Roadbed internal rebound modulus determination method based on dynamic and static modulus partition

Abstract

The invention discloses a roadbed internal rebound modulus determination method based on dynamic and static modulus partition, which comprises the following steps: firstly, establishing a plane strain finite element model of a roadbed pavement structure, determining a dynamic and static rebound modulus relationship of roadbed soil under different load action time, and identifying a threshold value of the load action time; then, establishing a load action time estimation equation under different vehicle speeds and depths from the top surface of the roadbed, determining critical depths of dynamic and static resilience moduli of the roadbed under various vehicle speed conditions, and carrying out dynamic and static modulus partitioning on the basis of the critical depths; and finally, constructing a constitutive model of the roadbed modulus to realize accurate calculation of the rebound modulus in the roadbed. By analyzing the dynamic and static resilience modulus of the roadbed and the relation between the dynamic and static resilience modulus and the vehicle speed, a dynamic and static modulus partitioning method and a critical depth determination technology are provided, roadbed design and construction are optimized, the stability and durability of a road structure are improved, the service life of a road is prolonged, the maintenance cost is reduced, and safe operation, economy and high efficiency of the road are ensured.

Description

Technical Field

[0001] The present invention belongs to the technical field of road engineering, and particularly relates to a method for determining the resilient modulus inside a subgrade based on the partition of dynamic and static moduli. Background Art

[0002] With the continuous expansion of the scale of transportation infrastructure, the problem of low service life of road engineering during the rapid construction process has gradually emerged. Compared with pavement diseases, subgrade diseases have characteristics such as concealment and progression, resulting in the long-existing phenomenon of "emphasizing pavement and neglecting subgrade" in road engineering research. However, from the perspectives of the difficulty of functional repair and the amount of engineering work, a durable subgrade is the key to improving the durability of road engineering. As the foundation of the pavement, the subgrade is the main structure of the road. The stability and durability of the subgrade directly affect the service life and safe operation of the road.

[0003] The dynamic resilient modulus of the subgrade is one of the key parameters in road structure design and has become a research hotspot in the field of road engineering due to its non-linear characteristics. The dynamic resilient modulus of subgrade soil is not only affected by the stress level but also closely related to the moisture condition, and shows a non-uniform distribution inside the subgrade. At present, in the research on the dynamic resilient modulus inside the subgrade, there are the following problems: Limitations in the study of static resilient modulus: Most studies on the static resilient modulus of subgrade soil are based on indoor load plate tests. However, such tests usually fail to fully consider the effect of confining pressure, resulting in test results that are difficult to truly reflect the stress state of the subgrade under actual use conditions. The data obtained in this case is not sufficient to accurately describe the behavior characteristics of subgrade soil in a complex environment. Insufficiencies in dynamic resilient modulus prediction models: Although existing prediction models for the dynamic resilient modulus of subgrade soil have considered multiple influencing factors such as compaction degree, water content, and stress state, these models generally ignore the influence of load application time on the modulus value. In fact, as the depth increases, the load application time inside the subgrade will be different, and this factor is crucial for accurately predicting the dynamic resilient modulus at different depths. The resilient modulus inside the subgrade has stress dependence and moisture correlation, and the resilient modulus inside the subgrade shows a non-uniform distribution. In existing research, for the resilient modulus inside the subgrade, it is considered to be all dynamic resilient modulus or simply takes the subgrade working area as the boundary, where the dynamic resilient modulus is considered inside the subgrade working area and the static resilient modulus is considered outside the subgrade working area, and these all lack theoretical support. The present invention first analyzes the correlation between dynamic and static resilient moduli, proposes the partition of dynamic and static moduli inside the subgrade based on this, and finally obtains the evolution law of the resilient modulus inside the subgrade with depth and proposes a corresponding numerical calculation method.

[0004] In summary, in order to more accurately evaluate and predict the resilient modulus inside the subgrade, future research needs to more deeply explore the influence mechanisms of factors including but not limited to the load application time, and develop new models that can comprehensively consider multiple factors. This will help improve the scientificity and rationality of road structure design and ensure the safety and economy of roads. Summary of the Invention

[0005] The purpose of the embodiments of the present invention is to provide a method for determining the resilient modulus inside the subgrade based on the partition of dynamic and static moduli, so as to achieve the accurate partition determination of the resilient modulus inside the subgrade, and at the same time consider the influence of multiple factors such as confining pressure and load application time, and improve the accuracy and reliability of predicting the resilient modulus inside the subgrade.

[0006] To solve the above technical problems, the technical solution adopted by the present invention is a method for determining the resilient modulus inside the subgrade based on the partition of dynamic and static moduli, which is specifically carried out according to the following steps:

[0007] S1. Establish a plane strain finite element model of the subgrade pavement structure to determine different load application times, determine the correlation between the dynamic and static resilient moduli of the subgrade soil under different load application times, and determine the load application time threshold;

[0008] S2. Establish an estimated equation for the load application time at different vehicle speeds and depths from the subgrade top surface and determine the critical depth of the dynamic and static resilient moduli of the subgrade at different vehicle speeds; establish a partition of dynamic and static moduli based on the critical depth of the dynamic and static resilient moduli of the subgrade;

[0009] S3. Construct a constitutive model of the subgrade modulus and complete the calculation of the resilient modulus inside the subgrade.

