Accumulated plastic strain test loading and characterization method of roadbed soil considering actual stress state and service history

Abstract

The invention discloses a method for testing and characterizing the cumulative plastic strain of subgrade soil in consideration of the actual stress state and service history. The method for testing and characterizing the cumulative plastic strain of subgrade soil is as follows: statically pressing a specimen in layers to a target compaction degree; simulating an overlying static load by using contact stress; and applying a cyclic load to the specimen. The method for characterizing the cumulative plastic strain of subgrade soil is as follows: constructing a characterization component for the cumulative plastic strain of subgrade soil, wherein the characterization component comprises connected integer-order viscoelastic elements and non-integer-order viscoplastic elements; converting the cyclic load into a constant load, deriving a deformation expression of subgrade soil in a one-dimensional case, extending a unified characterization formula for the cumulative plastic strain of subgrade soil in three dimensions under the action of dynamic cyclic loads, performing a test on the cumulative plastic strain of subgrade soil based on the loading method for testing the cumulative plastic strain of subgrade soil, constructing a multivariate regression equation of parameters of the unified characterization formula for the cumulative plastic strain of subgrade soil and working conditions, and realizing a unified characterization of the cumulative plastic strains of all subgrade soils.

Description

Technical Field

[0001] The invention belongs to the technical field of road engineering, and relates to a method for testing, loading and characterizing the accumulated plastic strain of roadbed soil taking into account the actual stress state and service history. Background Art

[0002] The rapid development of transportation infrastructure construction, the growth of demand for road transportation, the increase in the tonnage of passenger and freight vehicles, and the continuous improvement of road design and construction standards have all put forward strict requirements on the service level of the road system. Under traffic loads, the subgrade soil directly bears the large number of cycles of shearing transmitted from the upper part. The subgrade strength continues to deteriorate and the plastic strain continues to accumulate, resulting in the pavement structure being prone to many diseases such as rutting and cracking, which greatly restricts the road system from playing its due functions of safety, comfort, and durability. Therefore, in order to evaluate the long-term performance of the subgrade, it is of great engineering significance to correctly test and reasonably characterize the accumulated plastic strain of the subgrade soil.

[0003] Dynamic triaxial test is widely used to test the cumulative plastic strain of roadbed soil. The key lies in truly restoring the characteristics of soil in the roadbed. At present, the dynamic triaxial loading mode for testing the cumulative plastic strain of roadbed soil is far from unified. Analysis of existing technologies has found that there are two key drawbacks:

[0004] (1) Whether there is no contact stress or the contact stress σ c Setting it to a fixed 15 kPa or 0.2σ3 does not recognize the engineering fact that the overburden static load is related to the properties of the subgrade soil itself, that is, the overburden static load is actually a variable that changes with the properties of the subgrade soil, that is, the contact stress σ used to reproduce the overburden static load. c It should change with the properties of the roadbed soil, rather than a certain value;

[0005] (2) Whether applying cyclic load directly after applying confining pressure σ3, or consolidating the specimen at confining pressure σ3, or applying low-speed load for 100 s, or controlling the axial strain rate to less than 0.075% / h, none of them truly matches the engineering standards and rigid conditions for the static load effect on the roadbed soil during pavement construction and the static load deformation of the roadbed must be stable before opening to traffic. That is, before applying cyclic load, the contact stress σ3 should be used to consolidate the specimen under confining pressure σ3. c Cyclic load is applied to the static load constant pressure specimen until its axial deformation stops increasing to simulate the repeated dynamic shear of vehicle load, rather than any simple combination of other methods.

[0006] In summary, the data obtained from the experimental tests using existing technologies are not the true values ​​of the accumulated plastic strain of the roadbed soil corresponding to the actual project.

[0007] In addition to the dynamic triaxial test, it is equally important to reasonably characterize the cumulative plastic strain of the subgrade soil. The real meaning of "reasonable characterization" is: (1) Efficiently characterize the cumulative plastic strain of the subgrade soil under tens of thousands of cyclic loadings; (2) Uniformly characterize the cumulative plastic strain of different types of subgrade soils. These two points are indispensable. If (1) is not met, the analysis requirements for the results of long-term vehicle loads cannot be met; if (2) is not met, one model will be applicable to one or several types of soil, and another model will be applicable to other types of soil, making it impossible to choose during engineering design. At present, there are three main methods for characterizing the cumulative plastic strain of subgrade soil:

[0008] The first category is the characterization method based on the principles of classical soil mechanics. Some studies have constructed a hardening modulus field in the deviatoric stress space based on the hardening modulus interpolation method and the mapping center shift method. The proposed elastoplastic incremental characterization method can accurately characterize the undrained deformation characteristics of soft clay under cyclic loading. However, the computational cost required by this method is cumbersome and it is difficult to promote and apply it to actual projects. Some studies have introduced hardening parameters that reflect anisotropy into the elastoplastic double-sided model, and used the mapping center shift method to characterize the plastic accumulation of unsaturated soil under cyclic loading. However, due to the large amount of calculation of the model, only the calculation results of 10 loadings were obtained. Although they are consistent with the actual measured values, it is not realistic to use the characterization results of 10 loadings to guide engineering projects with tens of thousands of loadings.

[0009] The second type is the characterization method determined according to the experimental law of a given soil. The essence of the second type of characterization method is the mathematical fitting of the test results, which lacks theoretical support. At the same time, the empirical model can only be used for a given soil type and working condition range, that is, the model form obtained by the experimental law of a certain soil cannot well characterize the cumulative plastic strain results of other soils, that is, the applicability of the model is extremely limited;

[0010] The third category can be called other methods. Some studies have characterized the cumulative plastic strain of roadbed aggregates through the method of neural network. The neural network method must rely on a large amount of test data to ensure the accuracy of the characterization results. The lack of data leading to result deviation is a recognized drawback. The sample preparation, loading, and data processing processes of the cumulative plastic strain test of roadbed soil are very complicated and will inevitably consume a lot of manpower and material resources. Therefore, it is not realistic to provide a large amount of test data as the basis for the application of neural network methods. Some studies have established a characterization method for the cumulative plastic strain of soft clay based on the Kelvin model, but its theoretical foundation is wrong because the Kelvin model is essentially only suitable for describing one-dimensional static deformation problems under constant loads, and is not applicable to three-dimensional dynamic deformation problems under cyclic loads. The cumulative plastic strain is a typical three-dimensional dynamic deformation problem under cyclic loads, so it cannot correctly guide the characterization of the cumulative plastic strain of soil. Summary of the invention

[0011] The purpose of the embodiments of the present invention is to provide a loading method for cumulative plastic strain testing of roadbed soil taking into account the actual stress state and service history, so as to solve the problem of inaccurate cumulative plastic strain testing of roadbed soil in the prior art.

[0012] The purpose of the embodiments of the present invention is to provide a method for characterizing the cumulative plastic strain of roadbed soil taking into account the actual stress state and service history, so as to solve the problems of low accuracy, limited applicability, and difficulty in selection and application in actual engineering design of existing methods for characterizing the cumulative plastic strain of roadbed soil.

[0013] A technical solution adopted by an embodiment of the present invention is: a loading method for cumulative plastic strain test of subgrade soil considering the actual stress state and service history, and loading is performed according to the following steps:

[0014] The specimens are statically pressed layer by layer to the target compaction degree to simulate the actual filling process of the roadbed;

[0015] The contact stress was used to simulate the overlying static load and the specimen was statically loaded;

[0016] Cyclic loads are applied to the specimens to simulate the dynamic loads on the roadbed during operation.

[0017] Furthermore, the contact stress σ c Calculate according to the following formula:

[0018]

[0019] Among them, K0 is the static earth pressure coefficient and σ3 is the confining pressure.

[0020] Furthermore, the static load time of the simulated overlying static load is determined according to the following process:

[0021] The specimens were prepared by layered static pressing. The moisture content of the specimens was 1.6OMC and the compaction degree was 87%. Based on the contact stress σ c A controlled stress constant load test is carried out with the test confining pressures of 30 kPa and 120 kPa respectively. The constant load time is set for trial. If the stable state is not reached after the constant load time is reached, the sample is re-prepared and the constant load time is continued to be increased until the deformation stability time under the test confining pressure is found.

[0022] Another technical solution adopted by the embodiment of the present invention is: a method for characterizing the accumulated plastic strain of roadbed soil considering the actual stress state and service history, which is performed according to the following steps:

[0023] Constructing a characterization component of the accumulated plastic strain of the roadbed soil, the characterization component includes a connected integer-order viscoelastic element and a non-integer-order viscoplastic element;

[0024] The cyclic load is converted into a constant load, and the deformation expression of the subgrade soil in the one-dimensional case is derived based on the characterization component of the accumulated plastic strain of the subgrade soil;

[0025] Based on the one-dimensional deformation expression of subgrade soil, the unified characterization formula of the three-dimensional cumulative plastic strain of subgrade soil under dynamic cyclic loading is extended;

[0026] Based on the above-mentioned cumulative plastic strain test loading method of subgrade soil considering the actual stress state and service history, the cumulative plastic strain test of subgrade soil is carried out, and a multivariate regression equation of parameters of the unified characterization formula of cumulative plastic strain of subgrade soil and working conditions is constructed.

