Nonlinear prediction method of subgrade soil resilient modulus and k0 prediction method

Abstract

The application discloses a kind of considering nonlinear subgrade soil resilience modulus estimation method and estimation method, comprising: obtaining measured data under different compaction degree, moisture content and stress state by oedometer;According to the influence law of experimental result analysis normal stress, compaction degree and moisture content factor pair, determine the relationship with normal stress, compaction degree and moisture content respectively;The estimation model is constructed as the function of exponential form with physical constraint, and the model parameters in the estimation model are expressed as the polynomial of compaction degree and moisture content;Based on the estimation model, the static octahedral shear stress is calculated, so as to calculate the resilience modulus of subgrade soil.The application takes normal stress as the core and considers physical state, constructs the static soil pressure coefficient estimation model with clear physical meaning, measurable engineering parameters, and can be directly embedded into roadbed dynamic response analysis, and is used for subgrade soil resilience modulus estimation, simple, fast, improves calculation efficiency and accuracy.

Description

Technical Field

[0001] This invention belongs to the field of road engineering technology, and relates to a method for predicting the resilient modulus of subgrade soil considering nonlinearity. Prediction methods. Background Technology

[0002] The resilient modulus is a key parameter characterizing the stress-strain properties of a roadbed structure under traffic loads. Its value is related to factors such as the stress state, compaction degree, and moisture content. For fine-grained soils, the effects of cyclic stress and contact stress on the resilient modulus are diametrically opposed. Therefore, the dynamic deviatoric stress caused by the load and the static deviatoric stress generated by the self-weight stress are considered separately, and a resilient modulus prediction model considering the influence of dynamic and static stresses is proposed, as shown in equation (1). First, the applicable scope of the model is extended from the shallow dynamic load zone to the entire roadbed. In the model, the static deviatoric stress is calculated by equation (2).

[0003] (1)

[0004] In the formula, , , , These are model parameters; For volumetric stress; For dynamic octahedral shear stress; It represents static octahedral shear stress.

[0005] (2)

[0006] In the formula, The coefficient of earth pressure at rest. Let z be the unit weight of the subgrade, where z represents the distance from the point to be calculated in the subgrade to the top surface of the subgrade.

[0007] Therefore, the key to applying this model to conduct dynamic response analysis of roadbed structures lies in determining the coefficient of earth pressure at rest ( ). In earlier calculations, this value was often derived from an ideal elastic body and was frequently considered a constant. The coefficient of earth pressure at rest refers to the ratio of horizontal stress to vertical stress under strictly constrained lateral deformation; it is usually expressed as... The earth pressure coefficient at rest is crucial for determining the initial stress state of soil and the distribution of earth pressure on retaining structures, and is an indispensable design parameter in geotechnical engineering. However, numerous studies have shown that the earth pressure coefficient at rest is nonlinear and significantly influenced by factors such as the angle of internal friction, plasticity index, dry density, and degree of consolidation. Existing... The research is mainly divided into two aspects: the modification and extension of empirical formulas and the exploration of mechanisms based on microscopic states. However, the established... The prediction model either has too few parameters, causing it to lose sufficient physical meaning, or its mechanical mechanism is too complex, resulting in low practicality. Summary of the Invention

[0008] To address the aforementioned problems, this invention provides a method for predicting the resilient modulus of subgrade soil that considers nonlinearity. The estimation method, with normal stress as the core and considering physical properties, constructs a static earth pressure coefficient that has clear physical meaning, measurable engineering parameters, and can be directly embedded into the dynamic response analysis of roadbed. The prediction model improves prediction efficiency and accuracy.

[0009] The technical solution adopted in this invention is a method that considers nonlinearity. The estimation method includes the following steps:

[0010] S1, via Consolidation apparatus considers factors such as normal stress, degree of compaction, and moisture content. Consolidation tests were conducted to obtain results under different compaction degrees, moisture contents, and stress states. The measured data, Indicates the coefficient of earth pressure at rest;

[0011] S2: Analyze the effects of normal stress, compaction degree, and moisture content on the experimental results. The influence pattern, determine The relationship between these parameters and normal stress, compaction degree, and moisture content, respectively.