[0010] Further, the specific steps of S1 are as follows:

[0011] S101. Conduct basic performance tests on the subgrade soil samples to determine the optimum moisture content and maximum dry density of the soil samples;

[0012] S102. Establish a plane strain finite element model of the subgrade pavement structure and determine the load application time and intermittent time of the dynamic load inside the subgrade;

[0013] S103. Conduct dynamic resilient modulus tests on the target soil samples with different multiples of the optimum moisture content and different compaction degrees under different load application durations to fit and establish a prediction model considering moisture content, compaction degree, load application time and stress state;

[0014] S104. Conduct static triaxial tests on the target soil samples with different multiples of the optimum moisture content and different compaction degrees to fit and establish a static resilient modulus prediction model;

[0015] S105. Plot a curve of the ratio of dynamic resilience modulus to static resilience modulus under different load application times with the load application time as the abscissa and the ratio of dynamic to static resilience modulus as the ordinate, and determine the load application time threshold based on the ratio curve.

[0016] Further, the method for determining the load application time threshold is as follows: When the value of the ratio curve of dynamic to static resilience modulus in S105 tends to be stable, record the load application time at this time as the load application time threshold. When the load application time is less than the load application time threshold, the resilience modulus inside the subgrade is the dynamic resilience modulus; when the load application time is greater than or equal to the load application time threshold, the resilience modulus inside the subgrade is the static resilience modulus.

[0017] Further, the prediction model in S103 considering water content, degree of compaction, load application time, and stress state is specifically as follows:

[0018]

[0019] where M R is the dynamic resilience modulus; p a is the standard atmospheric pressure; t is the load application time; t0 is the common load application time; K is the degree of compaction; w is the actual water content; w opt is the optimum water content; k1 to k6 are model parameters, θ is the volumetric stress; τ oct is the octahedral shear stress.

[0020] Further, the static resilience modulus prediction model in S104 is specifically as follows:

[0021]

[0022] where M R静 is the static resilience modulus, τ oct静 is the static octahedral shear stress, k1 to k5 are model parameters, p a is the standard atmospheric pressure; K is the degree of compaction; w is the actual water content; w opt is the optimum water content; θ is the volumetric stress.

[0023] Further, S2 is specifically carried out according to the following steps:

[0024] S201. Based on the plane strain finite element model of the subgrade and pavement structure established in S1, determine the relationship between load application time and vehicle speed at different depths from the subgrade top surface, and the relationship between load application time and depth from the subgrade top surface at different vehicle speeds;

[0025] S202. Establish a prediction model for the load application time at different depths from the subgrade top surface at different vehicle speeds:

[0026]

[0027] where \(t\) is the load application time, \(e\) is the base of the natural logarithm, \(v\) is the vehicle speed, \(h\) is the depth from the subgrade top surface, and \(k_1\) to \(k_3\) are model parameters;

[0028] S203. A method for determining the depth from the subgrade top surface at a given vehicle speed and load application time based on the prediction model established in S202:

[0029]

[0030] S204. Substitute the load application time threshold into \(t\) in the formula in S203 to determine the critical depth of the dynamic and static resilient moduli of the subgrade, and determine the dynamic and static modulus zones based on the critical depth of the dynamic and static resilient moduli of the subgrade.

[0031] Furthermore, the specific dynamic and static modulus zones are as follows: when the depth from the subgrade top surface is less than or equal to the critical depth of the dynamic and static resilient moduli, the resilient modulus of the subgrade is the dynamic resilient modulus; when the depth from the subgrade top surface is greater than the critical depth of the resilient modulus, the resilient modulus of the subgrade is the static resilient modulus.

[0032] Furthermore, the specific steps of S3 are as follows:

[0033] S301. Perform finite element modeling for different working conditions of the subgrade;

[0034] S302. Establish a constitutive model for determining the subgrade modulus;

[0035] S303. Based on the finite element model in S301, determine the relationship between the subgrade thickness and the peak deflection values of the road surface and subgrade top surface, regard the subgrade as a half-space structure, and determine the minimum required thickness;

[0036] S304. Perform finite element modeling for the target subgrade working condition, introduce the constitutive model established in S302 into the finite element model established in S304, and determine the internal resilient modulus of the subgrade.

[0037] Furthermore, in S301, ABAQUS is used to perform finite element modeling for different working conditions of the subgrade, four-node ring elements CAX4 are used in the finite region, and infinite elements CINAX4 are used at the boundary;

[0038] The specific constitutive model for calculating the subgrade modulus in S302 is as follows:

[0039] When < the load application time threshold,

[0040]

[0041] When ≥ the load application time threshold,

[0042]

[0043] Then, the load application time threshold is used to replace the static resilient modulus in the constitutive model to characterize the static resilient modulus.

[0044] Among them, M is the resilient modulus inside the subgrade; p a is the standard atmospheric pressure; t1 is the load application time threshold; t0 is the common load application time; K is the degree of compaction; w is the actual moisture content; w opt is the optimum moisture content; k1 to k9 are model parameters, θ is the volumetric stress; τ oct is the octahedral shear stress; t is the load application time, e is the base of the natural logarithm, v is the vehicle speed, and h is the depth from the top surface of the subgrade.

[0045] Furthermore, the plane strain finite element model of the subgrade pavement structure in S1 is established using ABAQUS. The four-node element CEP4 is used in the finite region, and the infinite element CINPE4 is used at the boundary.

