trial function, and solid.II2s is the stress bias second invariant, test() and solid.II2s are both pre-defined variables in COMSOL, and abs represents the calculation of absolute value.

[0060] Further, the step S3 determines:

[0061] The permanent deformation of the roadbed top surface has a basin-shaped distribution characteristic that the middle part is large and the two sides are small in the transverse direction, and the position of the maximum value of the permanent deformation of the roadbed top surface is consistent with the center position of the vehicle load.

[0062] The step S4 fits a maximum value calculation formula of the permanent deformation of the roadbed structure based on the determined basin-shaped distribution characteristic of the permanent deformation of the roadbed top surface and the position of the maximum value of the permanent deformation of the roadbed top surface.

[0063] The beneficial effects of the embodiment of the application are:

[0064] 1. The derived permanent deformation viscoelastic plasticity model of the roadbed soil is regarded as an equivalent creep equation of total time t=NT, the derivative of the equation with respect to time is obtained, the creep rate equation of the creep of the roadbed soil equivalent to the permanent deformation of the roadbed soil is obtained, the creep rate equation is written into the creep module of the simulation platform COMSOL through the user-defined interface, the interaction between the cyclic stress amplitude and the permanent deformation of the roadbed is realized through the weak form partial differential equation, and the finite element calculation of the permanent deformation of the roadbed structure based on the viscoelastic plasticity model of the roadbed soil is realized; in terms of calculation capacity, the calculation efficiency is greatly improved, and the calculation time is reduced, and the permanent deformation calculation of the roadbed structure under 5000 million cyclic loads can be completed in about 6 hours, the problems of long calculation time and large resource consumption in numerical calculation method, and the problem of long calculation time and difficult convergence in the calculation of the several tens of loading results obtained in the limited calculation time far cannot meet the analysis demand of the permanent deformation of the roadbed structure under the million-level loading times are solved; in terms of calculation foundation, the Von-Mises plastic yield function is embedded in the creep module of COMSOL to update the stress distribution after each incremental step in real time, so that the plastic permanent deformation of the roadbed structure under cyclic loading influences the stress distribution in the roadbed at any time, and the stress distribution in the roadbed also reacts on the plastic permanent deformation of the roadbed structure at any time, that is, the permanent deformation of the roadbed and the stress distribution in the roadbed are coupled and influenced at any time, the problem of inaccurate calculation results of the layer summation method is solved;

[0065] 2. According to the finite element calculation results of the subgrade structure permanent deformation based on the subgrade soil viscoelastic-plastic mechanics model, the location of the maximum point of the subgrade permanent deformation is determined, the theoretical logic for establishing the calculation formula of the maximum value of the subgrade structure permanent deformation is clarified, the influence law and influence degree of the loading times, the state variable (the subgrade humidity), the load characteristics (the overloading degree, the driving speed), the pavement properties (the thickness of each structural layer, the modulus of each structural layer material) on the maximum value of the subgrade structure permanent deformation are comprehensively analyzed, the factors that have a significant influence on the maximum value of the subgrade structure permanent deformation are selected to establish a multiple calculation formula, the calculation formula of the maximum value of the subgrade structure permanent deformation is clear in logic, clear in theory, comprehensive in considered factors, and has a wider application range, and the limitations that the existing subgrade structure permanent deformation prediction model is more dependent on experience, the selection and description method of the influence factors lack theoretical support, the considered factors are not comprehensive, and the prediction model is difficult to popularize and apply in engineering design are solved. BRIEF DESCRIPTION OF DRAWINGS

[0066] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed to be used in the embodiments or the prior art description will be briefly introduced. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0067] Figure 1 is the pavement structure combination of the representative project investigated in the embodiments of the present application.

[0068] Figure 2 is the schematic diagram of the geometric size of the half-width subgrade-pavement calculation model in the embodiments of the present application.

[0069] Figure 3 is the typical calculation result cloud chart of the subgrade permanent deformation under different loading times in the embodiments of the present application.

[0070] Figure 4 is the calculation result of the subgrade permanent deformation under different humidification degrees and 5000 million times of cyclic loading in the embodiments of the present application.

[0071] Figure 5 is the calculation result of the subgrade permanent deformation under different driving speeds and 5000 million times of cyclic loading in the embodiments of the present application.

[0072] Figure 6 is the calculation result of the subgrade permanent deformation under different single tire deflections and 5000 million times of cyclic loading in the embodiments of the present application.

[0073] Figure 7 is the calculation result of the subgrade permanent deformation under different surface layer material moduli and 5000 million times of cyclic loading in the embodiments of the present application.

[0074] Figure 8 is the calculation result of the permanent deformation of the subgrade under the cyclic loading of 50 million times in the embodiment of the present application with different modulus of the base material.

[0075] Figure 9 is the calculation result of the permanent deformation of the subgrade under the cyclic loading of 50 million times in the embodiment of the present application with different modulus of the subbase material.

[0076] Figure 10 is the calculation result of the permanent deformation of the subgrade under the cyclic loading of 50 million times in the embodiment of the present application with different thickness of the surface layer.

[0077] Figure 11 is the calculation result of the permanent deformation of the subgrade under the cyclic loading of 50 million times in the embodiment of the present application with different thickness of the base layer.

[0078] Figure 12 is the calculation result of the permanent deformation of the subgrade under the cyclic loading of 50 million times in the embodiment of the present application with different thickness of the subbase layer.

[0079] Figure 13 is the calculation result of the maximum value of the permanent deformation of the subgrade corresponding to the supplementary working condition in the embodiment of the present application.