[0012] S3: By using grey relational analysis, it is determined that normal stress is the dominant factor. Based on the effect of normal stress on... The influence patterns, combined with the constitutive theory of soil and rock, are determined. The limit behavior that should be satisfied, thereby... The prediction model is constructed as an exponential function with physical constraints; and... The model parameters in the prediction model are expressed as polynomials of compaction degree and moisture content.

[0013] Furthermore, in S1, the static earth pressure coefficient consolidation test sets multiple normal stresses, multiple compaction degrees, and multiple moisture contents. The multiple normal stresses cover the overlying self-weight stress borne by the soil at a subgrade depth of 0~20m, the multiple compaction degrees cover 87%~96%, and the multiple moisture contents cover 0.8OMC~1.4OMC, with OMC being the optimum moisture content.

[0014] Further, in the S1, while the normal load is applied on the top of the sample, the lateral surface of the sample is wrapped by the water bag, and the stress is transmitted to the pressure sensor by squeezing the water bag, so as to measure the lateral stress under the current normal stress, and the lateral stress under the current stress state is calculated by the ratio of the lateral stress to the normal stress .

[0015] Further, the method for carrying out the consolidation test in the S1 is as follows:

[0016] The consolidation container is calibrated, the air inside the water bag is exhausted, the water injection amount required by the water bag during the test is determined, and air-free water is used as the injection liquid;

[0017] The ring knife sample is pressed into the consolidation container, and the water bag is injected with water according to the determined water injection amount;

[0018] The test is started, the pre-load is applied first, then the normal stress is applied in sequence, and the lateral stress is recorded every fixed time.

[0019] Further, the S3 includes the following steps:

[0020] S31, the correlation degree between the compaction degree, the water content and the normal stress is evaluated by the grey correlation degree method, and it is determined that the normal stress is the dominant factor;

[0021] S32, the prediction model considering the normal stress is established, and the expression is as follows:

[0022]

[0023] In the formula, σ is the normal stress, A and B are model parameters; is the standard atmospheric pressure;

[0024] S33: according to the change rule of the model parameters A and B respectively with the water content and the compaction degree, the expression of the model parameter A is as follows: ,

[0025] The expression of the model parameter B is as follows:

[0026]

[0027]

[0028] wherein, represents the water content, represents the compaction degree, , , ​​​​​are fitting parameters.

[0029] Further, the fitting parameters , , are determined by:

[0030] According to S1, carry out consolidation test, bring multiple compaction degree, moisture content and normal stress into the formula of S32 and S33, calculate to obtain , use the measured data obtained by test, through nonlinear least square method or stepwise linearization regression inversion to obtain fitting parameters , , , ; the subgrade soil of the same soil quality as the sample is fitted with the same parameters, and the static earth pressure coefficient of the subgrade soil to be measured is calculated by bringing in.

[0031] A nonlinear subgrade soil resilience modulus prediction method, comprising the following steps:

[0032] The prediction model is brought into the following formula to calculate the static octahedral shear stress , so as to calculate the resilience modulus of the subgrade soil by the following formula ;

[0033]

[0034]

[0035] wherein, is the density of the subgrade soil, is the acceleration of gravity, is the distance from the top surface of the subgrade to the point to be calculated in the subgrade; , , , are model parameters of the resilience modulus prediction model of the subgrade soil; is the bulk stress; is the dynamic octahedral shear stress; is the standard atmospheric pressure.

[0036] Further, the model parameters of the resilience modulus prediction model of the subgrade soil , , , are fitted and calibrated by carrying out dynamic triaxial tests on the test site.

[0037] The beneficial effects of the present application are:

[0038] ​1. The application couples the physical state (compaction degree, water content) of the subgrade soil with the stress state (normal stress) through the geotechnical constitutive mechanism, constructs a static earth pressure coefficient with clear physical meaning, measurable engineering parameters, and can be directly embedded into the dynamic response analysis of the subgrade, guided by the yield surface evolution theory The prediction model reveals and quantifies the nonlinear variation law of the subgrade soil under the influence of multiple factors such as normal stress, compaction degree and water content; the static earth pressure coefficient The prediction accuracy of the prediction model can reach 92%.