[0027] Furthermore, the characterization component of the accumulated plastic strain of the subgrade soil is constructed according to the following process:

[0028] A spring with an elastic modulus of E0 is used to represent elastic deformation, and a spring with an elastic modulus of E1 and a viscoelastic pot with a viscosity coefficient of η1 are connected in parallel to represent viscoelastic deformation. These two parts are connected in series to form a viscoelastic element.

[0029] Assume a yield stress of σ s The plastic friction plate is connected in parallel with a viscosity pot with a viscosity coefficient of η2 and a non-integer order of β to form a viscoplastic element to represent viscoplastic deformation;

[0030] The process of converting a cyclic load to a steady load is as follows:

[0031] The cyclic load is converted into a constant load using a piecewise function as shown in formula (4):

[0032]

[0033] Where: t is the deviatoric stress at time t, σ max is the cyclic stress amplitude, t1 is the load action time in each cycle, T is the cyclic load period, and N is the number of cyclic load actions;

[0034] Based on impulse equivalence, the cyclic load and equivalent constant load are equal to the area enclosed by the horizontal axis of the coordinate, as shown in formula (5):

[0035]

[0036] The constant load σ0 equivalent to the half-sine cyclic load of each cycle can be obtained, as shown in formula (6):

[0037]

[0038] Among them, π is the ratio of a circle to its circumference.

[0039] Furthermore, the derivation process of the roadbed soil deformation expression in the one-dimensional case is as follows:

[0040] The creep compliance J(t) of the viscoelastic element at time t is expressed as:

[0041]

[0042] Where: E0 is the elastic modulus of the viscoelastic element, E1 is the viscoelastic modulus of the viscoelastic element, η1 is the viscosity coefficient of the viscoelastic element;

[0043] Then the strain ε(t) corresponding to the time t after unloading is:

[0044]

[0045] Where σ0 is a constant load equivalent to the half-sine cyclic load of each cycle, J(t-t1) represents the creep compliance of the viscoelastic element at time t-t1;

[0046] For cyclic loads, the residual viscoelastic deformation ε after the i-th half-sine cyclic load lasts for [(Ni)T+t2] to the end of the N-th half-sine cyclic load period is Ni for:

[0047]

[0048] Where: T is the cyclic load period, N is the number of cyclic load actions, and t2 is the load interval time in each cycle;

[0049] Then, the total residual viscoelastic deformation ε generated by N cyclic loading is N for:

[0050]

[0051] In order to obtain a clear analytical form of equation (10), the residual viscoelastic deformation rate corresponding to the Nth cyclic load is constructed as:

[0052]

[0053] Considering that the number of cyclic load actions N changes continuously, the integral of equation (11) is supplemented with the condition that the residual viscoelastic deformation is also 0 when the number of load actions N is 0. At the same time, combined with the constant load σ0, the cyclic stress amplitude σ is obtained. max The one-dimensional residual viscoelastic deformation ε is represented by Rve for:

[0054]

[0055] The plastic friction plate of the non-integer order viscoplastic element is not triggered during the load interval, that is, the actual action time of the cyclic load on the viscoplastic element is L = Nt1, and the one-dimensional viscoplastic deformation ε corresponding to the non-integer order viscoplastic element is vp As shown in formula (13):

[0056]

[0057] Where: σ is the stress of the viscoplastic element, σ s is the yield stress of the viscoplastic element, η2 is the viscosity coefficient of the viscoplastic element, β is the non-integer order of the viscoplastic element, and Γ is the Gamma function;

[0058] Substituting L=Nt1 and constant load σ0 into equation (13), we can obtain the cyclic stress amplitude σ max The one-dimensional viscoplastic deformation ε is represented by vp As shown in formula (14):

[0059]

[0060] Furthermore, the process of the unified characterization formula of the three-dimensional roadbed soil cumulative plastic strain under the extended dynamic cyclic load is as follows:

[0061] The stress deviator S ij Instead of the stress in equation (12), ij represents the direction in the three-dimensional stress space, and the viscoelastic modulus E1 in equation (12) is replaced by the viscoelastic shear modulus G1 in the three-dimensional case, and the three-dimensional residual viscoelastic deformation is obtained: for:

[0062]

[0063] For non-integer-order viscoplastic elements, the yield function and plastic potential function are introduced to obtain the three-dimensional viscoplastic deformation for:

[0064]

[0065] Where: F is the yield function of the soil, F0 is the initial value of the yield function of the soil, ψ is the power function, Q is the plastic potential function, σ ij is the component of the stress σ of the viscoplastic element in the ij direction in the three-dimensional coordinates;

[0066] Using the associated flow law, the yield function F is equal to the plastic potential function Q, and equation (16) is transformed into:

[0067]

[0068] The yield function is the Drucker-Prager yield criterion, and the expression under triaxial compression is:

[0069]

[0070] Where: I1 is the first stress invariant, J2 is the second stress deviator invariant, α and K are two parameters in the Drucker-Prager yield function, c is the total cohesion of the soil, is the total internal friction angle of the soil;

[0071] When the roadbed soil cumulative plastic strain test is loaded, the confining pressure σ3 is equal to the intermediate principal stress σ2, so:

[0072]

[0073]

[0074] I1=3σ m =σ1+2σ3 (21)

[0075]

[0076] Where: m is the mean principal stress, S 11 is the stress deviator tensor in the z direction in three-dimensional coordinates;

[0077] Combining equations (15), (17) to (22) and setting the initial value of the yield function F0 = 1, we can obtain the accumulated plastic strain ε of the subgrade soil: p A unified representation formula for .

[0078] Furthermore, the process of constructing the parameters of the unified characterization formula of the roadbed soil cumulative plastic strain and the multivariate regression equation of the working conditions is as follows:

[0079] Conduct static triaxial test:

[0080] The static triaxial test adopts the unconsolidated and undrained loading method. The test ends when the axial strain reaches 15%. The test scheme is shown in the following table:

[0081] Moisture content / OMC Confining pressure / kPa Compaction degree / % <![CDATA[Shear rate / %·min -1 <!-- 5 -->]]> 1.0、1.2、1.4、1.6 30、60、90、120 87、90、93、96 0.8

[0082] The shear strength parameters of soil samples at different moisture contents and compaction degrees, namely, total cohesion c and total internal friction angle, were calculated by the Mohr-Coulomb strength criterion.

[0083] Conduct dynamic triaxial test:

[0084] The accumulative plastic strain test loading method of the roadbed soil considering the actual stress state and service history as mentioned above is adopted for load loading. Among them, the test scheme of cyclic load loading is shown in the table below. The cyclic load is applied in the form of a half-sine wave. Each working condition is repeated 10,000 times under undrained conditions. When the accumulative plastic strain of the soil sample reaches 5%, the loading is stopped. The accumulative plastic strain test results of the soil samples under different moisture contents, compaction degrees, cyclic stress amplitudes, confining pressures, load action times, and load interval times are obtained:

[0085]

[0086]

[0087] Among them, Group A investigated the effect of moisture content on the cumulative plastic strain of soil samples, Group B investigated the effect of compaction degree on the cumulative plastic strain of soil samples, Group C investigated the effect of cyclic stress amplitude on the cumulative plastic strain of soil samples, Group D investigated the effect of confining pressure on the cumulative plastic strain of soil samples, Group E investigated the effect of load action time on the cumulative plastic strain of soil samples, Group F investigated the effect of load intermittent time on the cumulative plastic strain of soil samples, and Group G was compared with Group D to understand the difference in cumulative plastic strain of soil samples caused by different contact stresses.

[0088] The algorithm combining Macquart and general global optimization is adopted to identify the parameters of the unified characterization formula of the cumulative plastic strain of the subgrade soil based on the above-mentioned static triaxial test and dynamic triaxial test results. A data point is extracted from the cumulative plastic strain test curve of the subgrade soil under each working condition at a certain interval of cyclic loading times for fitting, and the parameter fitting results of the unified characterization formula of the cumulative plastic strain of the subgrade soil corresponding to different moisture contents, compaction degrees, cyclic stress amplitudes, confining pressures, load action times, and load interval times are obtained.

[0089] Based on the parameter fitting results of the unified characterization formula for cumulative plastic strain of subgrade soil corresponding to different moisture contents, compaction degrees, cyclic stress amplitudes, confining pressures, load action time and load intermittent time, the variation law of each parameter in the unified characterization formula for cumulative plastic strain of subgrade soil with each influencing factor is obtained. Based on this, different function forms are selected to establish the regression relationship between each parameter in the unified characterization formula for cumulative plastic strain of subgrade soil and moisture content, compaction degree, cyclic stress amplitude, confining pressure, load action time and load intermittent time.