[0080] Figure 14 is the calculation result of the maximum value of the permanent deformation of the subgrade in the embodiment of the present application.

[0081] Figure 15 is the grey correlation degree between different influencing factors and the maximum value of the permanent deformation of the subgrade in the embodiment of the present application.

[0082] Figure 16 is the calculation result of the maximum value of the permanent deformation of the subgrade in the embodiment of the present application.

[0083] Figure 17 is the verification result of the maximum value of the permanent deformation of the subgrade in the embodiment of the present application. DETAILED DESCRIPTION

[0084] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, but not all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0085] The embodiment provides a subgrade structure permanent deformation calculation method based on a subgrade soil viscoelastic plastic mechanics model, comprising the following steps:

[0086] Determine the number of cyclic loading cycles N, state variables, load characteristics, and pavement properties;

[0087] Based on the number of cyclic loading N, state variables, load characteristics, and pavement properties, the maximum permanent deformation of the subgrade structure is calculated using the formula for calculating the maximum permanent deformation of the subgrade structure.

[0088] The formula for calculating the maximum permanent deformation of the roadbed structure is fitted according to the following process:

[0089] Step S1: Determine the calculation conditions and dimensions of the road finite element simulation model:

[0090] (1) Road surface section

[0091] Inorganic binder stabilized base / subbase courses are widely used in road engineering in my country. The current 6th edition of the general standard "Roadbed and Pavement Engineering" recommends thickness ranges for inorganic binder stabilized base / subbase course pavement structures, as shown in Table 1. Furthermore, based on surveys of some actual engineering pavement structures, such as... Figure 1 As shown, the thicknesses of the surface layer and base course vary within the recommended range in Table 1, while the thickness of the subbase course exceeds the recommended range given in Table 1. Therefore, the calculated subbase course thickness range is adjusted to 15–40 cm. Based on the range of elastic modulus values ​​for inorganic binder stabilized materials given in the "Specifications for Design of Highway Asphalt Pavement" (JTG D50-2017) and the explanatory notes (which should be multiplied by a structural layer modulus adjustment factor of 0.5 during structural analysis), and considering the decrease in material stiffness during service, the range of modulus variation for the base course material is determined to be 7000–14000 MPa, the range for the subbase course material modulus is determined to be 5000–10000 MPa, and the range for the asphalt mixture surface course material modulus is determined to be 5000–13500 MPa. Furthermore, the surface layer, base course, and subbase course are considered as linear elastic bodies, with Poisson's ratios of 0.3, 0.25, and 0.25 for the surface layer, base course, and subbase course materials, respectively, and material densities of 2.35 g / cm³. 3 2.10 g / cm 3 2.10 g / cm 3 .

[0092] Table 1. Thickness range of inorganic binder stabilized base / subbase pavement (cm)

[0093]

[0094] (2) Subgrade

[0095] The permanent deformation of subgrade structure is significantly affected by its humidity state. Since the equilibrium time of water content of subgrade from construction state to stable state is short compared with the service time of subgrade, and the most unfavorable state is considered to ensure that the calculated permanent deformation of subgrade structure is more strict and safe in controlling the service performance of pavement structure, the equilibrium water content is taken as a parameter to investigate the influence of humidity change on the permanent deformation of subgrade structure. In this embodiment, the required range of subgrade humidity change for calculation is determined to be 1.0OMC-1.6OMC, wherein OMC is the optimum moisture content.

[0096] (3) Load part

[0097] To investigate the influence of driving speed on the permanent deformation of subgrade structure, based on the allowable speed range of 60-120km / h of expressway, considering the congestion and overspeed, the range of driving speed is determined to be 40-140km / h. To investigate the influence of vehicle overload on the permanent deformation of subgrade structure, taking the standard load of 0.7MPa given in “Highway Asphalt Pavement Design Specification” (JTG D50-2017) as a reference, considering the maximum overload of 100%, the range of single-wheel ground pressure is determined to be 0.7-1.4MPa.

[0098] To make the calculation results of permanent deformation of subgrade structure meet the analysis requirements within the design service life of pavement, a reasonable number of cyclic loads needs to be set. The traffic department of planning and research institute investigated the fatigue life number of 7 asphalt pavement expressways in Shanghai area, and the results are shown in Table 2. It can be seen that when the axle load is out of range, the fatigue life number of each road fluctuates within 0.31×10 7 -2.46×10 7 “Highway Asphalt Pavement Design Specification” (JTG D50-2017) gives the design traffic volume of design lane within the design service life corresponding to different traffic load grades, as shown in Table 3. It can be seen that when the traffic load grade gradually increases, the traffic volume within the design service life will also increase. Considering the investigation results of fatigue life number of actual engineering and the design traffic volume given in the current “Highway Asphalt Pavement Design Specification”, the number of cyclic loads in numerical calculation is set to 5×10 7 times in this embodiment.