[0039] 2. The static earth pressure coefficient The prediction model is used for subgrade soil resilience modulus prediction, simple, fast, improves the calculation efficiency and accuracy; in full-scale test, compared with the calculation result under the traditional constant The resilience deflection prediction accuracy of the application method is improved by 46% compared with the traditional constant condition, which significantly improves the dynamic response analysis accuracy of the subgrade structure, and solves the long-neglected but significant technical blind spot. BRIEF DESCRIPTION OF DRAWINGS

[0040] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed to be used in the embodiments or prior art description will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0041] Figure 1 is the GJY type consolidation apparatus in the embodiments of the present application.

[0042] Figure 2 is the consolidation test test principle diagram in the embodiments of the present application.

[0043] Figure 3 is the consolidation test flow chart in the embodiments of the present application.

[0044] Figure 4 is the particle distribution curve in the embodiments of the present application.

[0045] Figure 5 is the relationship curve diagram between normal stress and lateral stress in the embodiments of the present application.

[0046] Figure 6 is the relationship curve diagram between the static earth pressure coefficient and the normal stress in the embodiments of the present application.

[0047] Figure 7 is the soil sample under different normal stresses in the embodiments of the present application.​​​ A curve graph of the relationship with the compaction degree.

[0048] Figure 8 is a curve graph of the correlation degree under different resolution coefficients in the embodiment of the present application. A curve graph of the relationship with the water content.

[0049] Figure 9 is a curve graph of the correlation degree under different resolution coefficients in the embodiment of the present application.

[0050] Figure 10 is a schematic diagram of an elliptical yield surface in the embodiment of the present application.

[0051] Figure 11 is a curve graph of the fitting relationship of parameter A in the embodiment of the present application.

[0052] Figure 12 is a curve graph of the fitting relationship of parameter B in the embodiment of the present application.

[0053] Figure 13 is a curve graph of the correlation degree under different water contents in the embodiment of the present application. A comparison graph of the predicted value and the actual value; wherein, Figure 13 (a) is a comparison graph of the water content of 10.44%, Figure 13 (b) is a comparison graph of the water content of 13.05%, Figure 13 (c) is a comparison graph of the water content of 15.66%, Figure 13 (d) is a comparison graph of the water content of 18.27%.

[0054] Figure 14 is a full-scale test site of a geotechnical test slot in the embodiment of the present application.

[0055] Figure 15 is a principle diagram of a loading system in the embodiment of the present application, wherein, Figure 15 (a) is a general schematic diagram, Figure 15 (b) is a detailed structure diagram.

[0056] Figure 16 is a three-dimensional finite element model of a test area of a geotechnical test slot in the embodiment of the present application.

[0057] Figure 17 is a three-dimensional scatter diagram of static load-dynamic load-deflection in the embodiment of the present application.

[0058] In the figure, 1. base, 2. sample, 3. lower permeable stone, 4. upper permeable stone, 5. loading cap, 6. water inlet, 7. water bag, 8. interface, 9. pore pressure instrument, 10. outer ring, 11. inner ring, 12. weight, 13. measuring rod, 14. L-shaped drag piece, 15. LVDT jack, 16. FTS actuator, 17. extension rod, 18. bolt. DETAILED DESCRIPTION

[0059] The technical solutions in the embodiments of the present application will be clearly and completely described below in conjunction with the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments of the present application, all other embodiments obtained by a person of ordinary skill in the art without creative effort belong to the scope of protection of the present application.

[0060] Embodiment 1,

[0061] A nonlinear consideration method The estimation method comprises the following steps:

[0062] S1: Based on the GJY type consolidation instrument, a static earth pressure coefficient (K0) consolidation test considering the factors of normal stress, compaction degree and water content is carried out.

[0063] S11: The test equipment is a GJY type consolidation instrument, which mainly comprises a consolidation container, an axial loading device (maximum load 400 kPa), a water bag 7, a pressure sensor (maximum range 1000 kPa, maximum allowable error 0.5% FS), a pore pressure instrument 9 and the like, and the test equipment is as shown in the figure. Figure 1 S12: The test principle is to use the properties of incompressibility and isotropy of water, to apply a normal load on the top of the sample 2, to fully wrap the side of the test piece by using the water bag 7, to transmit the stress to the pressure sensor by extruding the water bag 7, to measure the lateral stress under the current normal stress, and finally to calculate according to formula (3), so as to obtain the K0 under the current stress state. The test structure diagram is as shown in the figure, the sample 2 is placed on the base 1, the bottom and the top of the sample 2 are respectively placed with the lower water permeable stone 3 and the upper water permeable stone 4, the sample 2 is wrapped with the water bag 7, the water bag 7 is connected with the water inlet 6, the top of the upper water permeable stone 4 is provided with the loading cap 5, the side wall is provided with the penetrating interface 8, and the signal line led out at the interface 8 is connected with the pore pressure instrument 9.