[0090] Furthermore, the unified characterization formula of the accumulated plastic strain of the roadbed soil is as follows:

[0091]

[0092] Where: ε 11 is the strain in the z direction in three-dimensional coordinates, is the residual viscoelastic deformation in the z direction in three-dimensional coordinates, is the viscoplastic deformation in the z direction in three-dimensional coordinates, σ max is the cyclic stress amplitude, η1 is the viscosity coefficient of the viscoelastic element, η2 is the viscosity coefficient of the viscoplastic element, Γ is the Gamma function, t1 is the load action time in each cycle, T is the cyclic load period, N is the number of cyclic load actions, G1 is the viscoelastic shear modulus of the viscoelastic element in three dimensions, π is the circumference of the circle, 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, and σ3 is the confining pressure.

[0093] Furthermore, the parameters of the unified characterization formula for the cumulative plastic strain of the roadbed soil and the multivariate regression equation of the working conditions are as follows:

[0094]

[0095]

[0096]

[0097]

[0098] Where: G1 is the viscoelastic shear modulus of the viscoelastic element in three dimensions, 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, w is the actual moisture content, OMC is the optimal moisture content, K is the compaction degree, σ max is the cyclic stress amplitude, σ3 is the confining pressure, t1 is the load action time in each cycle, and t2 is the load interval time in each cycle.

[0099] The beneficial effects of the embodiments of the present invention are:

[0100] 1. According to the actual stress state of the subgrade soil, it is confirmed that the influence of the overlying static load generated by the deadweight of the pavement and subgrade on the cumulative plastic strain of the subgrade soil changes with the static earth pressure coefficient of the subgrade soil, and the contact stress determination method during the cumulative plastic strain test of the subgrade soil is clarified; according to the pavement structure construction process after the subgrade is completed, and the rigid requirement that the deformation of the subgrade must be stable before the road is opened to traffic, the constant load size and constant load duration of the constant load test on the soil sample before the cyclic load is applied are determined; furthermore, a loading mode for the cumulative plastic strain test of the subgrade soil is comprehensively formed considering the actual stress state and service history, which solves the problem of inaccurate cumulative plastic strain test of the subgrade soil;

[0101] 2. Based on the essential mechanism and formation principle of the cumulative plastic strain of subgrade soil under cyclic loading, elastic, viscoelastic and viscoplastic elements are used to describe the various deformations that constitute the cumulative plastic strain of subgrade soil respectively, and a characterization component of the cumulative plastic strain of subgrade soil is established. According to the principle of viscoelastic-plastic mechanics, the characterization formula of the cumulative plastic strain of subgrade soil is obtained, and a unified characterization of the cumulative plastic strain of all types of subgrade soil is achieved. The established characterization formula contains only four parameters, G1, η1, β, and η2, and each parameter has a clear physical meaning. A multivariate regression equation of G1, η1, β, η2 and moisture content, compaction degree, cyclic stress amplitude, confining pressure, load action time, and load interval time is established, which realizes the accurate characterization of the cumulative plastic strain of subgrade soil under tens of thousands of cyclic loadings under any combination of working conditions under the premise of a unified characterization formula, and the calculation cost is low, which solves the problems of low accuracy, limited applicability, and difficulty in selection and application in actual engineering design of the existing characterization method of cumulative plastic strain of subgrade soil. BRIEF DESCRIPTION OF THE DRAWINGS

[0102] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0103] Figure 1 It is the actual stress state of the roadbed soil in the embodiment of the present invention.

[0104] Figure 2 It is the static load test result of the subgrade soil under the condition of confining pressure with contact stress in the embodiment of the present invention.

[0105] Figure 3 This is the cumulative plastic strain test loading mode of the roadbed soil formed in the embodiment of the present invention.

[0106] Figure 4 It is a characterization component of the accumulated plastic strain of the roadbed soil in the embodiment of the present invention.

[0107] Figure 5 It is the cyclic load and equivalent constant load borne by the roadbed soil in the embodiment of the present invention.

[0108] Figure 6 It is the shear strength parameter test result of the roadbed soil at different moisture contents in the embodiment of the present invention.

[0109] Figure 7 It is the shear strength parameter test result of the roadbed soil under different compaction degrees in the embodiment of the present invention.

[0110] Figure 8 It is the cumulative plastic strain test result of the roadbed soil at different moisture contents in the embodiment of the present invention.

[0111] Fig. 9 It is the cumulative plastic strain test result of the roadbed soil under different compaction degrees in the embodiment of the present invention.

[0112] Fig.10 It is the cumulative plastic strain test result of the roadbed soil under different cyclic stress amplitudes in the embodiment of the present invention.

[0113] Fig.11 It is the cumulative plastic strain test result of the roadbed soil under different confining pressures in the embodiment of the present invention.

[0114] Fig.12 It is the cumulative plastic strain test result of the roadbed soil under different load action times in the embodiment of the present invention.

[0115] Fig.13 It is the cumulative plastic strain test result of the roadbed soil under different load interval times in the embodiment of the present invention.

[0116] Fig.14 It is the cumulative plastic strain test result of the roadbed soil under different contact stresses in the embodiment of the present invention.

[0117] Fig.15 It is the cumulative plastic strain test result of the roadbed soil under the random working condition supplemented in the embodiment of the present invention.

[0118] Fig.16 It is the evolution mode of the parameter G1 of the formula for characterizing the cumulative plastic strain of the roadbed soil in the embodiment of the present invention.

[0119] Fig.17 It is the evolution mode of the parameter η1 of the formula for characterizing the cumulative plastic strain of the roadbed soil in the embodiment of the present invention.

[0120] Fig.18 It is the evolution mode of the parameter β of the formula for characterizing the accumulated plastic strain of the roadbed soil in the embodiment of the present invention.

[0121] Fig.19 It is the evolution mode of the parameter η2 of the formula for characterizing the cumulative plastic strain of roadbed soil in the embodiment of the present invention.

[0122] Fig. 20 It is the regression equation accuracy of parameter G1 of the roadbed soil cumulative plastic strain characterization formula in the embodiment of the present invention.

[0123] Fig.21 It is the regression equation accuracy of the parameter η1 of the roadbed soil cumulative plastic strain characterization formula in the embodiment of the present invention.

[0124] Fig. 22It is the regression equation accuracy of the parameter β in the formula for characterizing the cumulative plastic strain of the roadbed soil in the embodiment of the present invention.

[0125] Fig.23 It is the regression equation accuracy of the parameter η2 of the roadbed soil cumulative plastic strain characterization formula in the embodiment of the present invention.

[0126] Fig.24 This is the verification result of the applicability of the cumulative plastic strain characterization formula of roadbed soil in the embodiment of the present invention to high liquid limit clay.

[0127] Fig.25 This is the verification result of the applicability of the cumulative plastic strain characterization formula of roadbed soil in the embodiment of the present invention to low liquid limit clay.

[0128] Fig.26 This is the verification result of the applicability of the cumulative plastic strain characterization formula of roadbed soil in the embodiment of the present invention to coarse-grained soil.

[0129] Fig. 27 This is the result of verifying the applicability of the cumulative plastic strain characterization formula for roadbed soil in the embodiment of the present invention to silty clay. DETAILED DESCRIPTION

[0130] The following will be combined with the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0131] Example 1

[0132] This embodiment proposes a method for testing the cumulative plastic strain of roadbed soil that takes into account the actual stress state and service history. When testing the cumulative plastic strain of roadbed soil, the actual occurrence characteristics of the soil in the roadbed should be restored as realistically as possible. Under the basic condition of transverse isotropy, the stress state of the soil unit in the roadbed is as follows: Figure 1 As shown, it is constrained by the confining pressure σ3 in the lateral direction and the dynamic load σ d , overlying static load σ c , and confining pressure σ3 act together. Among them, the vehicle dynamic load σ d It is a reciprocating load that causes the roadbed soil to produce cumulative plastic strain during a large number of cycles of loading and unloading. c It always exists due to the deadweight of the road surface and soil. Therefore, it is necessary to reasonably determine the static and dynamic load levels during the loading process, especially the contact stress σ simulating the overlying static load c setting level.

[0133] according to Figure 1, the static load condition of any soil unit in the roadbed can be expressed by formula (1):

[0134] σ c +σ3=ρgh (1)

[0135] Where: ρ can be regarded as the comprehensive density of the upper soil layer and pavement structure of any soil unit in the roadbed, g is the gravitational acceleration, and h is the distance between the soil unit and the top surface of the surface layer.