[0046] Compared with the prior art, the beneficial effects of the present invention include the following points:

[0047] 1. By analyzing the correlation between the dynamic and static resilient moduli, the present invention proposes a method for partitioning the dynamic and static moduli inside the subgrade, thereby more accurately evaluating the resilient moduli of each layer inside the subgrade. This helps to improve the accuracy of road structure design and ensure the stability and durability of the subgrade under actual use conditions.

[0048] 2. Based on the numerical simulation using ABAQUS software, the present invention determines the critical depth of the dynamic and static resilient moduli inside the subgrade and clarifies the maximum calculation thickness of the subgrade modulus. The present invention provides a clear reference basis for subgrade design, avoids problems of over-design or under-design, and improves the economy and safety of the project.

[0049] 3. The present invention not only proposes a new method for discriminating the dynamic and static resilient moduli, but also reveals the variation law of the subgrade modulus with depth through numerical calculation methods. This is of great significance for understanding the mechanical behavior of the subgrade at different depths and optimizing the subgrade design and construction schemes.

[0050] 4. The present invention emphasizes the importance of the subgrade in road engineering. By deeply studying the dynamic resilient modulus of the subgrade, it provides technical support for improving the overall durability and safety of the road. This helps to change the traditional research tendency of "emphasizing the pavement and neglecting the subgrade" and promotes the comprehensive development of road engineering.

[0051] 5. The present invention converts the influence of the load application time on the dynamic resilient modulus of the subgrade into the influence of vehicle speed on the dynamic resilient modulus of the subgrade, filling the gap in existing research. The incorporation of these factors makes the prediction model more comprehensive and accurate, contributing to a better simulation of the dynamic response of the subgrade under actual service conditions.

[0052] In summary, the present invention provides a scientific basis for road structure design, which helps to extend the service life of the road, reduce maintenance costs, and ensure the safe operation and economic efficiency of the road. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0054] Figure 1 It is a plane strain finite element calculation model diagram established in Embodiment 1;

[0055] Figure 2 It is the vertical stress time history curve at different depths from the subgrade top surface under different vehicle speeds in Embodiment 1. Among them, (a) is 20 km / h, (b) is 40 km / h, (c) is 60 km / h, (d) is 80 km / h, (e) is 100 km / h, and (f) is 120 km / h;

[0056] Figure 3 It is the ratio of the dynamic resilient modulus to the static resilient modulus under different load application times in Embodiment 1. Among them, (a) is 0.8 OMC water content, (b) is 1 OMC water content, (c) is 1.2 OMC water content, and (d) is 1.4 OMC water content;

[0057] Figure 4 It is the relationship diagram between the load application time and the vehicle speed at different depths from the subgrade top surface in Embodiment 1;

[0058] Figure 5 It is the relationship diagram between the load application time and the depth from the subgrade top surface under different vehicle speeds in Embodiment 1;

[0059] Figure 6 It is the comparison diagram between the actual value and the predicted value of the load application time in Embodiment 1;

[0060] Figure 7 It is the relationship diagram between the peak value of the road surface deflection and the subgrade thickness at a vehicle speed of 120 km / h in Embodiment 1;

[0061] Figure 8It is the relationship diagram between the peak deflection of the subgrade top surface at 120 km / h and the subgrade thickness in Embodiment 1

[0062] Figure 9 It is the relationship between the resilient modulus inside the subgrade and the depth from the subgrade top surface in Embodiment 1. Among them, (a) is 20 km / h, (b) is 40 km / h, (c) is 60 km / h, (d) is 80 km / h, (e) is 100 km / h, and (f) is 120 km / h;

[0063] Figure 10 It is the finite element modulus calculation result under the conditions of 87% compaction degree, 0.8 OMC water content, 20 km / h vehicle speed, and 32 m subgrade thickness in Embodiment 2;

[0064] Figure 11 It is the finite element model under the conditions of 87% compaction degree, 0.8 OMC water content, 20 km / h vehicle speed, and 1 m subgrade thickness. Specific implementation mode

[0065] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0066] This implementation mode first analyzes the correlation between the dynamic and static resilient moduli, and based on this, proposes the division of the dynamic and static moduli inside the subgrade. Finally, the evolution law of the resilient modulus inside the subgrade with depth is obtained and the corresponding numerical determination method is proposed. The specific process is as follows:

[0067] Embodiment 1

[0068] S1. Determine the correlation between the dynamic and static resilient moduli of subgrade soil;

[0069] To explore the correlation between the dynamic and static resilient moduli, select the working conditions of 96% compaction degree and different water contents. Take the load action time as the abscissa and the ratio of the dynamic and static resilient moduli as the ordinate to plot the ratio of the dynamic resilient modulus to the static resilient modulus under different load action times.

[0070] S101. Conduct basic performance tests on the selected soil samples, including liquid limit, plastic limit, particle analysis, and compaction test. Scientifically name the soil sample as sandy low liquid limit clay, and determine the optimum water content of the soil sample as 12.1% and the maximum dry density as 1.89 g / cm 3 .

[0071] S102. Determine the action-intermittent time of the dynamic load inside the subgrade

[0072] S1021. Use ABAQUS to select a typical pavement structure in China to establish a plane strain model as shown in Figure 1 . The model is 40 m long, and normal constraints are applied at x = 0 and x = 40. Four-node element CEP4 is used in the finite region, while infinite element CINPE4 is used at the boundary to reduce the number of elements and eliminate the influence of wave reflection. A gradient division method is adopted, and the mesh size ranges from 0.02 m to 0.25 m from top to bottom.