[0064] (3) Figure 2 In formula (3):

[0065] is the normal stress; is the lateral stress.

[0066] S13: The test process is as shown in the figure:

[0067] S13: The test process is as shown in the figure: Figure 3

[0068] ​​​​​(1) Use rigid correction block to correct the consolidation container, exhaust the air inside the water bag 7, and determine the required water injection amount of the water bag 7 during the test. It is worth noting that, in order to reduce the influence of gas on the test accuracy, the embodiment selects to use the gas-free water obtained after boiling, sealing and natural cooling as the injection liquid.

[0069] (2) Press the cutting ring sample into the consolidation container, and inject the water bag 7 according to the determined water injection amount. In order to ensure that the soil sample is in full contact with the water bag 7, stop injecting water when the pore pressure gauge 9 reads slightly more than zero.

[0070] (3) Start the test, first apply a pre-load of 1 kPa, then apply a normal stress of 12.5 kPa, 25 kPa, 50 kPa, 100 kPa, 200 kPa, 300 kPa, and 400 kPa in turn, record the lateral stress reading every 1 hour, and when the hourly increment of each level of lateral stress is not greater than 1.0 kPa, the next level of normal stress can be applied. In this way, until the last level of lateral stress reaches stability, that is, the test under this working condition is completed.

[0071] S14: In order to study the influence of compaction degree, water content and normal stress on the low liquid limit clay containing sand , 4 compaction degrees (covering 87% ~ 96%), 4 water contents (covering 0.8OMC ~ 1.4OMC, OMC is the optimum water content) and 7 levels of normal stress (excluding pre-load, covering 0 ~ 20m roadbed depth) are set for consolidation test, and the detailed test conditions are shown in Table 1.

[0072] Table 1 Consolidation test scheme

[0073]

[0074] S2: According to the experimental results, analyze the influence of normal stress, compaction degree and water content factors on . The test soil sample is low liquid limit clay containing sand, the particle size distribution curve is shown in Figure 4 , and the basic physical properties are shown in Table 2.

[0075] Table 2 Basic physical parameters of clay

[0076]

[0077] S21: Relationship between lateral stress and normal stress, as Figure 5As shown in the figure, under a given compaction state, the curves generally exhibit a positive correlation, meaning that as the normal stress increases, the lateral stress also increases. Specifically, when the normal stress gradually increases from 12.5 kPa to 400 kPa, the lateral stresses of samples with compaction degrees of 87%, 90%, 93%, and 96% increase from 3 kPa, 2.7 kPa, 2.5 kPa, and 2.4 kPa to 161 kPa, 139 kPa, 135 kPa, and 125 kPa, respectively, which are approximately 54 times, 51 times, 54 times, and 52 times the initial values ​​(3 kPa, 2.7 kPa, 2.5 kPa, and 2.4 kPa), showing a significant increase. Furthermore, it can be seen that the relationship between lateral stress and vertical stress is closely related to the compaction degree. When equal normal stress is applied, as the compaction degree gradually increases, the lateral stress shows a gradually decreasing trend, with a maximum decrease of up to 25%.

[0078] S22: The relationship between the stress and the normal stress;

[0079] like Figure 6 As shown, from the perspective of the entire loading process, It is not a constant, but rather increases with increasing normal stress, exhibiting significant nonlinear characteristics. Specifically, normal stress - The relationship curve exhibits a monotonically increasing trend, which can be mainly divided into three stages: a rapid increase period, a relatively rapid increase period, and a slow increase period. This occurs when the normal stress is relatively small (0~50 kPa). It increases rapidly; the normal stress continues to increase (50~200kPa). The growth rate slowed down; when the normal stress exceeded 200 kPa, It tends to stabilize. This is because in the initial stage of loading, the normal stress is relatively small, the interlocking and friction between soil particles have not been fully utilized, the constraint on lateral deformation is relatively strong, and the normal stress is difficult to be effectively converted into lateral stress, leading to... Although the stress increased rapidly, it remained at a relatively low level. As the normal stress increased, the soil sample underwent yielding failure, the deformation shifted from elastic to plastic, particle slippage, rotation, and fragmentation became dominant, the soil was compressed, and the structure tended to stabilize. The porosity continues to rise. Towards the later stages of loading, the porosity decreases significantly, compressible space diminishes, particle contact area increases, and friction becomes the dominant factor resisting deformation. The growth rate has slowed and is gradually stabilizing.