[0099] Table 2 Fatigue life of road structure under different axle loads

[0100] Route name Standard case 25% axle load overrun 100% axle load overrun Shanghai-Nanjing Expressway 2.46 x 10 7 ]]> 1.13 x 10 7 ]]> 3.09 x 10 6 ]] Jiaxing-Liuqi Expressway 9.74 x 10 6 ]] 4.67 x 10 6 ]] 1.10 x 10 6 ]]> Shanghai-Jiaxing Expressway 1.65 x 10 7 ]]> 7.52 x 10 6 ]]> 2.12 x 10 6 <!-- 9 -->]]> Shanghai-Hangzhou Expressway 9.87 x 10 6 ]]> 4.71 x 10 6 ]]> 1.14 x 10 6 ]]> Xinpingjin Expressway 1.96 x 10 7 ]]> 9.14 x 10 6 ]]> 2.38 x 10 6 ]]> Shanghai-Qingdao-Beijing Expressway 2.08 x 10 7 ]]> 9.86 x 10 6 ]]> 2.42 x 10 6 ]]> Suburban ring line 4.51 x 10 6 ]]> 2.17 x 10 6 ]]> 6.64 x 10 5 ]]>

[0101] Table 3 Design traffic load grade

[0102] Design traffic load grade Extremely heavy Extra heavy Heavy Medium Light Cumulative traffic volume of designed lane within design life (10 6 )]]> ≥50 50～19 19～8 8～4 ＜4

[0103] (4) Road finite element simulation model size

[0104] A reasonable simulation model is a prerequisite for ensuring that the calculation results meet the engineering practice. Considering the axisymmetric characteristics of road engineering and not considering the yin and yang slope effect in the embodiment of the application, a half-width road calculation model is established with the center line of the central separation belt as the starting point, which meets the analysis requirements while ensuring the calculation efficiency. This embodiment carries out research on two-way four-lane, and the structure thickness and material modulus of the surface layer, base layer and subbase layer can be flexibly adjusted according to different research levels. The roadbed fill height is 6m, the roadbed soil Poisson's ratio is 0.35, and the foundation thickness is 2m. Since the overload condition is one of the factors affecting the permanent deformation of the roadbed structure that needs to be analyzed in this embodiment, and the maximum overload degree is considered to be 100%, the driving load position is uniformly set in the outer lane as a large heavy vehicle. In order to clearly show, taking the pavement structure of "0.2m surface layer + 0.4m base layer + 0.2m subbase layer" as an example, the specific size of the road finite element simulation model is drawn in Figure 2 .

[0105] (5) Calculation condition scheme design

[0106] According to the above discussion results, the calculation conditions shown in Table 4 are designed to investigate the influence law of roadbed humidity w, driving speed v, single tire pressure M, surface layer material modulus E pave , base layer material modulus E base , subbase layer material modulus E subb , surface layer thickness H pave , base layer thickness H base , subbase layer thickness H subb on the permanent deformation of the roadbed structure. It should be noted that the factors to be investigated in each group are denoted as x, and the other factors are controlled as the order of "w-v-M-E pave -E base -E subb -H pave -H base -H subb ".

[0107] Table 4 Design of roadbed structure permanent deformation calculation condition

[0108]

[0109]

[0110] Step S2, based on the viscoelastic-plastic mechanics model of roadbed soil, the finite element calculation of the permanent deformation of the roadbed structure is carried out:

[0111] In the inventor's earlier application No. 2024105065398, the expression of the subgrade soil viscoelastic-plastic mechanics model shown in formula (1) is given, and the model parameters and working conditions of formula (2) to formula (5) are given as an example of typical clay in Changsha, Hunan:

[0112]

[0113]

[0114]

[0115]

[0116]

[0117] In the formula: ε p is the permanent deformation of the subgrade soil, G1 is the viscoelastic shear modulus of the viscoelastic element in three-dimensional case, η1 is the viscosity coefficient of the viscoelastic element, β is the non-integer order of the viscoplastic element, η2 is the viscosity coefficient of the viscoplastic element, Γ is the Gamma function, σ max is the cyclic stress amplitude, σ3 is the confining pressure, N is the number of cyclic load actions, π is the circular constant, c is the total cohesion of the soil, is the total internal friction angle of the soil, w is the actual water content, OMC is the optimum water content, K is the compaction degree, T is the cyclic load period, t1 is the load action time in each cycle, t2 is the load interval time in each cycle, T=t1+t2, abs represents the calculation of absolute value. It can be seen from formula (1) that the model can represent the permanent deformation of the subgrade soil with the change of the number of cyclic loads N, and can also be regarded as the equivalent creep equation of the total time t=NT. Therefore, the creep module formula (1) to (5) in the solid mechanics module of COMSOL is used to carry out finite element calculation of the permanent deformation of the subgrade structure in the embodiment. The Von-Mises yield function is embedded in the creep module of COMSOL to update the stress distribution after each incremental step in real time, and the creep rate equation is used as the control equation, and the self-established creep rate equation is written through the self-defined interface of the software to realize the analysis requirements.

[0118] Taking the derivative of formula (1) with respect to time, that is The creep rate equation of the equivalent subgrade soil creep of the subgrade soil permanent deformation is obtained as the calculation control equation, as shown in formula (6):

[0119]

[0120] As can be seen from formula (6), the variables in the creep rate equation are still G1, η1, β, η2, and formula (2) to formula (5) give the functional relationship of the model parameters G1, η1, β, η2 and the water content, the compaction degree, the cyclic stress amplitude, the confining pressure, the load action time, the load intermittent time, which can be introduced by writing G1, η1, β, η2 in the COMSOL simulation platform.

[0121] For the number of cyclic loading times, it is realized by the expression floor(t / T)+1, where t is the total creep time, T is the cycle of cyclic loading, floor is the rounding function in COMSOL, and +1 is to avoid the initial loading (loading number is 0) which cannot be calculated.