[0136] At the same time, the confining pressure σ3 and the static earth pressure coefficient K0 have the following relationship:

[0137] σ3=K0ρgh (2)

[0138] From equations (1) and (2), we can get the contact stress σ c The relationship between it and the confining pressure σ3 is shown in formula (3):

[0139]

[0140] Formula (3) clearly shows that the contact stress σ c The size of is directly dependent on the static earth pressure coefficient K0.

[0141] In this embodiment, common clay in Changsha, Hunan, is selected, and its static earth pressure coefficient K0 is 0.56. Substituting the K0 value of Changsha clay into formula (3), the contact stress σ of Changsha clay in the cumulative plastic strain test is calculated. c =0.8σ3. It can be seen that the existing technology sets the contact stress to 0, 0.2σ3, and 15kPa without considering the performance differences of the soil itself. In other words, the difference in the overlying static load caused by the different static earth pressure coefficients of various types of roadbed soils is not reasonably reflected in the existing loading method.

[0142] In actual roadbed engineering, the roadbed is first compacted and filled to the design elevation, and then the deflection and compaction of the roadbed top surface are tested. Only after the test is qualified can the subbase, base layer, surface layer and other pavement structure layers be paved, and the roadbed structure will be put into operation immediately after the inspection is completed. Therefore, between the end of the compaction and filling of the roadbed and the opening to traffic, the roadbed will produce creep deformation under the action of the overlying static load due to the construction and deadweight of the pavement structure layer, and the actual history of the roadbed structure corresponds one by one to the loading steps of the dynamic triaxial test of the roadbed soil, and the following loading method for the cumulative plastic strain test of the roadbed soil considering the actual stress state and service history is obtained:

[0143] The test specimens are statically compacted in layers (e.g. 5 layers) to the target compaction degree to simulate the actual filling process of the roadbed;

[0144] Contact stress is used to simulate the overlying static load, and the specimen is statically loaded to simulate the creep deformation of the roadbed during the pavement structure construction;

[0145] Cyclic loads are applied to the specimens to simulate the dynamic loads on the roadbed during operation.

[0146] It is necessary to determine the time when the creep deformation of the roadbed soil under static load no longer increases in order to reproduce the engineering standards and hard conditions that the static load deformation of the roadbed must be stable before it is opened to traffic in actual projects.

[0147] In order to reveal the influence of complex conditions on the static load deformation of roadbed soil, it is often necessary to set different test levels for multiple influencing factors during research. Considering that the time required for the soil sample to reach a stable state under static load will vary due to different moisture content, compaction degree, and confining pressure, it is impossible to determine the different durations of soil sample deformation reaching a stable state under dozens of different working conditions through experiments before applying cyclic loads. Therefore, it is necessary to find a static load time that can ensure that the deformation of soil samples under all working conditions can reach a stable state. Analysis shows that the higher the moisture content and the lower the compaction degree, the longer the deformation stability time of the soil sample, but the law of influence of confining pressure cannot be directly judged. Due to the overlying static load σ c =0.8σ3. As the confining pressure increases, although the constraint effect against deformation is enhanced, the overlying load that causes deformation also increases. Similarly, this problem also exists when the confining pressure decreases. Therefore, it is necessary to carry out tests for both high and low confining pressures. The common clay in Changsha, Hunan, was still used. Two cylindrical specimens with a diameter of 100mm and a height of 200mm were prepared by a 5-layer static pressure method. The moisture content of the specimens was 1.6OMC and the compaction degree was 87%. The Dynatriax-100 / 14 triaxial testing system was used to carry out a controlled stress (0.8σ3) constant load test. The test confining pressures were 30kPa and 120kPa respectively. The constant load time (60min) was set for trial. If the stable state is not reached after the constant load time, the sample is re-prepared and the constant load time is continued to increase until the deformation stability time is found. The test results are as follows Figure 2 As shown, the relationship between static load axial deformation and static load time under 30kPa and 120kPa confining pressure levels is given, where x is the horizontal axis independent variable, i.e., static load time, and y is the vertical axis independent variable, i.e., static load axial deformation. It can be seen that the static load deformation under a confining pressure of 120kPa is greater than that under a confining pressure of 30kPa, and the time taken for the specimen to deform to a stable state is also longer. In order to avoid the influence of sample preparation errors, the static load time can be uniformly taken as 60min to ensure that the static load deformation of soil samples under all working conditions can reach a stable state. The above analysis clarifies the magnitude of the contact stress and the duration of the static load, based on which a relationship can be formed. Figure 3 The cumulative plastic strain test loading mode shown in the figure reproduces the actual stress state and service history of the roadbed soil. In the figure, the loading of σ3 simulates the lateral and upper constraints on the roadbed soil during the actual roadbed filling process, and σ cThe loading simulates the creep deformation of the roadbed during the pavement structure construction process. The subsequent cyclic load loading simulates the dynamic load of the roadbed during operation. T is the cyclic load period, t1 is the load action time in each cyclic load period, t2 is the load interval time in each cyclic load period, and σ max is the cyclic stress amplitude, and other symbols have the same meanings as above.

[0148] Example 2

[0149] This embodiment provides a method for characterizing the cumulative plastic strain of roadbed soil taking into account the actual stress state and service history.

[0150] For the accumulated plastic strain of subgrade soil, the most important thing to pay attention to is the deformation at the end of each cyclic loading cycle. Since the elastic deformation has been restored at the moment of unloading, the deformation at the end of each cycle is the sum of the unrecovered residual viscoelastic deformation generated by the viscoelastic element and the viscoplastic deformation generated by the viscoplastic element. In order to characterize the essential mechanism and formation principle of the accumulated plastic strain of subgrade soil, we first constructed Figure 4 The characterization component of the accumulated plastic strain of the roadbed soil shown in the figure uses a spring with an elastic modulus of E0 to represent the elastic deformation, a spring with an elastic modulus of E1 and a viscosity pot with a viscosity coefficient of η1 in parallel to represent the viscoelastic deformation, and these two parts are connected in series to form a viscoelastic element; in addition, a yield stress of σ is used s The plastic friction plate is connected in parallel with a viscosity pot with a viscosity coefficient of η2 and a non-integer order of β to form a viscoplastic element to represent viscoplastic deformation. Its working principle is that when the stress σ of the model is greater than the yield stress σ of the plastic friction plate s When the plastic friction plate closes, the viscoplastic element starts to work, and the viscoplastic deformation accumulates. Figure 4As shown, the viscoelastic element is connected to the viscoplastic element, which comprehensively characterizes the elastic deformation, viscoelastic deformation and viscoplastic deformation. It should be noted that the traditional viscoelastic element and viscoplastic element are both integer-order linear elements, which are obtained by combining linear springs or viscoelastic pots. The linear characteristics of the basic elements make it impossible to describe nonlinear deformation in any combination. Therefore, such elements cannot be used to describe the nonlinear cumulative plastic strain of the roadbed soil. This embodiment breaks through this traditional cognitive limitation for the first time, and uses a combination of elements to characterize the nonlinear cumulative plastic strain of the roadbed soil. The order of the viscoelastic element is changed to a non-integer order, thereby changing the order of the viscoplastic element to a non-integer order, so that it is between the fluid deformation when the order is 0 and the linear deformation when the order is 1, and theoretically achieves applicability to nonlinear deformation. However, since non-integer-order elements are used to describe nonlinear deformation for the first time, the traditional integer-order element expression is no longer applicable. At the same time, the combined element is strictly only applicable to simulating the one-dimensional deformation of materials under static constant loads, and is not applicable to the description of the three-dimensional cumulative plastic strain of roadbed soil under dynamic cyclic loads. The derivation Figure 4 The expression of the characterization component shown in the figure becomes a technical difficulty that must be overcome. To this end, based on the characterization component of the accumulated plastic strain of the subgrade soil, Figure 5 The cyclic loads shown are converted to constant loads, and then the expressions for the deformation of the subgrade soil are derived for the one-dimensional case and extended to the three-dimensional case.

[0151] The driving cyclic load is applied to the roadbed structure in the form of a half-sine wave, and the cyclic load is converted into a constant load using a piecewise function such as formula (4):

[0152]

[0153] Where: t is the deviatoric stress at time t, σ max is the cyclic stress amplitude, t1 is the load action time in each cyclic load cycle, T is the cyclic load period, and N is the number of cyclic load actions.

[0154] Based on impulse equivalence, the cyclic load and equivalent constant load are equal to the area enclosed by the horizontal axis of the coordinate, as shown in formula (5):

[0155]

[0156] The constant load σ0 equivalent to the half-sine cyclic load of each cycle can be obtained, as shown in formula (6):

[0157]

[0158] Among them, π is the ratio of a circle to its circumference.

[0159] The derivation process of the roadbed soil deformation expression in one-dimensional case is as follows:

[0160] First, the viscoelastic deformation is analyzed. Figure 4 The creep compliance J(t) of the viscoelastic element shown can be expressed as:

[0161]

[0162] Wherein: E0 is the elastic modulus of the viscoelastic element, E1 is the viscoelastic modulus of the viscoelastic element, η1 is the viscosity coefficient of the viscoelastic element, e is a natural constant, and the other symbols have the same meanings as above.