[0080] S23: The relationship between compaction degree and compaction degree;

[0081] like Figure 7 As shown, when the normal stress remains constant, as the compaction degree gradually increases from 87% to 96%, It shows a clear downward trend, especially at high compaction degrees, where the decrease is even more pronounced. For example, at 96% compaction degree... The decrease was approximately 28%. This is because, under low compaction, the soil structure is loose, with larger pores, weaker interactions between particles, lower contact friction, and higher compressibility. Under external forces, it is more prone to relative slippage. When normal stress is applied, the lateral stress response is strong, resulting in a larger... Value; Under high compaction, the soil becomes denser, pores are compressed, the contact force between particles is enhanced, shear strength increases, and the soil structure tends to be stable. Under normal stress, the specimen transmits stress in the horizontal direction more fully, thus leading to The concentration decreases. Furthermore, as the normal stress increases, the soil sample at the same compaction degree... The pressure gradually increases, and the higher the compaction degree, the smaller the increase, but the minimum increase still reaches over 60%. This demonstrates the coupling effect of normal stress and compaction degree. It has a significant impact.

[0082] S24: The relationship between moisture content;

[0083] like Figure 8 As shown, under a certain normal stress, with the increase of moisture content, It is also gradually increasing, and continues to increase along with the increase in normal stress. Specifically, under the condition of constant normal stress, when the moisture content increases from 10.44% to 18.27%, The increase can be as low as 43%. Under the same moisture content conditions, as the normal stress increases, The growth rate was at least 46%. This is because under lower normal stress, the original cementation between soil particles only partially fails. Increased moisture content further weakens the structural bonds, reducing interparticle interaction and increasing the stress required to maintain lateral restraint. The initial cementation is largely destroyed at high normal stress, and the effect of moisture content mainly stems from the decrease in matrix suction. The increase was limited. This experiment was limited to low-pressure conditions (0~400 kPa), and no significant slowdown in the increase was observed. It can be determined that the coupling effect of water content and normal stress will influence... It has a significant impact.

[0084] S3: Construction of the prediction model;

[0085] Due to the soil during the loading process The changes in compaction degree, moisture content, and normal stress exhibit highly nonlinear characteristics, which can be seen from... It is not a constant, but is closely related to its physical properties and stress state. Therefore, simply measuring it by a single index such as the internal friction angle or plasticity index, or by the recommended values ​​in relevant specifications, is not sufficient for a specific state. Its applicability is not high, therefore it is necessary to establish The functional relationship between vertical stress, compaction degree, and moisture content.

[0086] S31: Grey Relational Analysis. Grey relational analysis is commonly used to analyze the degree of influence of different factors on a target, and is particularly suitable for uncertain analyses involving small sample sizes and missing information. As can be seen from the preceding analysis, normal stress, compaction degree, and moisture content have a significant impact on... It has varying degrees of impact, in order to accurately construct In predicting the model, determining which index to use as the main variable is particularly important. Therefore, it is necessary to evaluate the relationship between compaction degree, moisture content, and normal stress using the grey relational analysis method. The degree of correlation.

[0087] Normal stress, compaction degree and moisture content have an effect on The degree of influence results are as follows Figure 9 As shown. It can be seen that, regardless of whether the resolution coefficient is constant or as the resolution coefficient continues to increase, the normal stress affects... The effects of compaction degree and moisture content are clearly dominant. The degree of their impact is quite similar.