[0122] For the water content w and the compaction degree K, they can be directly assigned and called by the way of predefining variables, which affect the model parameters and the model variables c, It should be noted that the actual water content w and the compaction degree K have been written into the COMSOL finite element calculation model through the multiple regression equation of G1, η1, β, η2, but the model variables c, still exist in the creep rate equation shown in formula (6), so in order to make the total cohesion c of the soil and the total internal friction angle of the soil be expressed in the calculation model as the water content and the compaction degree as G1, η1, β, η2, the functional relationship of the total cohesion c of the soil and the total internal friction angle of the soil with the water content and the compaction degree is given, as shown in formula (7) to (8):

[0123] c=32.18(12.38K-10.38)(-18.52w+4.57) (7)

[0124]

[0125] In the formula, w is the actual water content, and K is the compaction degree.

[0126] For the confining pressure, it can be converted by the overburden stress.

[0127] For the cyclic loading, it is applied by the expression LoadIntensity*(Pulse(x-a)+Pulse(x-b)), where LoadIntensity is the load amplitude, the standard load corresponding to each tire pressure of 0.7 MPa is equal to 113.6 kPa, the tire action diameter is 0.213 m, the corresponding Pulse is the square wave function with the lower limit of -0.1065 m and the upper limit of 0.1065 m, and a and b correspond to the positions of the center points of the left and right two wheel groups, which can be given specific coordinates when the geometric model is established. In the embodiment, the position of the driving load is as shown in Figure 2As shown, and the center point of the two wheels on the left and right sides is 1.8 m apart, so the abscissa of a is 6.225, and the abscissa of b is 8.025, that is, the implementation statement of the cyclic load in COMSOL is LoadIntensity*(Pulse(x-6.225)+Pulse(x-8.025)).

[0128] For the load action time t1 and the load intermittent time t2, the expressions of the load action time t1, the load intermittent time t2, the vehicle speed and the roadbed depth are written, as shown in equations (9) and (10):

[0129] t1 = 107.22 [Ln(e + v)] -3.52 (h + 1) 0.36 (9)

[0130] t2 = 0.50 (h + 1) -0.11 v 0.40 (10)

[0131] In the formula: v is the vehicle speed, and h is the depth of the roadbed top surface downward.

[0132] Because the cyclic stress amplitude of each point and the deformation of the point exist a mutual nesting relationship, an additional dependent variable is created in the weak form partial differential equation finite element method to define the octahedral shear stress and give an initial value, and the cyclic stress amplitude is converted into the octahedral shear stress, so that it can be recognized by COMSOL, and the cyclic relationship can be run. Specifically, a new physical field V is created in the weak form partial differential equation module, and an independent variable V1 is defined, and V1 is the value of the octahedral shear stress. The weak form of V1 is defined as -(V1-sqrt(abs(solid.II2s)*2 / 3))*test(V1), wherein test() represents a trial function, and solid.II2s is the stress bias second invariant. test() and solid.II2s are both predefined variables in COMSOL, and can be directly called. abs represents the calculation of the absolute value. When calculating, the relative tolerance of the solver is set to 0.002, and the absolute tolerance is set to 0.02, that is, the difference between the calculation results of the previous two times under a single time step is within 0.2%, and the overall difference is within 2%, that is, the calculation accuracy of the permanent deformation of the roadbed structure is considered to meet the requirements, and the finite element iteration is ended.

[0133] wherein, σ1, σ2, σ3 are the principal stresses in three directions respectively.

[0134] In step S3, based on the finite element calculation results of the permanent deformation of the roadbed structure under different working conditions, the permanent deformation influencing factors of the roadbed structure and the corresponding permanent deformation evolution law of the roadbed structure are determined.

[0135] Taking the subgrade humidity 1.40 M C, the driving speed 100 km / h, the single tire pressure 0.7 MPa, the surface layer material modulus 12000 MPa, the base layer material modulus 10000 MPa, the bottom base layer material modulus 8000 MPa, the surface layer thickness 20 cm, the base layer thickness 40 cm, and the bottom base layer thickness 20 cm as examples, the cloud maps of the calculation results of the permanent deformation of the subgrade structure under different loading times are shown in Figure 3 It can be seen that the permanent deformation of the top surface of the subgrade caused by the cyclic load has a basin-shaped distribution in the lateral direction, with the middle being large and the two sides being small, and the position of the maximum permanent deformation is approximately equivalent to the midpoint position of the left and right wheel groups. At the same time, with the increase of the cyclic loading times, the permanent deformation of the subgrade structure continues to accumulate, and the increase rate is faster in the early loading stage, and the increase rate of the permanent deformation slows down when the loading reaches a certain number. It is worth emphasizing that the evolution characteristics of the permanent deformation of the subgrade structure with the loading times are influenced by the subgrade humidity, load characteristics, pavement properties, and other comprehensive factors, and should be analyzed according to the specific factors.

[0136] Further extraction of the calculation results in the cloud map, and drawing of the permanent deformation of the subgrade structure on the cross section after loading 5000 million times to reveal its distribution characteristics, drawing of the relationship between the maximum value of the permanent deformation of the subgrade structure and the loading times under different research levels of each factor to reveal the influence characteristics of different factors on the permanent deformation of the subgrade structure under long-term dynamic load, and drawing of the relationship between the maximum value of the permanent deformation of the subgrade structure after loading 5000 million times and different levels of each influencing factor to reveal the evolution mode of the permanent deformation of the subgrade structure with different influencing factors. According to the corresponding calculation results calculated by formulas (1) to (5) under different working conditions, the calculation results of the permanent deformation of the subgrade structure under the influence of 9 factors such as subgrade humidity, driving speed, overload degree, material modulus of each layer of pavement, and thickness of each layer of pavement are drawn, as shown in Figures 4-12 It is to be noted that the description model of each evolution mode only gives a general formula in this step, and the specific parameters are not given, because the description model of each single variable will eventually form a multiple calculation formula of the maximum value of the permanent deformation of the subgrade structure, and therefore the parameters of each description model will be determined by fitting the calculation results under all working conditions.