[0163] The deformation of the subgrade soil at time t is the sum of all load responses during the entire loading process. Therefore, if the constant load σ0 is Figure 5 The action stops at time t1, which is equivalent to applying a stress equal to and opposite to the constant load σ0. Then the strain ε(t) corresponding to the time t after unloading is:

[0164]

[0165] Wherein, J(t-t1) represents the creep compliance of the viscoelastic element at time t-t1.

[0166] For cyclic loads, the residual viscoelastic deformation ε after the i-th half-sine cyclic load lasts for [(Ni)T+t2] to the end of the N-th half-sine cyclic load period is Ni for:

[0167]

[0168] Where: t2 is the load interval time in each cycle, and other symbols have the same meanings as above.

[0169] Then, the total residual viscoelastic deformation ε generated by N cyclic loading is N for:

[0170]

[0171] In order to obtain a clear analytical form of equation (10), the residual viscoelastic deformation rate corresponding to the Nth cyclic load is constructed as:

[0172]

[0173] Considering that the number of cyclic load actions N changes continuously, the integral of equation (11) and the condition that the residual viscoelastic deformation is also 0 when the number of load actions N is 0 are added. At the same time, combined with equation (6), the cyclic stress amplitude σ can be obtained: max The one-dimensional residual viscoelastic deformation ε is represented by Rve for:

[0174]

[0175] Secondly, considering the viscoplastic deformation, it is noted that Figure 4 The plastic friction plate of the non-integer-order viscoplastic element is not triggered during the load interval (the load during the load interval is 0, which is less than the yield stress σ of the plastic friction plate). s , so the plastic friction plate cannot be triggered), that is, the actual action time of the cyclic load on the viscoplastic element is L = Nt1, and the one-dimensional viscoplastic deformation ε corresponding to the non-integer order viscoplastic element vp As shown in formula (13):

[0176]

[0177] Where: σ is the stress of the viscoplastic element, σ s is the yield stress of the viscoplastic element, η2 is the viscosity coefficient of the viscoplastic element, β is the non-integer order of the viscoplastic element, and Γ is the Gamma function.

[0178] Substituting L = Nt1 and equation (6) into equation (13) (σ = σ0), the cyclic stress amplitude σ can be obtained max The one-dimensional viscoplastic deformation ε is represented by vp As shown in formula (14):

[0179]

[0180] The process of expanding the unified characterization formula of three-dimensional roadbed soil cumulative plastic strain under dynamic cyclic loading is as follows:

[0181] The constitutive equations of the components in one dimension and three dimensions are similar in form. Based on this, the stress deviator S ij Instead of the stress in equation (12), ij represents the direction in the three-dimensional stress space, and ij represents the normal direction on the plane. For example, ij is 11, which represents the z direction of the three-dimensional coordinate (perpendicular to the xy plane). At the same time, the viscoelastic modulus E1 in equation (12) is replaced by the viscoelastic shear modulus G1 in the three-dimensional case, and the three-dimensional residual viscoelastic deformation is obtained. for:

[0182]

[0183] For non-integer-order viscoplastic elements, the existence of plastic friction plates cannot be directly analogized to the one-dimensional form. The yield function and plastic potential function are introduced to obtain the three-dimensional viscoplastic deformation for:

[0184]

[0185] Where: F is the yield function of the soil, F0 is the initial value of the yield function of the soil, ψ is the power function (the power is usually 1), Q is the plastic potential function, σ ij It is the component of the stress σ of the viscoplastic element in the ij direction in the three-dimensional coordinates. The other symbols have the same meanings as above.

[0186] Using the associated flow law, the yield function F is equal to the plastic potential function Q, and equation (16) is transformed into:

[0187]

[0188] The yield function is the Drucker-Prager yield criterion, and the expression under triaxial compression is:

[0189]

[0190] Where: I1 is the first stress invariant, J2 is the second stress deviator invariant, α and K are two parameters in the Drucker-Prager yield function, c is the total cohesion of the soil, is the total internal friction angle of the soil.

[0191] When the roadbed soil cumulative plastic strain test is loaded, the confining pressure σ3 is equal to the intermediate principal stress σ2, so:

[0192]

[0193]

[0194] I1=3σ m =σ1+2σ3 (21)

[0195]

[0196] Where: m is the mean principal stress, S 11 is the stress deviator tensor in the z direction in three-dimensional coordinates.

[0197] Considering that the accumulated plastic strain of soil under cyclic loading has a typical response of axial increase, the first principal strain, i.e., the strain ε in the z direction in the three-dimensional coordinates, is used as 11 By analyzing (15), (17) to (22) and setting the initial value of the yield function F0 = 1, the accumulated plastic strain ε of the subgrade soil is obtained: p The unified characterization formula is:

[0198]

[0199] Where: is the residual viscoelastic deformation in the z direction in three-dimensional coordinates, is the viscoplastic deformation in the z direction in three-dimensional coordinates.

[0200] The process of constructing the multivariate regression equation of parameters and working conditions for the unified characterization formula of roadbed soil cumulative plastic strain is as follows:

[0201] Taking the common clay in Changsha, Hunan as an example, this paper specifically explains how to construct the parameters of the unified characterization formula for the cumulative plastic strain of roadbed soil and the multivariate regression equation of working conditions. Referring to JTG 3430-2020 "Highway Geotechnical Test Code", the limit moisture content, optimal moisture content, maximum dry density, particle grading and specific gravity of the soil samples in the embodiment shown in Table 1 were measured.

[0202] Table 1 Basic engineering properties parameters of soil samples in the examples

[0203]

[0204] From the analysis of formula (23), it can be seen that the unified characterization formula for the cumulative plastic strain of the subgrade soil derived in this embodiment contains both the shear strength parameters, namely, the total cohesion c of the soil and the total internal friction angle And the dynamic index, namely the soil accumulated plastic strain ε p Therefore, it is necessary to carry out a static triaxial test to obtain the shear strength parameters, and based on the cumulative plastic strain test loading method of the subgrade soil considering the actual stress state and service history of Example 1, a dynamic triaxial test is carried out to test the cumulative plastic strain of the test sample.

[0205] The unsaturated subgrade soil compacted at the optimum moisture content (OMC) has a moisture content that increases during the operation period due to the continuous influence of alternating sunny and rainy weather and eventually stabilizes near the equilibrium moisture content. Based on a large amount of field measurements and indoor test data, the equilibrium moisture content of clay is about 0.9 times the plastic limit. For this reason, this embodiment sets the moisture content of the specimens to 1.0 OMC, 1.2 OMC, 1.4 OMC, and 1.6 OMC in combination with the test results in Table 1 to represent the possible humidity range in the clay subgrade. As the moisture content increases, the compaction degree of the subgrade soil also decreases. Considering the sample preparation error and the obvious regularity, the compaction degree of the specimens is set to 87%, 90%, 93%, and 96%. During specimen preparation, 5 layers were evenly statically pressed into cylindrical specimens with a diameter of 100 mm and a height of 200 mm. After the first 4 layers were compacted, the surface was roughened with a scraper to ensure close connection between layers. After sample preparation, the specimen was wrapped with plastic wrap and left to stand for 1 to 3 days to ensure uniform humidity of the specimen, and then static and dynamic triaxial tests were carried out.

[0206] Static triaxial test:

[0207] Taking into account the over-consolidation stress history of the soil during the compaction process and the low permeability characteristics of clay, consolidation and drainage generally only occur during the roadbed filling stage. Therefore, the static triaxial test adopts a non-consolidation and non-drainage loading method. The axial loading rate is 0.8% / min, and the test ends when the axial strain reaches 15%. The test confining pressure is 30kPa, 60kPa, 90kPa, and 120kPa, and it is carried out in the Dynatriax 100 / 14 static and dynamic triaxial system produced by Controls / WF, Italy. The test scheme is shown in Table 2. According to the results of the static triaxial test, the shear strength parameters of the example soil samples at different moisture contents and compaction degrees, namely the total cohesion c and the total internal friction angle, were calculated by the Mohr-Coulomb strength criterion. like Figure 6 and Figure 7 As shown, it can be seen that as the moisture content increases or the compaction degree decreases, the total cohesion and the total internal friction angle of the soil sample in the embodiment decrease accordingly.