[0088] S32: The test results show that: It gradually increases with the increase of normal stress, and the rate of increase gradually slows down, from which it is inferred that... It is a parameter related to normal stress and has an upper limit. The following explanation, combined with soil constitutive theory, further illustrates that the yielding behavior of soil is usually mediated by body stress. -Eccentric stress It is described by a quasi-elliptical yield surface in space. For example... Figure 10 As shown, with the increase of normal stress, corresponding to the increase of subgrade depth, As the soil density gradually increases, the soil sample compaction increases, which in turn has two effects: ① Critical stress ratio Gradually reduce until residual strength is reached. ② Under the influence of hardening law, the boundary surface continues to expand outward. During this process, the stress state can be approximated as the intersection of the critical state line and the boundary surface, as... The increase gradually shifts to the lower right. Therefore, as... The continuous increase getting closer ,Right now Gradually approaching Its value is generally 0.4~0.5 for fine-grained soils. In this process, corresponding to a specific... of It exhibits a decreasing trend until it reaches zero. Therefore, for soil at extremely deep depths, when the normal stress approaches its maximum value, it exhibits an isotropic hydrostatic pressure state. Approaching zero Accordingly, it reaches a peak value of 1.0. This extreme behavior reveals The normal stress is a function with an upper limit.

[0089] visible, The relationship with normal stress needs to satisfy the following three conditions: (1) When hour, (2) It is a monotonically decreasing function; (3) when hour, To reduce the number of fitting parameters, it is assumed that under maximum normal stress, the shear strength of the soil and rock is completely lost due to mineral phase transformation, amorphization, and chemical bond rearrangement. Approaching 0, at this point Equation (4) is used to describe the normal stress and The relationship.

[0090] (4)

[0091] In the formula: A and B are the fitting parameters; Standard atmospheric pressure.

[0092] S33: As Figure 11 , Figure 12 As shown, parameters A and B both change with compaction degree and moisture content. It can be seen that parameter A decreases with increasing moisture content and increases with increasing compaction degree. Therefore, a polynomial approach can be considered. A fitting was performed. Parameter B generally increases with increasing moisture content, but the overall trend and final value of B differ significantly at different moisture contents. However, at the same moisture content, changes in compaction degree have no significant effect on B. Therefore, parameter B is only fitted using a polynomial with respect to moisture content. .

[0093] The fitting results are as follows:

[0094] (5)

[0095] (6)

[0096] (7)

[0097] Substituting the parameter results (5), (6), and (7) into the polynomial, we obtain:

[0098] (8)

[0099] (9)

[0100] In the formula: It refers to the degree of compaction; It refers to the moisture content.

[0101] Substituting equations (8) and (9) into equation (4), we get:

[0102] (10)

[0103] The subgrade soil used in the embodiments of the present invention The final prediction model is shown in equation (10). Equation (10) is used to predict the following under different operating conditions. Under conditions of 10.44%, 13.05%, 15.66%, and 18.27%, at different compaction degrees, The curves showing the variation of normal stress are as follows: Figure 13 As shown in Figures (a)-(d), the lines represent predicted values, and the graphs represent measured values. It can be seen that the predicted... It decreases with increasing compaction degree, increases with increasing moisture content, and increases with increasing normal stress, consistent with measured values. They exhibit the same evolutionary pattern, with a prediction accuracy of up to 92%, demonstrating good performance. However, due to the limited soil types used in this embodiment, the relationships between moisture content and compaction in A and B may not be applicable to other soils. Further research is needed for other soil types. Consolidation test, fitting parameters A and B.

[0104] Example 2,

[0105] A method for predicting the resilient modulus of subgrade soil considering nonlinearity includes the following steps:

[0106] As mentioned earlier, previous studies neglected to consider... The nonlinear characteristics of [the system]. For this reason, the original calculation [is first...]. Regarding Poisson's ratio The formula is (11):

[0107] (11)

[0108] Replace equation (11) with equation (10) determined in embodiment 1 of the present invention, and substitute equation (10) into equation (2) to calculate. Thus, the resilient modulus of the subgrade soil can be calculated using equation (1). .

[0109] The verification embodiment 1 establishes The effectiveness and superiority of the prediction model in the calculation of the resilient modulus of subgrade soil:

[0110] A full-scale test site was built. A full-scale indoor comprehensive test platform with a width of 3m, a length of 15m and a height of 4m was built, as shown in Figure 14 The test site is a cylindrical shape with a diameter of 2m and a depth of 3m, which is isolated by a custom-made split mold and wrapped with waterproof geotextile on the outside, and PVC water injection pipes are pre-embedded to realize dynamic regulation of the humidity of the subgrade. When filling, the water content and compaction degree of each layer are strictly controlled, and a plurality of humidity sensors are embedded in the form of back excavation to monitor the internal state in real time.