[0137] It can be seen from Figure 4 (a) to Figure 12 (a) that the permanent deformation of the top surface of the subgrade has a basin-shaped distribution in the lateral direction, with the middle being large and the two sides being small, and the position of the maximum value is approximately equivalent to the center position of the vehicle load, i.e., the maximum value of the permanent deformation of the subgrade structure is determined. Figure 4 (b) to Figure 12(b)It is known that the maximum permanent deformation of subgrade structure increases with the increase of subgrade wetting degree and vehicle overload degree, and decreases with the increase of driving speed, surface layer thickness, base layer thickness, sub-base layer thickness, surface layer material modulus, base layer material modulus and sub-base layer material modulus, i.e. the influencing factors of the maximum permanent deformation of subgrade structure are determined. From the above, Figure 4 (c)~ Figure 12 (c)It is known that after 50 million cycles of loading, the maximum permanent deformation of subgrade structure has a clear monotonic increase and decrease change rule with the increase of subgrade wetting degree, vehicle overload degree, driving speed, surface layer thickness, base layer thickness, sub-base layer thickness, surface layer material modulus, base layer material modulus and sub-base layer material modulus, and the relationship between the maximum permanent deformation of subgrade structure and wetting degree is described by an exponential function, the relationship between the maximum permanent deformation of subgrade structure and driving speed is described by a power function, the relationship between the maximum permanent deformation of subgrade structure and overload degree is described by a linear function, the relationship between the maximum permanent deformation of subgrade structure and the material modulus of each structure layer of pavement is described by a linear function, and the relationship between the maximum permanent deformation of subgrade structure and the thickness of each structure layer of pavement is described by an exponential function, with a description accuracy of more than 98%, i.e. the evolution pattern of the maximum permanent deformation of subgrade structure is determined.

[0138] Step S4, based on the influencing factors of the permanent deformation of subgrade structure and the corresponding evolution law of the permanent deformation of subgrade structure, the calculation formula of the maximum permanent deformation of subgrade structure is fitted:

[0139] In engineering analysis, the maximum permanent deformation of subgrade structure is most concerned by researchers and designers. In addition, due to the generation of the permanent deformation of subgrade structure, a certain depth of void area appears between the top of subgrade and the bottom of pavement structure, which hinders the transmission of driving load from pavement structure to subgrade, and the bending tensile stress and strain of each structure layer of pavement are generated, and the dynamic response of each structure layer of pavement corresponding to the position of the maximum permanent deformation of subgrade structure is also most obvious. Therefore, in order to comprehensively analyze the service performance of subgrade and pavement structure, it is necessary to establish the calculation formula of the maximum permanent deformation of subgrade structure.

[0140] To establish a reasonable calculation formula of the maximum permanent deformation of subgrade structure, the influencing factors should be considered comprehensively. In addition to the number of loading times, other influencing factors can be divided into three categories: the first category can be called state variable, i.e. the inherent properties of subgrade, such as moisture content, compaction degree, filling height, etc.; the second category can be called load characteristics, i.e. the dependent properties of driving load, such as driving speed, overload degree, lateral distribution, etc.; the third category can be called pavement properties, i.e. the bearing performance of pavement structure, such as structure combination, layer thickness, material modulus, etc. Based on this, when establishing the calculation formula of the maximum permanent deformation of subgrade structure, the required variables should be selected from the three categories of influencing factors, and the general expression of the formula can be written as formula (11):

[0141] ε pmax =f(N)·f(δ)·f(χ)·f(λ) (11)

[0142] Where: ε pmax Let f(N) be the maximum permanent deformation of the subgrade structure, f(δ) be the influence function of the number of cyclic loading, f(χ) be the influence function of the state variables, f(χ) be the influence function of the load characteristics, the overload degree of the load characteristics is reflected in the single tire pressure M, and f(λ) be the influence function of the pavement properties.

[0143] As shown in Table 4, this embodiment designed 52 calculation conditions by controlling variables to examine the roadbed moisture w, vehicle speed v, single tire pressure M, and surface material modulus E. pave Base material modulus E base Subbase material modulus E subb Surface layer thickness H pave Base layer thickness H base Subbase thickness H subb The influence of nine factors on the permanent deformation of the roadbed structure, although Figure 4 (c)~ Figure 12 (c) The evolution pattern of the maximum permanent deformation of the subgrade structure with respect to various factors was obtained. However, the reliability of the calculation formula between the maximum permanent deformation of the subgrade structure and 9 factors such as subgrade humidity w was slightly poor based on the calculation results of only 52 working conditions. Therefore, 28 supplementary working conditions as shown in Table 5 were randomly generated within the respective ranges of different factors.

[0144] Table 5 shows the stochastic working conditions used to supplement the calculation results of permanent deformation of the subgrade structure.

[0145]

[0146]

[0147] As can be seen, the 28 randomly generated working conditions in Table 5 effectively cover the possible range of variation of various influencing factors, filling the gaps beyond the representative working conditions designed by the controlled variable method, and ensuring the comprehensiveness of the working conditions in the calculation results. The calculation method for this part is the same as described in step S2, and the maximum permanent deformation results of the subgrade structure obtained from the calculation of each group of working conditions are as follows: Figure 13 As shown.