[0073] S1022. For the selected typical pavement structure, the surface layer is asphalt concrete, and the base course and sub-base course are both cement stabilized macadam. The pavement structure parameters are shown in Table 1. There is full continuity between each layer.

[0074] Table 1 Pavement structure parameters

[0075] Stratum Material type Thickness (m) Resilient modulus (MPa) Poisson's ratio Surface course Asphalt concrete 0.18 10000 0.3 Base course Cement stabilized macadam 0.40 8000 0.25 Subbase course Cement stabilized macadam 0.20 6000 0.25 Subgrade Subgrade soil 10.0 60 0.35

[0076] S1023. Use an implicit dynamic solver with a solution time of 60 ms and a calculation step size of 1 ms. The load consists of two moving loads with a distance of 1.4 m, both with an action radius of 0.213 m, a magnitude of 707 kPa, and moving speeds of 20 km / h, 40 km / h, 60 km / h, 80 km / h, 100 km / h, and 120 km / h respectively.

[0077] S1024. In Abaqus, select positions at different depths from the top surface of the subgrade, extract the output data of the ODB field variables at these positions, and then obtain the curves of the vertical stress varying with time at different depths under different vehicle speed conditions; Figure 2 are the time history curves of the vertical stress at different vehicle speeds and different depths from the top surface of the subgrade; as can be seen from Figure 2 , when the driving speeds are 20 km / h, 40 km / h, 60 km / h, 80 km / h, 100 km / h, and 120 km / h, the load action time ranges are 1.87 s - 6.14 s, 0.95 s - 3.04 s, 0.65 s - 2.02 s, 0.48 s - 1.52 s, 0.37 s - 1.23 s, and 0.31 s - 1.01 s respectively.

[0078] S1025. There are significant differences in the load action time at different vehicle speeds and different depths from the top surface of the subgrade. Therefore, when conducting the dynamic triaxial test, the influence of the load action time should be fully considered. Based on the results of S1024, with the load action time range of 0.31 s - 6.14 s, a selection method of increasing by backward difference is adopted, and five load action times of 0.2 s, 0.6 s, 1.4 s, 2.6 s, and 4.2 s are selected to conduct the test. For the load intermittent time, 0.8 s is uniformly selected as the load intermittent time to conduct the test research.

[0079] S103. Dynamic resilient modulus test

[0080] S1031. Conduct dynamic resilient modulus tests under compaction degrees of 87%, 90%, 93%, and 96%, optimum water contents of 0.8, 1.0, 1.2, and 1.4 times, and load application durations of 0.2, 0.6, 1.4, 2.6, and 4.2 s.

[0081] S1032. Based on the results of the dynamic resilient modulus tests, fit and establish a prediction model that comprehensively considers water content, compaction degree, load application time, and stress state, as shown in the following formula:

[0082]

[0083] In the formula: M R is the dynamic resilient modulus; p a is the standard atmospheric pressure, usually taken as 101 kPa; t is the load application time, s; t0 is the common load application time, taken as 0.2 s; K is the compaction degree, %; w is the actual water content, %; w opt is the optimum water content, %; k1 to k6 are model parameters, θ is the volumetric stress, θ = σ1 + σ2 + σ3, σ1 is the maximum principal stress, σ2 is the intermediate principal stress, σ3 is the minimum principal stress, and in the dynamic triaxial test, σ3 is the confining pressure; τ oct is the octahedral shear stress.

[0084] S104. Static resilient modulus test

[0085] S1041. Conduct static triaxial tests under compaction degrees of 87%, 90%, 93%, and 96% and optimum water contents of 0.8, 1.0, 1.2, and 1.4 times.

[0086] S1042. Select compaction degree, relative water content, confining pressure, and static deviator stress to fit and establish a new static resilient modulus prediction model, as shown in the following formula:

[0087]

[0088] In the formula: τ oct静 is the static octahedral shear stress. The meanings of other symbols are the same as above.

[0089] In this embodiment, the steps of the dynamic and static resilient modulus tests in S103 and S104 are as follows:

[0090] (1) Remove the triaxial cell cover, and then wipe the triaxial cell base clean for standby.

[0091] (2) Take out the test specimens required, and tear off the surface plastic wrap. Place the permeable stone and filter paper on the triaxial cell base in sequence.

[0092] (3) Slip the rubber membrane over the custom-made steel sleeve, then turn on the suction device, insert the suction pipe into the small hole of the steel sleeve so that the rubber membrane tightly adheres to the inner wall of the steel sleeve. Then, while sucking, slip the rubber membrane over the specimen.

[0093] (4) Place filter paper and permeable stone on the top of the specimen in sequence, and slip the lower end of the rubber membrane over the platform of the triaxial cell base. Then remove the steel sleeve, place the loading plate on the permeable stone at the upper part of the specimen. Slip two rubber rings over the upper and lower parts of the rubber membrane respectively. Attention should be paid to making the rubber rings slip over the grooves to ensure the sealing effect.

[0094] (5) After assembling the triaxial cell, place the triaxial cell on the loading frame, tighten the top fixing screw, connect the loading rod, and insert the confining pressure pipe. Then turn on the instrument and adjust the position of the triaxial cell through the up and down buttons on the panel so that the top of the loading cover is aligned with the center of the loading rod and makes quick contact.

[0095] (6) Turn on the air valve, servo system, and computer in sequence. Then open the test software, select the test template and the storage location of the test data, and input the test parameters and loading sequence.