[0111] Test scheme. In view of the fact that the traditional test method cannot consider the pavement constraint, the loading system used in the embodiment of the application includes a loading device and a collection system. As shown in Figure 15 Fig. (a) and (b), the entire loading device includes an inner ring 11 and an outer ring 10, the inner ring 11 is connected with a FTS actuator 16, the top of the FTS actuator 16 is connected with an extension rod 17, which is mainly used for simulating driving dynamic load; and the outer ring 10 is placed with a weight 12 above, which is used for simulating the pavement constraint, the outer ring static load is 1kPa, 1 group of weights is 5kPa, 2 groups of weights are 15kPa, and 3 groups of weights are 25kPa. The top of the inner ring 11 and the outer ring 10 is installed with a horizontally extending measuring rod 13 through a bolt 18, the measuring rod 13 is parallel to the surface of the subgrade to be tested, the measuring rod 13 is fixed through an L-shaped drag piece 14, an LVDT jack 15 is arranged on the measuring rod 13, the diameter of the inner ring 11 is 0.4m, and the diameter of the outer ring 10 is 0.4m. The loading is applied in the form of dynamic and static force combination loading of the inner and outer rings, in order to fully collect deflection data, 5 displacement sensors LVDT are arranged at the center of the inner ring r=0.0 and the left and right positions r=30, 60cm, which are installed on the measuring rod 13 through the LVDT jack 15. The collection system is realized by an LVDT independent of the loading system, and the accuracy is higher than that of the traditional test method.

[0112] Based on this system, the research on the test verification of the prediction model for the resilient modulus of subgrade soil is carried out:

[0113] First, loading tests considering the combination of static and dynamic loads were conducted, and rebound deflection (i.e., measured deflection) was collected simultaneously. The static load was set to six levels: 1 kPa, 5 kPa, 10 kPa, 15 kPa, 20 kPa, and 25 kPa, and the dynamic load was set to six levels: 50 kPa, 60 kPa, 70 kPa, 80 kPa, 90 kPa, and 100 kPa, with an application time of 0.2 s. To avoid the influence of stress history, the static load levels were increased sequentially, and dynamic load tests were conducted at 50 kPa, 60 kPa, 70 kPa, 80 kPa, 90 kPa, and 100 kPa under each static load level (a total of 36 groups). Each loading cycle lasted 100 cycles, and the average of the last five results was taken as the rebound deflection result of this level sequence. Then, a dynamic triaxial test was conducted on soil samples taken at the test site to calibrate the four-parameter model (as shown in equation (1)) (determining the model parameters). , , , Furthermore, a four-parameter numerical model based on full-scale experiments was developed, such as... Figure 16 As shown, calculations are performed sequentially under various loading conditions (36 operating cases). Nonlinear theoretical deflection.

[0114] Subsequently, without altering the numerical model, 36 sets of subgrade structural response calculations were redone, and rebound deflection was collected again. The results were then analyzed using measured deflection and a four-parameter model (without considering...). Theoretical deflection of nonlinear characteristics), four-parameter model (considering) Theoretical deflection of nonlinear characteristics to verify The correctness of the nonlinear model, the results are as follows Figure 17 As shown, Figure 17 Each dot of the same color represents a working condition. Figure 17 Not considered In the calculation of nonlinear theoretical deflection, The calculation is performed using formula (11).

[0115] It can be seen that, compared to Considering it as a constant, the spring modulus calculated by taking into account its nonlinear characteristics using the method of Embodiment 1 of this invention brings a 46% improvement in accuracy, and at lower static load levels, it produces a smaller value than the previous model. This results in lower confining pressure and less stiffness, leading to increased rebound deflection. Conversely, at higher static load levels, the rebound deflection is smaller than in the previous model. Therefore, improving the static earth pressure coefficient model for roadbeds is of great significance for improving the calculation accuracy of the dynamic rebound modulus of roadbeds.

[0116] The coefficient of earth pressure at rest refers to the ratio of horizontal stress to vertical stress under strictly constrained lateral deformation. It is usually expressed as... This indicates that it is crucial in determining the initial stress state of the soil and the distribution of earth pressure on retaining structures, and is an indispensable design parameter in geotechnical engineering.

[0117] The above description is merely a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention are included within the scope of protection of the present invention.