[0208] Table 2 Static triaxial test scheme

[0209] Moisture content / OMC Confining pressure / kPa Compaction degree / % <![CDATA[Shear rate / %·min -1 > 1.0、1.2、1.4、1.6 30、60、90、120 87、90、93、96 0.8

[0210] Dynamic triaxial test:

[0211] The load loading is carried out by the cumulative plastic strain test loading method of the subgrade soil considering the actual stress state and service history described in Example 1. The stress level is one of the key conditions of the dynamic triaxial test. The confining pressure of 30-120 kPa and the cyclic stress amplitude of 40-130 kPa can basically cover the actual stress level of the subgrade soil in my country, including the overweight situation. Therefore, the test confining pressure is selected as 30 kPa, 60 kPa, 90 kPa, 120 kPa, and the cyclic stress amplitude is selected as 40 kPa, 70 kPa, 100 kPa, and 130 kPa. Under the typical asphalt pavement structure in my country, the load action time at different depths inside the subgrade at different driving speeds is 0.4s-4.0s, and the load interval time is 0-3.0s. As for the load action time, it is also necessary to consider the possible overspeed phenomenon in actual situations, so a 0.2s test level is added, and the load action time is set to 0.2s, 0.6s, 1.4s, 2.6s, and 4.2s respectively. As for the load interval time, it is also necessary to consider the situation where the actual vehicle distance is greater than the minimum safe vehicle distance, so a 4.0s test level is added, and the load interval time is set to 0, 0.8s, 1.8s, 3.0s, and 4.0s respectively. The dynamic triaxial test was still carried out in the Dynatriax100 / 14 static and dynamic triaxial system produced by Controls / WF Company of Italy. The test scheme of cyclic load loading is shown in Table 3. The cyclic load was applied in the form of a half-sine wave. Each working condition was repeated 10,000 times under undrained conditions. When the cumulative plastic strain of the soil sample reached 5%, the loading was stopped. The cumulative plastic strain test results of the soil samples under different moisture contents, compaction degrees, cyclic stress amplitudes, confining pressures, load action time, and load interval time were obtained. In Table 3: Group A investigates the effect of moisture content on the cumulative plastic strain of the soil samples of the embodiment; Group B investigates the effect of compaction degree on the cumulative plastic strain of the soil samples of the embodiment; Group C investigates the effect of cyclic stress amplitude on the cumulative plastic strain of the soil samples of the embodiment; Group D investigates the effect of confining pressure on the cumulative plastic strain of the soil samples of the embodiment; Group E investigates the effect of load action time on the cumulative plastic strain of the soil samples of the embodiment; Group F investigates the effect of load intermittent time on the cumulative plastic strain of the soil samples of the embodiment; Group G is compared with Group D to clearly understand the difference in cumulative plastic strain of the soil samples of the embodiment due to different contact stresses.

[0212] Table 3 Dynamic triaxial test scheme

[0213]

[0214] According to the dynamic triaxial test results, the cumulative plastic strain test results of the soil samples of the embodiment under different moisture contents, compaction degrees, cyclic stress amplitudes, confining pressures, load action times, and load interval times are as follows: Figure 8 to Figure 13As shown. It can be seen that the cumulative plastic strain of the roadbed soil presents three obvious characteristics: state sensitivity. The increase in moisture content not only leads to an increase in the cumulative plastic strain, but also changes from a stable state to an unstable creep state when it exceeds a certain level. At the same time, the cumulative plastic strain decreases significantly with the increase in compaction degree; stress dependence. When the cyclic stress amplitude increases or the confining pressure decreases, the cumulative plastic strain increases accordingly, and the development rate accelerates; time correlation. The longer the load action time and the shorter the load interval time, the greater the cumulative plastic strain. However, the influence of the load interval time has a critical value, and the cumulative plastic strain remains basically unchanged beyond this critical value. In addition, the cumulative plastic strain test results of the soil samples of the embodiment under different contact stresses are shown as follows. Fig.14 It can be clearly observed that the contact stress under the four confining pressure levels is 0.2 times the confining pressure (σ c =0.2σ3) is significantly greater than the cumulative plastic strain obtained when the contact stress is 0.8 times the confining pressure (σ c =0.8σ3). Taking the results after 10,000 cycles of loading as an example, the cumulative plastic strain corresponding to the contact stress of 0.2 times the confining pressure under confining pressures of 30kPa, 60kPa, 90kPa, and 120kPa is 7.2 times, 11.4 times, 9.8 times, and 10.3 times the contact stress of 0.8 times the confining pressure, respectively. This test result proves that the existing technology does not set the contact stress or uses 15kPa and 0.2 times the confining pressure as the contact stress, which is significantly different from the cumulative plastic strain results obtained by the loading method that considers the influence of different degrees of overlying static loads.

[0215] In actual situations, as the depth increases, the overburden static load on the roadbed soil gradually increases, and it lasts throughout the entire process of the vehicle load during the operation period. Therefore, when using contact stress to simulate the overburden static load, the contact stress value method related to the static soil pressure coefficient K0 proposed in this embodiment should be used. For roadbed soils of different depths, due to the attenuation characteristics of the vehicle dynamic load from top to bottom, the corresponding cumulative plastic strain gradually decreases with increasing depth, which also explains Fig.14 According to the experimental law in , the greater the contact stress, the greater the corresponding overlying static load, that is, the deeper the corresponding roadbed depth, the smaller the cumulative plastic strain result.

[0216] The algorithm combining Macquart and general global optimization is used to identify the parameters of the unified characterization formula of the accumulated plastic strain of the subgrade soil shown in formula (23) based on the above static triaxial test and dynamic triaxial test results. In order to achieve better fitting results, the test curve of the accumulated plastic strain of the subgrade soil under each working condition is extracted for fitting every certain number of cyclic loading (such as 200 times). The fitting results of the unified characterization formula of the accumulated plastic strain of the subgrade soil corresponding to different water content, compaction degree, cyclic stress amplitude, confining pressure, load action time, and load interval time are shown in Tables 4 to 9.

[0217] Table 4 Parameter fitting results of unified characterization formula for accumulated plastic strain of subgrade soil at different moisture contents

[0218] Moisture content / OMC <![CDATA[G1(MPa)]]> <![CDATA[η1(MPa·s)]]> β <![CDATA[η2(MPa·s)]]> <![CDATA[R 2 ]]> 1.0 30.21 11.99 0.268 53.07 99.67 1.2 15.32 10.02 0.215 10.09 99.89 1.4 5.74 8.01 0.162 1.08 99.62 1.6 0.61 7.33 0.103 0.61 98.71

[0219] Table 5 Parameter fitting results of unified characterization formula for accumulated plastic strain of subgrade soil under different compaction degrees

[0220] Compactness(%) <![CDATA[G1(MPa)]]> <![CDATA[η1(MPa·s)]]> β <![CDATA[η2(MPa·s)]]> <![CDATA[R 2 ]]> 87 0.62 3.09 0.022 0.71 98.84 90 1.31 5.92 0.110 0.82 99.30 93 5.74 8.01 0.162 1.08 99.62 96 15.05 10.30 0.181 1.42 99.89

[0221] Table 6 Parameter fitting results of unified characterization formula for accumulated plastic strain of subgrade soil under different cyclic stress amplitudes

[0222] Cyclic stress amplitude (kPa) <![CDATA[G1(MPa)]]> <![CDATA[η1(MPa·s)]]> β <![CDATA[η2(MPa·s)]]> <![CDATA[R 2 ]]> 40 8.53 20.22 0.222 4.97 99.48 70 5.74 8.01 0.162 1.08 99.62 100 2.63 5.02 0.150 0.22 99.25 130 0.18 3.52 0.145 0.03 96.91

[0223] Table 7 Parameter fitting results of unified characterization formula for cumulative plastic strain of subgrade soil under different confining pressures

[0224]

[0225]

[0226] Table 8 Parameter fitting results of unified characterization formula for accumulated plastic strain of subgrade soil under different load action times

[0227]

[0228] Table 9 Parameter fitting results of unified characterization formula for accumulated plastic strain of subgrade soil under different load intermittent times

[0229] Load intermittent time (s) <![CDATA[G1(MPa)]]> <![CDATA[η1(MPa·s)]]> β <![CDATA[η2(MPa·s)]]> <![CDATA[R 2 ]]> 0.0 97.88 45.91 0.238 2.10 99.66 0.8 35.91 40.88 0.201 1.81 99.67 1.8 25.89 35.89 0.182 1.60 99.62 3.0 20.91 31.10 0.153 1.44 99.63 4.0 18.55 27.22 0.124 1.36 99.78

[0230] It can be seen from Tables 4 to 9 that the correlation coefficients between the unified characterization formula for cumulative plastic strain of subgrade soil shown in formula (23) and the test data are all above 0.9, indicating that the characterization formula can be well matched with the test curve of cumulative plastic strain of subgrade soil. At the same time, the parameter identification results show that the parameters of the characterization formula are sensitive to changes in moisture content, compaction degree, cyclic stress amplitude, confining pressure, load action time, and load intermittent time, that is, the parameters G1, η1, β, and η2 change monotonically with changes in moisture content, compaction degree, cyclic stress amplitude, confining pressure, load action time, and load intermittent time.