[0096] (7) Install two displacement sensors on the top columns of the triaxial cell respectively, make the lower part of them contact with the triaxial cell, adjust to make the readings in the software be near zero, and finally tighten the screws.

[0097] (8) Click Start to conduct the test. If the deformation of the specimen exceeds 5% during the preloading stage, stop the test and analyze the reasons.

[0098] S105. Determine the correlation between the dynamic and static resilient moduli of subgrade soil

[0099] To explore the correlation between the dynamic and static resilient moduli, select the working conditions of different water contents with a compaction degree of 96%. Take the load application time as the abscissa and the ratio of the dynamic and static resilient moduli as the ordinate to plot the ratio of the dynamic resilient modulus to the static resilient modulus under different load application times, as Figure 3 shown.

[0100] It can be seen from Figure 3 that when the load application time is greater than 1.4 s, the ratio of the dynamic and static resilient moduli stabilizes around 1. This indicates that when the load application time is long enough, the dynamic resilient modulus and the static resilient modulus tend to be the same. The dynamic resilient modulus after a long enough load application time can be regarded as the static resilient modulus. Similarly, the static resilient modulus can also be regarded as the dynamic resilient modulus with an extremely long load application time. Therefore, the dynamic and static resilient moduli should not be simply distinguished by the loading method, but should be considered from the aspect of the influence of the load application time on the resilient modulus.

[0101] During the process where the resilient modulus of subgrade soil shows a downward trend with the increase of load application time, within 1.4 seconds of load application time, the resilient modulus inside the subgrade is the dynamic resilient modulus. The resilient modulus inside the subgrade is the dynamic resilient modulus. When the load application time is greater than 1.4 s, the resilient modulus inside the subgrade is no longer affected by the load application time, and the resilient modulus inside the subgrade at this time is the static resilient modulus.

[0102] S2. Determine the critical depth of the dynamic and static resilient moduli of the subgrade

[0103] S201. In S1024, Abaqus was used for modeling and calculation to obtain the load application time at different vehicle speeds and depths from the subgrade top surface. To further clarify the relationship between the load application time and vehicle speed and depth from the subgrade top surface, the load application time is now taken as the vertical coordinate, and the vehicle speed and depth from the subgrade top surface are taken as the horizontal coordinates respectively. As shown in Figure 4 and Figure 5 the relationships between the load application time and vehicle speed at different depths from the subgrade top surface and the relationships between the load application time and depth from the subgrade top surface at different vehicle speeds are obtained;

[0104] As shown in Figure 4 it can be seen that when the depth from the subgrade top surface is constant, the load application time decreases non-linearly with the increase of vehicle speed. Taking the depth of 0 m from the subgrade top surface as an example, the load application times at vehicle speeds of 20 km / h, 40 km / h, 60 km / h, 80 km / h, 100 km / h, and 120 km / h are 1.87 s, 0.95 s, 0.65 s, 0.48 s, 0.37 s, and 0.31 s respectively.

[0105] As shown in Figure 5 it can be seen that when the vehicle speed is constant, the load application time increases with the increase of the depth from the subgrade top surface. Taking the vehicle speed of 20 km / h as an example, the load application times at depths from the subgrade top surface of 0 m, 1 m, 2 m, 3 m, 4 m, 5 m, 6 m, 7 m, 8 m, and 9 m are 1.87 s, 3.59 s, 4.11 s, 4.56 s, 4.86 s, 5.09 s, 5.31 s, 5.53 s, 5.76 s, and 6.14 s respectively.

[0106] S202. To achieve a rapid prediction of the load application time at different depths from the subgrade top surface at different vehicle speeds, a prediction model is established:

[0107]

[0108] where: t is the load application time, s; e = 2.71828; v is the vehicle speed, km / h; h is the depth from the subgrade top surface, m. The prediction model parameters and prediction effects of the load application time at different depths from the subgrade top surface at different vehicle speeds are shown in Table 2 and Figure 6 . The prediction accuracy R of the model 2It reached 0.99, indicating good estimation accuracy.

[0109] Table 2 Model parameters

[0110] <![CDATA[k1]]> <![CDATA[k2]]> <![CDATA[k3]]> <![CDATA[R 2 > 237.664 -3.983 0.385 0.991

[0111] S203, given the vehicle speed and load action time, the depth from the top surface of the roadbed can be calculated according to the model established in S202;

[0112]

[0113] Where, h is the depth from the top of the roadbed, m; t is the load action time, s; e = 2.71828 is the base of the natural logarithm; v is the vehicle speed, km / h; k1, k2, k3 are model parameters.

[0114] S204, when the load action time t is 1.4s, the critical depth of the dynamic and static elastic modulus under each vehicle speed is shown in Table 3. Taking the vehicle speed of 60km / h as an example, the critical depth of the dynamic and static elastic modulus is 2.89m. When calculating the internal modulus field of the roadbed, the roadbed elastic modulus is a dynamic elastic modulus related to the load action time within the range of less than 2.89m from the top surface of the roadbed. The roadbed elastic modulus is a static elastic modulus that is not related to the load action time within the range of greater than 2.89m from the top surface of the roadbed. When the depth from the top surface of the roadbed is equal to 2.89m, the dynamic and static elastic moduli are equal. It can also be seen from Table 3 that when the vehicle speed is 20km / h, the critical depth of the dynamic and static elastic modulus is -0.79m, which means that at this speed, the elastic modulus of the entire roadbed is a static elastic modulus that is not related to the load action time. At the same time, it is noted that when the vehicle speed is 100km / h and 120km / h, the corresponding critical depths of the dynamic and static elastic modulus of the roadbed are 11.47m and 17.42m respectively, which exceeds the conventional dynamic stress influence range. This is due to the limitations of the elastic system. The elastic system does not consider the loss during wave transmission, so the critical depth is too large. The subsequent numerical calculation considering the viscoelasticity of the roadbed soil can be carried out to better match the actual situation. At the same time, the partition here has nothing to do with the roadbed work area. It is only based on the load action time to perform dynamic and static elastic modulus partitioning, and the actual load size is not considered.