[0148] As shown in Table 4, the influencing factors of permanent deformation of the subgrade structure are: the state variable is the subgrade humidity w; the load characteristics are the vehicle speed v and the single tire pressure M; and the pavement properties are the surface material modulus E. pave Base material modulus E base Subbase material modulus E subb Surface layer thickness H paveBase layer thickness H base Subbase thickness H subb Based on the numerical calculation results of 80 working conditions (52 designed working conditions in Table 4 and 28 randomly generated working conditions in Table 5), the following calculations were performed: Figure 4 (c)~ Figure 12 (c) The maximum permanent deformation of the subgrade structure given was fitted with different descriptive functions of the evolution mode of each influencing factor, and the parameter values ​​of the influence functions of each factor were obtained, as shown in Table 6. It should be noted that, to improve the fitting effect, during fitting, one data point was extracted from the curve of the maximum permanent deformation of the subgrade structure with the number of loading cycles for each working condition every 500,000 cycles of loading, i.e., the total number of data points was 80 × (5000 ÷ 50) = 8000. It should be noted that... Figure 4 (b)~ Figure 12 (b) shows the evolution of the maximum permanent deformation of the subgrade structure with the number of loading cycles. Table 6 uses f(N) = a·N b It is described in the form of.

[0149] Table 6. Influence function of maximum permanent deformation of roadbed structure and its parameter values ​​(V1.0)

[0150]

[0151]

[0152] As can be seen from the positive and negative signs of the parameters in Table 6, the proposed influence functions effectively capture the variation law of the maximum permanent deformation of the subgrade structure with the increase and decrease of different influencing factors. Furthermore, substituting the specific values ​​of each influence function and its parameters into equation (11), we can obtain the formula for calculating the maximum permanent deformation of the subgrade structure, V1.0, which is:

[0153] ε pmax =f(N)·f(w)·f(v)·f(M)·f(E pave )·f(E base )·f(E subb )·f(H pave )·f(H base )·f(H subb (12)

[0154] Where f(w) is the influence function of roadbed humidity w, f(v) is the influence function of vehicle speed v, f(M) is the influence function of single tire pressure M, and f(E) is the influence function of roadbed humidity w. pave E represents the modulus of the surface material. pave The influence function, f(E) base E represents the modulus of the base material. base The influence function, f(E) subb E represents the modulus of the base material. subbThe influence function, f(H) pave H represents the surface layer thickness. pave The influence function, f(H) base H represents the thickness of the base layer. base The influence function, f(H) subb H represents the thickness of the subbase layer. subb The influence function. The prediction effect of formula V1.0 for calculating the maximum permanent deformation of the roadbed structure is as follows: Figure 14 As shown, R 2 It reached 99.83%.

[0155] although Figure 14 The results show that the established formula V1.0 for calculating the maximum permanent deformation of the subgrade structure can accurately predict the maximum permanent deformation of the subgrade structure under the influence of multiple factors. However, it is also noted that there is a problem with the parameter values ​​in Table 6, namely the modulus E of the surface material. pave Base material modulus E base Subbase material modulus E subb The magnitude of parameter 'a' in the corresponding influence function is significantly smaller than that of other parameters. This means that the maximum permanent deformation of the subgrade structure changes very little with the variation of the material modulus of each pavement structural layer. Therefore, using the material modulus of each pavement structural layer as a variable will not improve the accuracy of the calculation formula and will reduce the calculation efficiency due to the large number of variables in the formula. To ensure the rigor of the analysis, a grey relational analysis was conducted on the numerical calculation results of 80 working conditions, including the 52 working conditions designed in Table 4 and the 28 randomly generated working conditions in Table 5. The maximum permanent deformation of the subgrade structure was used as the parent sequence, and the number of cyclic loading N, subgrade humidity w, vehicle speed v, single tire pressure M, and pavement material modulus E were also considered. pave Base material modulus E base Subbase material modulus E subb Surface layer thickness H pave Base layer thickness H base Subbase thickness H subb As a subsequence, the sensitivity coefficient ρ is set to 0.5 in the analysis of geotechnical engineering problems. After regularization and initialization of 8000 data points, the different degrees of influence of 10 influencing factors on the maximum permanent deformation of the roadbed structure are obtained, such as... Figure 15 As shown. By Figure 15 It can be seen that the grey relational degree between the material modulus of each pavement structural layer and the maximum permanent deformation of the subgrade structure is less than 0.5, while the grey relational degree of other factors exceeds 0.8. This further illustrates that the influence of the material modulus of each pavement structural layer on the maximum permanent deformation of the subgrade structure is limited. Figure 4 (c)~ Figure 12 This can also be confirmed in (c). Taking the modulus of the surface material as an example, when E paveWhen the pressure increases from 5000MPa to 13500MPa, the reduction in the maximum permanent deformation of the subgrade structure is less than 0.3mm. Based on this, the influence of the change in the modulus of each structural layer of the pavement on the maximum permanent deformation of the subgrade structure is no longer considered. The influence function of the remaining factors is refitted using 8000 data points corresponding to 80 calculation conditions. The parameter values ​​are shown in Table 7.