[0231] It can be seen from the dynamic triaxial test scheme shown in Table 3 that there are 6 influencing factors considered when conducting the cumulative plastic strain test of subgrade soil in this embodiment, namely, water content, compaction degree, cyclic stress amplitude, confining pressure, load action time, and load interval time. Among them, the first 4 influencing factors are set with 4 test levels each, and the last 2 influencing factors are set with 5 test levels each. If a comprehensive test is carried out, 4×4×4×4×5×5=6400 different working conditions need to be tested, which is difficult to complete within a limited time. Therefore, Table 3 uses the control variable method to design 21 different working conditions to examine the influence of 6 factors such as water content on the cumulative plastic strain of subgrade soil, and the parameter fitting results of the characterization formula shown in Tables 4 to 9 are obtained based on the test data. Although Tables 4 to 9 show the variation of parameters G1, η1, β, and η2 of the unified characterization formula of the accumulated plastic strain of the roadbed soil with various factors, the reliability of the multiple regression equation between the parameters G1, η1, β, and η2 and six factors such as water content established only through the fitting results of 21 groups of test data is slightly weak, so 22 new working conditions were randomly generated within the boundary range of different influencing factors, as shown in Table 10. The test soil, molding method, specimen size, test equipment, and loading method corresponding to the randomly generated working conditions are the same as those mentioned above. The test results under each group of working conditions are shown in the figure below. Fig.15 shown.

[0232] Table 10 Random working conditions used to supplement the cumulative plastic strain test data of roadbed soil

[0233]

[0234]

[0235] The same method of combining Macquart and general global optimization is used to transform the unified characterization formula of the accumulated plastic strain of subgrade soil shown in Equation (23) into Fig.15 The test curve shown in the figure is fitted, and the results are shown in Table 11. As can be seen from Table 11, the correlation coefficients of the test data fitting of formula (23) are all above 0.9, indicating that the unified characterization formula of the cumulative plastic strain of roadbed soil shown in formula (23) can also be well matched with the cumulative plastic strain test curve under random working conditions.

[0236] Table 11 Parameter fitting results of unified characterization formula for cumulative plastic strain of subgrade soil under random working conditions

[0237]

[0238]

[0239] According to the parameter fitting results of the unified characterization formula for cumulative plastic strain of subgrade soil shown in Tables 4 to 9, the variation law of the parameters G1, η1, β, and η2 of the unified characterization formula for cumulative plastic strain of subgrade soil with various influencing factors is obtained as follows: Figure 16 to Figure 19 As shown. Figure 16 to Figure 19 It can be seen that G1, η1, β, η2 show significant changes with different influencing factors. Based on this, different function forms are selected to establish the regression relationship between parameters G1, η1, β, η2 and water content, compaction degree, cyclic stress amplitude, confining pressure, load action time, and load interval time.

[0240] In some embodiments, this embodiment constructs a regression relationship as shown in equations (24) to (27):

[0241]

[0242]

[0243]

[0244]

[0245] Where: G1 is the viscoelastic shear modulus of the viscoelastic element in three dimensions, 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, w is the actual moisture content, OMC is the optimal moisture content, K is the compaction degree, σ max is the cyclic stress amplitude, σ3 is the confining pressure, t1 is the load action time in each cycle, and t2 is the load interval time in each cycle.

[0246] When formulas (24) to (27) were established, the unified characterization formula parameters under 43 different working conditions were used, including 21 working conditions designed in Table 3 and 22 random working conditions supplemented in Table 10, and the accuracy was as follows: Figure 20 to Figure 23 As shown. Figure 20 to Figure 23 It can be seen that the correlation coefficient R 2All of them are greater than 0.9, indicating that formulas (24) to (27) can reasonably describe the unified characterization formula parameters G1, η1, β, and η2 under different working conditions. In order to verify the applicability and accuracy of the unified characterization formula for the cumulative plastic strain of subgrade soil proposed in this technology and the multivariate regression equation of its parameters, the test data of high liquid limit clay in the embodiment and other soil types in the existing literature were used to carry out verification. According to the boundary ranges of different factors, 8 verification conditions shown in Table 12 were randomly generated. First, static and dynamic triaxial tests were carried out under each working condition. Then, each group of working conditions were substituted into the above formulas (24) to (27) to obtain the parameters G1, η1, β, and η2. Then, G1, η1, β, η2 and the working conditions were substituted into formula (23) to obtain the calculated value of the cumulative plastic strain of subgrade soil, and the calculated value and test value under the same working condition were compared. The verification results of the unified characterization formula for the cumulative plastic strain of subgrade soil using the test data of high liquid limit clay in this embodiment are as follows. Fig.24 As shown, it can be seen that the calculated value is very close to the dynamic triaxial test result, that is, the established unified characterization formula for the cumulative plastic strain of the roadbed soil can accurately characterize the cumulative plastic strain of the high liquid limit clay in this embodiment.

[0247] Table 12 Working conditions for verifying the unified characterization formula for the cumulative plastic strain of roadbed soil

[0248]

[0249] In addition to the high liquid limit clay in this example, the proposed unified characterization formula for the cumulative plastic strain of subgrade soil is verified by using the experimental data of the cumulative plastic strain of low liquid limit clay in the literature (Undrained cyclic loading response of subgrade soil subjected to varying moisture content and stress level [J]. International Journal of Geomechanics, 2023, 23 (2): 04022284), the experimental data of critical dynamic stress of coarse-grained soil filling in railway subgrade [J]. Rock and Soil Mechanics, 2020, 41 (6): 1865-1873) and the experimental data of silty clay in the literature (Comparative study of dynamic and static strength characteristics of two types of silty clay [J]. Rock and Soil Mechanics, 2012, 33 (3): 665-673). Four verification conditions are selected in each literature and are indicated in the form of "soil quality-water content-compactness-cyclic stress amplitude-confining pressure-load action time-load interval time". The verification results of the unified characterization formula of the cumulative plastic strain of roadbed soil using the test data of different soil types are as follows: Figure 25 to Figure 27As shown, it can be seen that the calculated value (dashed line) obtained according to the unified characterization formula for the cumulative plastic strain of roadbed soil is consistent with the measured result of the cumulative plastic strain test (hollow point), indicating that the unified characterization formula for the cumulative plastic strain of roadbed soil established in this embodiment has a good prediction effect on the cumulative plastic strain of different types of roadbed soil.

[0250] The above description is only a preferred embodiment of the present invention and is not intended to limit the protection scope of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention are included in the protection scope of the present invention.

Claims

1. A method for characterizing the cumulative plastic strain of roadbed soil considering the actual stress state and service history, characterized in that: Follow these steps: Constructing a characterization component of the accumulated plastic strain of the roadbed soil, the characterization component includes a connected integer-order viscoelastic element and a non-integer-order viscoplastic element; The cyclic load is converted into a constant load, and the deformation expression of the subgrade soil in the one-dimensional case is derived based on the characterization component of the accumulated plastic strain of the subgrade soil; Based on the one-dimensional deformation expression of subgrade soil, the unified characterization formula of the three-dimensional cumulative plastic strain of subgrade soil under dynamic cyclic loading is extended; Based on the following cumulative plastic strain test loading method of subgrade soil considering the actual stress state and service history, the cumulative plastic strain test of subgrade soil is carried out, and the multivariate regression equation of parameters and working conditions of the unified characterization formula of cumulative plastic strain of subgrade soil is constructed; The loading method for the cumulative plastic strain test of subgrade soil considering the actual stress state and service history is loaded according to the following steps: The specimens are statically pressed layer by layer to the target compaction degree to simulate the actual filling process of the roadbed; The contact stress was used to simulate the overlying static load and the specimen was statically loaded; Apply cyclic loads to the specimens to simulate the dynamic loads on the roadbed during operation; The contact stress σ c Calculate according to the following formula: Where K0 is the static earth pressure coefficient, σ3 is the confining pressure; The static load time of the simulated overlying static load is determined according to the following process: The specimens were prepared by layered static pressing. The moisture content of the specimens was 1.6OMC and the compaction degree was 87%. Based on the contact stress σ c Carry out controlled stress constant load test, with the test confining pressure of 30kPa and 120kPa respectively, set the constant load time for trial, if the stable state is not reached after the constant load time, re-sample and continue to increase the constant load time until the deformation stable time under the test confining pressure is found; The parameters of the unified characterization formula for the cumulative plastic strain of the roadbed soil and the multivariate regression equation of the working conditions are as follows: Where: G1 is the viscoelastic shear modulus of the viscoelastic element in three dimensions, 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, w is the actual moisture content, OMC is the optimal moisture content, K is the compaction degree, σ max is the cyclic stress amplitude, σ3 is the confining pressure, t1 is the load action time in each cycle, and t2 is the load interval time in each cycle.