Claims

1. A method considering nonlinearity The prediction method is characterized by, Includes the following steps: S1, via Consolidation apparatus considers factors such as normal stress, degree of compaction, and moisture content. Consolidation tests were conducted to obtain results under different compaction degrees, moisture contents, and stress states. The measured data, Indicates the coefficient of earth pressure at rest; S2: Analyze the effects of normal stress, compaction degree, and moisture content on the experimental results. The influence pattern, determine The relationship between these parameters and normal stress, compaction degree, and moisture content, respectively. S3: By using grey relational analysis, it is determined that normal stress is the dominant factor. Based on the effect of normal stress on... The influence patterns, combined with the constitutive theory of soil and rock, are determined. The limit behavior that should be satisfied, thereby... The prediction model is constructed as an exponential function with physical constraints; and... The model parameters in the prediction model are expressed as polynomials of compaction degree and moisture content; S3 includes the following steps: S31, the grey relational analysis method was used to evaluate compaction degree, moisture content, and normal stress. The degree of correlation determines that normal stress is the dominant factor; S32, Establishing a system that considers normal stress The prediction model is: （1） In the formula: Here, A and B represent the normal stress, and A and B are model parameters. Standard atmospheric pressure; S33: Based on model parameters , Determine model parameters by comparing the variation patterns of moisture content and compaction degree. The expression is: （2） Model parameters The expression is: （3） in, Indicates moisture content, Indicates the degree of compaction. , , All are fitted parameters; The fitting parameters , , The method for determining it is as follows: Conducted in accordance with S1 Consolidation test: Multiple sets of compaction degree, moisture content and normal stress were substituted into equations (1)-(3) to calculate the results. The results obtained from the experiment The measured data were used to obtain the fitting parameters through nonlinear least squares method or stepwise linearized regression inversion. , , The fitting parameters for the subgrade soil with the same soil material as the sample are the same. Substituting these parameters into equations (1)-(3) yields the coefficient of static earth pressure of the subgrade soil to be tested. .

2. The method considering nonlinearity according to claim 1 The prediction method is characterized by, In S1, the static earth pressure coefficient consolidation test sets multiple normal stresses, multiple compaction degrees, and multiple moisture contents. The multiple normal stresses cover the overlying self-weight stress borne by the soil at a subgrade depth of 0~20m, the multiple compaction degrees cover 87%~96%, and the multiple moisture contents cover 0.8OMC~1.4OMC, with OMC being the optimum moisture content.

3. The method considering nonlinearity according to claim 1 The prediction method is characterized by, In step S1, while applying a normal load to the top of the specimen, the side of the specimen is wrapped with a water bladder (7). Utilizing the incompressibility and isobaric properties of water, the stress is transferred to the pressure sensor by squeezing the water bladder (7), thereby measuring the lateral stress under the current normal stress. The stress under the current stress state is calculated by the ratio of the lateral stress to the normal stress. .

4. The method considering nonlinearity according to claim 3 The prediction method is characterized by, The method for conducting the consolidation test in S1 is as follows: The solidification container was calibrated, the air inside the water bladder (7) was purged, the required amount of water to be injected into the water bladder (7) was determined, and de-aired water was used as the injection liquid. Press the ring cutter sample into the consolidation container and inject water into the water bladder according to the determined injection volume (7). To begin the experiment, a preload was applied, followed by progressively increasing normal stresses, with lateral stresses recorded at fixed intervals.

5. A method for predicting the resilient modulus of subgrade soil considering nonlinearity, characterized in that, Includes the following steps: Considering as described in claim 1 nonlinear The prediction method is constructed Substitute the predicted model into equation (4) to calculate the static octahedral shear stress. Thus, the resilient modulus of the subgrade soil can be calculated using equation (5). ; （4） （5） in, The density of the subgrade soil, It is the acceleration due to gravity. This represents the distance from the point to be calculated in the roadbed to the top surface of the roadbed. , , , The model parameters for predicting the resilient modulus of subgrade soil; For volumetric stress; For dynamic octahedral shear stress; Standard atmospheric pressure.

6. The method for predicting the resilient modulus of subgrade soil considering nonlinearity according to claim 5, characterized in that, Model parameters of the roadbed soil resilient modulus prediction model , , , Fitting calibration was performed by conducting dynamic triaxial tests using soil samples taken from the test site.

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