[0156] Table 7. Influence function of maximum permanent deformation of roadbed structure and its parameter values ​​(V2.0)

[0157]

[0158] As shown in Table 7, the signs of the parameters of each influence function conform to the law of increase or decrease of the maximum permanent deformation of the subgrade structure with respect to each factor. Substituting the specific values ​​of each influence function and its parameters into Equation (11) according to Equation (12), we obtain the formula for calculating the maximum permanent deformation of the subgrade structure, V2.0, as shown in Equation (13):

[0159] ε pmax =f(N)·f(w)·f(v)·f(M)·f(H pave )·f(H base )·f(H subb (13)

[0160] Simplifying and rearranging equation (13), we get:

[0161]

[0162] Where: ε pmax (mm) represents the maximum permanent deformation of the roadbed structure, N (ten thousand times) represents the number of cyclic loading cycles, w / OMC represents the degree of wetting of the roadbed, v (km / h) represents the driving speed, M (MPa) represents the single tire pressure, and H pave (cm), H base (cm), H subb (cm) corresponds to the thickness of the surface layer, base layer, and subbase layer.

[0163] Based on the determined number of cyclic loading N, subgrade moisture content w, optimum moisture content OMC, driving speed v, single tire pressure M, and surface layer thickness H. pave Base layer thickness H base Subbase thickness H subb The maximum permanent deformation of the subgrade structure is calculated using the formula (14) shown in equation (14). The calculation results are as follows: Figure 16 As shown, by Figure 16 It can be seen that although the accuracy is reduced by 0.02% compared to V1.0, R 2 =99.81% fully meets the analysis requirements.

[0164] To verify the rationality and accuracy of the proposed maximum permanent deformation calculation formula V2.0 of the subgrade structure, according to the boundary range of each factor, the "RAND()" function in EXCEL was used to randomly generate 12 verification working conditions shown in Table 8. It can be seen that the 12 randomly generated verification working conditions effectively cover the possible variation range of each influencing factor, which can ensure the comprehensiveness of the verification work.

[0165] Table 8 Working condition for verifying the maximum permanent deformation calculation formula V2.0 of the subgrade structure

[0166]

[0167] First, the numerical calculation of the permanent deformation of the subgrade structure under each working condition was carried out in COMSOL, and the calculation method and steps were the same as described in S2. Then, each group of working conditions was substituted into the formula (14) of the embodiment of the present application to calculate the maximum permanent deformation of the subgrade structure. The calculated values of the numerical calculation and the calculated values of the embodiment of the present application under the same working conditions were compared, and the verification results are shown in Table 9. Figure 17 Figure 17 It can be seen that the calculated values of the embodiment of the present application are very close to the numerical calculation results, that is, the proposed calculation formula V2.0 can accurately represent the maximum permanent deformation of the subgrade structure.

[0168] The above only describes the preferred embodiments of the present application, and is not used to limit the protection scope of the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principles of the present application shall be included in the protection scope of the present application.​

Claims

1. A method for calculating permanent deformation of a subgrade structure based on a viscoelastoplastic mechanics model of subgrade soil, characterized by, The method comprises the following steps: Determining the number of cyclic loads N , state variables, load characteristics, pavement properties; Based on the number of cyclic loading N The maximum permanent deformation of the subgrade structure is calculated by using the maximum permanent deformation calculation formula of the subgrade structure according to the state variable, load characteristics and pavement properties. The maximum permanent deformation calculation formula of the roadbed structure is fitted according to the following process: Step S1, determining the calculation conditions and the size of the road finite element simulation model; Step S2, based on the viscoelastic-plastic mechanics model of the roadbed soil, performing finite element calculation of the permanent deformation of the roadbed structure; Step S3, based on the finite element calculation results of the permanent deformation of the roadbed structure under different conditions, determining the influencing factors of the permanent deformation of the roadbed structure and the corresponding evolution law of the permanent deformation of the roadbed structure; Step S4, based on the influencing factors of the permanent deformation of the roadbed structure and the corresponding evolution law of the permanent deformation of the roadbed structure, fitting the maximum permanent deformation calculation formula of the roadbed structure; In the step S1, when designing the calculation conditions: The thickness of the subbase is adjusted to 15-40 cm, the modulus of the base material is adjusted to 7000-14000 MPa, the modulus of the subbase material is adjusted to 5000-10000 MPa, the modulus of the asphalt mixture surface layer is adjusted to 5000-13500 MPa, the surface layer, the base and the subbase are regarded as linear elastic bodies, the Poisson's ratios of the surface layer, the base and the subbase are respectively taken as 0.3, 0.25 and 0.25, and the material densities are respectively taken as 2.35 g / cm 3 , 2.10 g / cm 3 , 2.10 g / cm 3 , The roadbed part: the required roadbed humidity change range is determined to be 1.0OMC~1.6OMC, wherein OMC is the optimum moisture content; Load part: the change range of driving speed is determined as 40-140 km / h, the change range of single wheel ground pressure is determined as 0.7-1.4 MPa, and the cycle loading times is set as 5x10 7 times; The calculation conditions shown in the following table were designed, and the factors investigated in each group of conditions are denoted as x , other factors are controlled according to the order of w - v - M - E pave - E base - E subb - H pave - H base - H subb , wherein w is the subgrade humidity, v is the driving speed, M is the single tire pressure, E pave is the surface layer material modulus, E base is the base layer material modulus, E subb is the subbase layer material modulus, H pave is the surface layer thickness, H base is the base layer thickness, H subb is the subbase layer thickness: ； The viscoelastic-plastic mechanics model of the roadbed soil in the step S2 is: (1) (2) (3) (4) (5) In the formula: is the permanent deformation of subgrade soil, is the cyclic stress amplitude, is the viscoelastic shear modulus of the viscoelastic element in three-dimensional conditions, is the viscous coefficient of the viscoelastic element, T is the cycle of cyclic load, t 1 is the load action time within each cycle, t 2 is the load intermittent time within each cycle, T=t 1+ t 2, N is the number of cyclic load actions, β is the non-integer order of the viscoplastic element, c is the total cohesion of the soil body, φ is the total internal friction angle of the soil body, π is the circular constant, η 2 is the viscous coefficient of the viscoplastic element, is the Gamma function, w is the actual water content, and OMC is the optimum water content, K is the compaction degree, σ 3 is the confining pressure, abs denotes the calculation of the absolute value; In the step S2, the creep module formula (1)-(5) of COMSOL is used to perform finite element calculation of the permanent deformation of the roadbed structure, and the creep rate equation shown in formula (6) is used as the calculation control equation: (6) wherein represents the derivation of the expression (1) with respect to time.