2. The method for characterizing the accumulated plastic strain of roadbed soil considering the actual stress state and service history according to claim 1 is characterized in that: The characterization component of the accumulated plastic strain of the subgrade soil is constructed according to the following process: A spring with an elastic modulus of E0 is used to represent elastic deformation, and a spring with an elastic modulus of E1 and a viscoelastic pot with a viscosity coefficient of η1 are connected in parallel to represent viscoelastic deformation. These two parts are connected in series to form a viscoelastic element. Assume a yield stress of σ s The plastic friction plate is connected in parallel with a viscosity pot with a viscosity coefficient of η2 and a non-integer order of β to form a viscoplastic element to represent viscoplastic deformation; The process of converting a cyclic load to a steady load is as follows: The cyclic load is converted into a constant load using a piecewise function as shown in formula (6): Where: t is the deviatoric stress at time t, σ max is the cyclic stress amplitude, t1 is the load action time in each cycle, T is the cyclic load period, and N is the number of cyclic load actions; Based on impulse equivalence, the cyclic load and equivalent constant load are equal to the area enclosed by the horizontal axis of the coordinate, as shown in formula (7): The constant load σ0 equivalent to the half-sine cyclic load of each cycle can be obtained, as shown in formula (8): Among them, π is the ratio of a circle to its circumference.

3. The method for characterizing the accumulated plastic strain of roadbed soil considering the actual stress state and service history according to claim 1 is characterized in that: The derivation process of the roadbed soil deformation expression in the one-dimensional case is as follows: The creep compliance J(t) of the viscoelastic element at time t is expressed as: Where: E0 is the elastic modulus of the viscoelastic element, E1 is the viscoelastic modulus of the viscoelastic element, η1 is the viscosity coefficient of the viscoelastic element; Then the strain ε(t) corresponding to the time t after unloading is: Where σ0 is a constant load equivalent to the half-sine cyclic load of each cycle, J(t-t1) represents the creep compliance of the viscoelastic element at time t-t1; For cyclic loads, the residual viscoelastic deformation ε after the i-th half-sine cyclic load lasts for [(Ni)T+t2] to the end of the N-th half-sine cyclic load period is Ni for: Where: T is the cyclic load period, N is the number of cyclic load actions, and t2 is the load interval time in each cycle; Then, the total residual viscoelastic deformation ε generated by N cyclic loading is N for: In order to obtain a clear analytical form of equation (12), the residual viscoelastic deformation rate corresponding to the Nth cyclic load is constructed as: Considering that the number of cyclic load actions N changes continuously, the integral of equation (13) is supplemented with the condition that the residual viscoelastic deformation is also 0 when the number of load actions N is 0. At the same time, combined with the constant load σ0, the cyclic stress amplitude σ is obtained. max The one-dimensional residual viscoelastic deformation ε is represented by Rve for: The plastic friction plate of the non-integer order viscoplastic element is not triggered during the load interval, that is, the actual action time of the cyclic load on the viscoplastic element is L = Nt1, and the one-dimensional viscoplastic deformation ε corresponding to the non-integer order viscoplastic element is vp As shown in formula (15): Where: σ is the stress of the viscoplastic element, σ s is the yield stress of the viscoplastic element, η2 is the viscosity coefficient of the viscoplastic element, β is the non-integer order of the viscoplastic element, and Γ is the Gamma function; Substituting L=Nt1 and constant load σ0 into equation (15), we can obtain the cyclic stress amplitude σ max The one-dimensional viscoplastic deformation ε vp As shown in formula (16):

4. The method for characterizing the accumulated plastic strain of roadbed soil considering the actual stress state and service history according to claim 3 is characterized in that: The process of the unified characterization formula of the three-dimensional roadbed soil cumulative plastic strain under the extended dynamic cyclic load is as follows: The stress deviator S ij Instead of the stress in equation (14), ij represents the direction in the three-dimensional stress space, and the viscoelastic modulus E1 in equation (14) is replaced by the viscoelastic shear modulus G1 in the three-dimensional case, and the three-dimensional residual viscoelastic deformation is obtained: for: For non-integer-order viscoplastic elements, the yield function and plastic potential function are introduced to obtain the three-dimensional viscoplastic deformation for: Where: F is the yield function of the soil, F0 is the initial value of the yield function of the soil, ψ is the power function, Q is the plastic potential function, σ ij is the component of the stress σ of the viscoplastic element in the ij direction in the three-dimensional coordinates; Using the associated flow law, the yield function F is equal to the plastic potential function Q, and equation (18) is transformed into: The yield function is the Drucker-Prager yield criterion, and the expression under triaxial compression is: Where: I1 is the first stress invariant, J2 is the second stress deviator invariant, α and K are two parameters in the Drucker-Prager yield function, c is the total cohesion of the soil, is the total internal friction angle of the soil; When the roadbed soil cumulative plastic strain test is loaded, the confining pressure σ3 is equal to the intermediate principal stress σ1, so: I1=3σ m =σ1+2σ3 (23) Where: m is the mean principal stress, S 11 is the stress deviator tensor in the z direction in three-dimensional coordinates; Combining equations (17), (19) to (24) and setting the initial value of the yield function F0 = 1, we can obtain the accumulated plastic strain ε of the subgrade soil: p A unified representation formula for .

5. The method for characterizing the accumulated plastic strain of roadbed soil considering the actual stress state and service history according to claim 1 is characterized in that: The process of constructing the parameters of the unified characterization formula of the roadbed soil cumulative plastic strain and the multivariate regression equation of the working conditions is as follows: Conduct static triaxial test: The static triaxial test adopts the unconsolidated and undrained loading method. The test ends when the axial strain reaches 15%. The test scheme is shown in the following table: The shear strength parameters of soil samples at different moisture contents and compaction degrees, namely, total cohesion c and total internal friction angle, were calculated by the Mohr-Coulomb strength criterion. Conduct dynamic triaxial test: The cyclic loading method of the roadbed soil cumulative plastic strain test considering the actual stress state and service history is used for load loading. The test scheme of cyclic loading is shown in the table below. The cyclic load is applied in the form of a half-sine wave. Each working condition is repeated 10,000 times under undrained conditions. When the cumulative plastic strain of the soil sample reaches 5%, the loading is stopped. The cumulative plastic strain test results of the soil samples under different moisture contents, compaction degrees, cyclic stress amplitudes, confining pressures, load action time, and load interval time are obtained: Among them, Group A investigated the effect of moisture content on the cumulative plastic strain of soil samples, Group B investigated the effect of compaction degree on the cumulative plastic strain of soil samples, Group C investigated the effect of cyclic stress amplitude on the cumulative plastic strain of soil samples, Group D investigated the effect of confining pressure on the cumulative plastic strain of soil samples, Group E investigated the effect of load action time on the cumulative plastic strain of soil samples, Group F investigated the effect of load intermittent time on the cumulative plastic strain of soil samples, and Group G was compared with Group D to understand the difference in cumulative plastic strain of soil samples caused by different contact stresses. The algorithm combining Macquart and general global optimization is adopted to identify the parameters of the unified characterization formula of the cumulative plastic strain of the subgrade soil based on the above-mentioned static triaxial test and dynamic triaxial test results. A data point is extracted from the cumulative plastic strain test curve of the subgrade soil under each working condition at each fixed number of cyclic loading intervals for fitting, and the parameter fitting results of the unified characterization formula of the cumulative plastic strain of the subgrade soil corresponding to different moisture contents, compaction degrees, cyclic stress amplitudes, confining pressures, load action times, and load interval times are obtained. Based on the parameter fitting results of the unified characterization formula for cumulative plastic strain of subgrade soil corresponding to different moisture contents, compaction degrees, cyclic stress amplitudes, confining pressures, load action time and load intermittent time, the variation law of each parameter in the unified characterization formula for cumulative plastic strain of subgrade soil with each influencing factor is obtained. Based on this, different function forms are selected to establish the regression relationship between each parameter in the unified characterization formula for cumulative plastic strain of subgrade soil and moisture content, compaction degree, cyclic stress amplitude, confining pressure, load action time and load intermittent time.

6. The method for characterizing the accumulated plastic strain of roadbed soil considering the actual stress state and service history according to claim 1 is characterized in that: The unified characterization formula of the accumulated plastic strain of the roadbed soil is as follows: Where: ε 11 is the strain in the z direction in three-dimensional coordinates, is the residual viscoelastic deformation in the z direction in three-dimensional coordinates, is the viscoplastic deformation in the z direction in three-dimensional coordinates, σ max is the cyclic stress amplitude, η1 is the viscosity coefficient of the viscoelastic element, η2 is the viscosity coefficient of the viscoplastic element, Γ is the Gamma function, t1 is the load action time in each cycle, T is the cyclic load period, N is the number of cyclic load actions, G1 is the viscoelastic shear modulus of the viscoelastic element in three dimensions, π is the circumference of the circle, 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, and σ3 is the confining pressure.

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