[0115] Table 3 Critical depth of dynamic and static partitions at different vehicle speeds

[0116] Vehicle speed (km / h) 20 40 60 80 100 120 Critical depth (m) -0.79 0.42 2.89 6.60 11.47 17.42

[0117] S3. Calculation method of internal rebound modulus of roadbed

[0118] S301. Use the method in the "Automated Batch Processing Software V1.0 for Asphalt Pavement Finite Elements Considering Material Nonlinear Characteristics Based on ABAQUS" (Registration Number: 2022SR0875907) to perform finite element modeling calculations for a total of 576 working conditions with four moisture contents, four compaction degrees, six vehicle speeds, and six subgrade thicknesses; the modeling results are as follows Figure 11 An example of the finite element model at a compaction degree of 87%, a moisture content of 0.8 OMC, a vehicle speed of 20 km / h, and a subgrade thickness of 1 m is listed and shown.

[0119] S302. In some possible implementation manners, four-node annular elements CAX4 are used in the finite region during the modeling process, and infinite elements CINAX4 are used at the boundary to reduce the number of elements and eliminate the influence of wave reflection.

[0120] S303. The pavement structure parameters are shown in Table 4. There is complete continuity between each layer, and the bottom of the model is rigidly constrained. The gradient division method is adopted, with the mesh size ranging from 0.03 m to 0.5 m from left to right and from 0.06 m to 0.5 m from top to bottom. An implicit dynamic solver is used, with a solution time of 60 ms and a calculation step size of 1 ms. The load is a semi-sine pulse load, with an action radius of 0.15 m, a magnitude of 707 kPa, and an action time of 0.1 s.

[0121] Table 4 Pavement Structure Parameters

[0122]

[0123] S304. Since the model is an axisymmetric model, it is impossible to simulate the loads at different vehicle speeds. The influence of vehicle speed on the resilient modulus is reflected through the load action time. Specifically, the vehicle speed is considered by substituting the model parameters, that is, the vehicle speed affects the load action time, and the load action time affects the resilient modulus.

[0124] S305. Combine the models established in S1032 and S202 to construct the constitutive model for finally calculating the subgrade modulus:

[0125]

[0126] In the formula: M is the internal resilient modulus of the subgrade, and t1 is the load action time threshold; the meanings of other symbols are the same as above;

[0127] When The resilient modulus is calculated using the above formula;

[0128] When Then t = 1.4 s, which is used to characterize the static resilient modulus.

[0129] S306. Based on the relationship between the subgrade thickness and the deflection peak values of the road surface and the subgrade top surface in the finite element model established in S301, as followsFigure 7 , Figure 8 As shown, it can be obtained that both the peak surface deflection and the peak subgrade surface deflection increase with the increase of water content and the decrease of compaction degree. At the same time, it can be seen that both the peak surface deflection and the peak subgrade surface deflection increase with the increase of subgrade thickness and tend to be stable after the subgrade thickness reaches 16 m. When calculating the dynamic response of the subgrade and pavement, the subgrade is regarded as a half-space structure, and 16 m is exactly the minimum required thickness for the subgrade to be regarded as a half-space when establishing the finite element model.

[0130] The 16 m proposed in this embodiment as the minimum required thickness for the subgrade to be regarded as a half-space in the finite element model has nothing to do with the engineering significance. It is only the size convergence thickness for finite element modeling. Its relatively large thickness is caused by the elastic assumption. When performing numerical calculations, the modeling height of the subgrade model is not the same as the actual subgrade height. For example, for a certain subgrade with a height of 5 m, it is still necessary to be greater than or equal to 16 m when modeling under the elastic assumption.

[0131] S307. A finite element model of the subgrade with a compaction degree of 87%, a water content of 0.8 OMC, a vehicle speed of 20 km / h, and a subgrade thickness of 32 m is established. The constitutive model established in S302 is introduced into the finite element model to calculate the resilient modulus inside the subgrade. The calculation results are as Figure 9 shown.

[0132] From Figure 9 it can be seen that the resilient modulus inside the subgrade shows a trend of first increasing and then stabilizing with the increase of depth, and the stable depth is about 18 m from the subgrade surface.

[0133] In this embodiment, the ratio of the dynamic and static resilient moduli obtained from the laboratory tests decreases with the increase of the loading time of the dynamic resilient modulus, and the ratio tends to 1 when the load acting time reaches 1.4 s. Based on this, it is proposed that the dynamic and static moduli cannot be simply distinguished by the load acting mode, but should be distinguished by the load acting time. When the load acting time is less than 1.4 s, it is the dynamic resilient modulus, and when it is greater than 1.4 s, it is the static resilient modulus. Based on the calculation results of ABAQUS in this embodiment, a prediction equation for the load acting time at different vehicle speeds and depths from the subgrade surface is established, and the critical depths of the dynamic and static resilient moduli corresponding to 1.4 s at different vehicle speeds are obtained.