2. The method according to claim 1, wherein The state variable is subgrade humidity w The load characteristic is vehicle speed v The single tire pressure M The pavement property is surface layer thickness H pave The base layer thickness H base The subbase layer thickness H subb ; The maximum permanent deformation calculation formula of the roadbed structure is shown in formula (14), and the maximum permanent deformation of the roadbed structure is calculated: (14) wherein: The maximum permanent deformation calculation formula of the roadbed structure is shown in formula (13), and the maximum permanent deformation of the roadbed structure is calculated: pmax is the maximum value of permanent deformation of the subgrade structure, N is the number of cyclic loads, OMC is the optimum moisture content, w is the degree of wetting of the subgrade.

3. The method according to claim 1, wherein The state variable is subgrade humidity w The load characteristic is vehicle speed v The single tire pressure M The pavement property is surface layer thickness H pave The base layer thickness H base The subbase layer thickness H subb ; The maximum permanent deformation calculation formula of the roadbed structure is shown in formula (12), and the maximum permanent deformation of the roadbed structure is calculated: (13) wherein, In the step S2, when the creep module formula (1)-(5) of COMSOL is used to perform finite element calculation of the permanent deformation of the roadbed structure: pmax is the maximum value of permanent deformation of the subgrade structure, f N is the influence function of the number of cycles of loading, w is the influence function of the humidity of the subgrade, v is the influence function of the speed of the vehicle, M is the influence function of the single tire pressure, H pave is the influence function of the thickness of the surface layer, H base is the influence function of the thickness of the base layer, H subb is the influence function of the thickness of the subbase layer, according to the following table:​​​​​​​ 。 4. The method according to claim 1, wherein The state variable is subgrade moisture w The load characteristic is vehicle speed v The load characteristic is single tire pressure M The pavement property is surface layer material modulus E pave The pavement property is base layer material modulus E base The pavement property is subbase layer material modulus E subb The pavement property is surface layer thickness H pave The pavement property is base layer thickness H base The pavement property is subbase layer thickness H subb ; floor (12) wherein, floor pmax is an influence function of the maximum value of permanent deformation of the subgrade structure, f N is an influence function of the number of cycles of loading, w is an influence function of the humidity of the subgrade, v is an influence function of the speed of the vehicle, M is an influence function of the single tire pressure, E pave is an influence function of the modulus of the surface layer material, E base is an influence function of the modulus of the base layer material, E subb is an influence function of the modulus of the sub-base layer material, H pave is an influence function of the thickness of the surface layer, H base is an influence function of the thickness of the base layer, H subb is an influence function of the thickness of the sub-base layer, calculated according to the following table:​​​​​​​​​​ 。 5. The method according to claim 1, wherein φ For the number of cycles to failure N is achieved by the expression φ ( t / T )+1, where t is the total time of creep, T is the period of the cyclic loading, σ is the floor function in COMSOL; For water content w and compaction K , direct assignment calls by way of pre-defined variables; For the total cohesion of soil c The total internal friction angle between the soil and the soil LoadIntensity The total cohesion of the soil is shown by equations (7) to (8). c The total internal friction angle between the soil and the soil Pulse The functional relationship between moisture content and compaction degree is written into COMSOL: (7) (8) For confining pressure Pulse 3 , converted by overburden stress; For cyclic loading, the expression LoadIntensity σ x a V1-sqrt x b abs is applied, where a , b correspond to the positions of the center points of the left and right wheel groups, respectively.​​​​​​​ For the load action time t 1 and the load intermittent time t 2, write according to formula (9)~(10) shown: (9) (10) In the formula: v V is the vehicle speed, h H is the depth of the subgrade top surface. For the cyclic stress amplitude solid.II max The cyclic stress amplitude is converted to octahedral shear stress, and an additional dependent variable is created to define the octahedral shear stress and assigned an initial value in the weak form partial differential equation finite element method, specifically: Create a new physical field in the weak form partial differential equation module V and define the independent variables V1 , V1 i.e. the value of octahedral shear stress, define V1 its weak form as - ( *test(V1) ( test ( solid.II 2 s ) * 2 / 3)) test where: solid.II2s () is the trial function, abs 2 s is the second invariant of stress deviator, In the step S3, the following is determined: () and The permanent deformation of the top surface of the roadbed has a basin-shaped distribution characteristic that the middle is large and the two sides are small in the transverse direction, and the position of the maximum permanent deformation of the top surface of the roadbed is consistent with the center position of the vehicle load; are both predefined variables in COMSOL, The maximum permanent deformation calculation formula of the roadbed structure is fitted based on the determined basin-shaped distribution characteristic of the permanent deformation of the top surface of the roadbed and the position of the maximum permanent deformation of the top surface of the roadbed. abs() indicates the calculation of absolute value.

6. The method of claim 1, wherein the method is characterized by: ​ ​ ​

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