[0134] In this embodiment, based on ABAQUS, the peak deflection values of the road surface and the subgrade top surface under 576 working conditions with four water contents, four compaction degrees, six vehicle speeds, and six subgrade thicknesses were obtained. It was found that the peak deflection values increased with the increase of water content, the decrease of compaction degree, and the decrease of vehicle speed. When the subgrade thickness reached 16 m, the peak deflection values of the road surface and the subgrade top surface no longer increased. Therefore, 16 m was taken as the minimum required thickness of the subgrade when the finite element model could be regarded as a half-space. Finally, in this embodiment, the finite element calculation results of the resilient modulus inside the subgrade were analyzed, and it was found that the resilient modulus inside the subgrade increased with the increase of the depth from the subgrade top surface and tended to be stable after reaching a depth of 18 m from the subgrade top surface.

[0135] Example 2

[0136] Low liquid limit clay was selected, and the basic soil property tests were completed according to the current "Highway Geotechnical Test Regulations". The results are shown in Table 5.

[0137] Table 5 Results of basic soil property tests

[0138]

[0139] The dynamic triaxial tests were carried out under the conditions of a compaction degree of 87%, a water content of 0.8 OMC, and a vehicle speed of 20 km / h (the load application duration was 4.2 s), and the formula was used for fitting to obtain the predicted model parameters as shown in Table 6.

[0140] Table 6 Predicted model parameters of dynamic resilient modulus

[0141] <![CDATA[k1]]> <![CDATA[k2]]> <![CDATA[k3]]> <![CDATA[k4]]> <![CDATA[k5]]> <![CDATA[k6]]> <![CDATA[R 2 > 1.218 -0.030 4.55 -0.92 0.22 -0.73 0.91

[0142] The static resilient modulus tests were carried out under the conditions of a compaction degree of 87% and a water content of 0.8 OMC, and the formula was used for fitting to obtain the predicted model parameters as shown in Table 7.

[0143] Table 7 Predicted model parameters of static resilient modulus

[0144] <![CDATA[k1]]> <![CDATA[k2]]> <![CDATA[k3]]> <![CDATA[k4]]> <![CDATA[k5]]> <![CDATA[R 2 > 0.469 0.001 -1.549 0.356 -1.103 0.879

[0145] According to the rapid prediction model formula of the load application time at different depths from the subgrade top surface under different vehicle speeds, the model parameters are shown in Table 8.

[0146] Table 4 Rapid prediction model parameters of the load application time at different depths from the subgrade top surface under different vehicle speeds

[0147] <![CDATA[k1]]> <![CDATA[k2]]> <![CDATA[k3]]> <![CDATA[R 2 > 237.664 -3.983 0.385 0.991

[0148] The finite element model was established under the working conditions of 87% compaction degree, 0.8OMC moisture content, 20 km / h vehicle speed, and 32 m subgrade thickness. The pavement structure parameters are shown in Table 9. And the constitutive model calculated by the subgrade modulus shown by the formula:

[0149]

[0150] The constitutive model is shown, and the model parameters are shown in Table 10.

[0151] Table 9 Pavement Structure Parameters

[0152]

[0153] Table 10 Model Parameters of the Constitutive Model for Subgrade Modulus Calculation

[0154] <![CDATA[k1]]> <![CDATA[k2]]> <![CDATA[k3]]> <![CDATA[k4]]> <![CDATA[k5]]> <![CDATA[k6]]> <![CDATA[k7]]> <![CDATA[k8]]> <![CDATA[k9 <!-- 10 -->]]> 1.218 237.664 -3.983 0.385 -0.030 4.55 -0.92 0.22 -0.73

[0155] The finite element calculation results with a selected subgrade modeling thickness of 32 m were analyzed. Figure 10 The finite element modulus calculation results are for 87% compaction degree, 0.8OMC moisture content, 20 km / h vehicle speed, and 32 m subgrade thickness.

[0156] Each embodiment in this specification is described in a related manner. For the same and similar parts between each embodiment, reference can be made to each other. The key point of each embodiment is to illustrate the differences from other embodiments. In particular, for the system embodiment, since it is basically similar to the method embodiment, the description is relatively simple, and reference can be made to the partial description of the method embodiment for the related parts.

[0157] 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 determining the resilient modulus inside a subgrade based on dynamic and static modulus partitioning, characterized in that The specific steps are as follows: S1. Establish a plane strain finite element model of the subgrade and pavement structure to determine the action time of different loads, determine the correlation between the dynamic and static resilient moduli of subgrade soil under different load action times, and determine the load action time threshold; S2. Establish an estimated equation for the load action time at different vehicle speeds and depths from the subgrade top surface, and determine the critical depth of the dynamic and static resilient moduli of the subgrade at different vehicle speeds; establish a dynamic and static modulus partition based on the critical depth of the dynamic and static resilient moduli of the subgrade; S3. Construct a constitutive model of the subgrade modulus and complete the calculation of the internal resilient modulus of the subgrade.

2. The method for determining the resilient modulus inside a roadbed based on the partition of static and dynamic moduli according to claim 1, wherein The specific steps of S1 are as follows: S101. Conduct basic performance tests on subgrade soil samples to determine the optimum moisture content and maximum dry density of the soil samples; S102. Establish a plane strain finite element model of the subgrade and pavement structure to determine the action time and intermittent time of the internal dynamic load of the subgrade; S103. Conduct dynamic resilient modulus tests on target soil samples with different multiples of the optimum moisture content and different compaction degrees under different load action durations to fit and establish a prediction model considering moisture content, compaction degree, load action time and stress state; S104. Conduct static triaxial tests on target soil samples with different multiples of the optimum moisture content and different compaction degrees to fit and establish a static resilient modulus prediction model; S105. Plot the ratio curve of the dynamic resilient modulus to the static resilient modulus under different load action times with the load action time as the abscissa and the ratio of the dynamic and static resilient moduli as the ordinate, and determine the load action time threshold based on the ratio curve.

3. The method for determining the resilient modulus inside a roadbed based on the partition of dynamic and static moduli according to claim 2, characterized in that, The method for determining the load action time threshold is: when the value of the ratio curve of the dynamic and static resilient moduli in S105 tends to be stable, record the load action time at this time as the load action time threshold. When the load action time is less than the load action time threshold, the internal resilient modulus of the subgrade is the dynamic resilient modulus; when the load action time is greater than or equal to the load action time threshold, the internal resilient modulus of the subgrade is the static resilient modulus.

4. A method for determining the resilient modulus inside a roadbed based on dynamic and static modulus zoning according to claim 2, characterized in that The prediction model considering moisture content, compaction degree, load action time and stress state in S103 is specifically: Among them, M R is the dynamic resilient modulus; p a is the standard atmospheric pressure; t is the load application time; t0 is the common load application time; K is the degree of compaction; w is the actual moisture content; w opt is the optimum moisture content; k1 to k6 are model parameters, θ is the volumetric stress; τ oct is the octahedral shear stress.

5. The method for determining the resilient modulus inside a roadbed based on the partition of static and dynamic moduli according to claim 2, wherein, The static resilient modulus prediction model in S104 is specifically: Among them, M R静 is the static resilience modulus, τ oct静 is the static octahedral shear stress, k1 to k5 are model parameters, p a is the standard atmospheric pressure; K is the degree of compaction; w is the actual water content; w opt is the optimum water content; θ is the volumetric stress.

6. The method for determining the resilient modulus inside a roadbed based on the partition of dynamic and static moduli according to claim 1, characterized in that, The specific steps of S2 are as follows: S201. Based on the plane strain finite element model of the subgrade and pavement structure established in S1, determine the relationship between the load action time and vehicle speed at different depths from the subgrade top surface, and the relationship between the load action time and depth from the subgrade top surface at different vehicle speeds; S202. Establish a prediction model for the load action time at different depths from the subgrade top surface at different vehicle speeds: where t is the load action time, e is the base of the natural logarithm, v is the vehicle speed, h is the depth from the subgrade top surface, and k1 to k3 are model parameters; S203. Determine the method for determining the depth from the subgrade top surface for a given vehicle speed and load action time based on the prediction model established in S202; S204. Substitute the load action time threshold into t in the formula in S203 to determine the critical depth of the dynamic and static resilient moduli of the subgrade, and determine the dynamic and static modulus partition based on the critical depth of the dynamic and static resilient moduli of the subgrade.

7. A method for determining the resilient modulus inside a subgrade based on dynamic and static modulus zoning according to claim 6, characterized in that The specific dynamic and static modulus zoning is as follows: when the depth from the roadbed top surface is less than or equal to the critical depth of the dynamic and static resilient modulus, the roadbed resilient modulus is the dynamic resilient modulus; when the depth from the roadbed top surface is greater than the critical depth of the resilient modulus, the roadbed resilient modulus is the static resilient modulus.

8. The method for determining the resilient modulus inside a subgrade based on dynamic and static modulus partitioning according to claim 1, wherein The specific steps of S3 are as follows: S301. Conduct finite element modeling for different working conditions of the roadbed; S302. Establish a constitutive model for determining the roadbed modulus; S303. Based on the finite element model in S301, determine the relationship between the roadbed thickness and the deflection peak values of the road surface and the roadbed top surface, regard the roadbed as a half-space structure, and determine the minimum required thickness; S304. Conduct finite element modeling for the target roadbed working condition, introduce the constitutive model established in S302 into the finite element model established in S304, and determine the internal resilient modulus of the roadbed.

9. A method for determining the resilient modulus inside a roadbed based on dynamic and static modulus zoning according to claim 8, characterized in that In S301, ABAQUS is used to conduct finite element modeling for different working conditions of the roadbed. Four-node ring element CAX4 is used in the finite region, and infinite element CINAX4 is used at the boundary; The specific constitutive model for calculating the roadbed modulus in S302 is as follows: When <When the load application time threshold is reached, When ≥ When the load application time threshold is reached, Then use the load action time threshold to replace the expression of the static resilient modulus in the constitutive model; Among them, M is the resilient modulus inside the subgrade; p a is the standard atmospheric pressure; t1 is the load application time threshold; t0 is the common load application time; K is the degree of compaction; w is the actual moisture content; w opt is the optimum moisture content; k1 to k9 are model parameters, θ is the volumetric stress; τ oct is the octahedral shear stress; t is the load application time, e is the base of the natural logarithm, v is the vehicle speed, and h is the depth from the subgrade top surface.

10. A method for determining the resilient modulus inside a subgrade based on the partition of dynamic and static moduli according to claim 1, characterized in that In S1, the plane strain finite element model of the roadbed pavement structure is established using ABAQUS. Four-node element CEP4 is used in the finite region, and infinite element CINPE4 is used at the boundary.

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