Method for estimating the dynamic elastic modulus of basalt fiber cement silt soil for roadbeds in seasonally frozen areas

Abstract

This invention discloses a method for predicting the dynamic elastic modulus of basalt fiber cement silt used in roadbeds in seasonally frozen areas. The specific steps are as follows: Samples are prepared, and freeze-thaw cycle tests are conducted on the samples, followed by staged loading dynamic triaxial tests to obtain the dynamic stress and strain of the soil under different confining pressures. Hysteresis curves are plotted, and based on the Hardin-Drnevich hyperbolic model, the maximum dynamic elastic modulus and final dynamic stress amplitude of the sample are obtained. A reference dynamic strain is introduced to obtain the normalized secant dynamic elastic modulus. Based on the nonlinear least squares method, statistical analysis is performed on the test data under different confining pressures and freeze-thaw cycle numbers to obtain a prediction model characterizing the relationship between the maximum dynamic elastic modulus and the final dynamic stress amplitude and the confining pressure and the number of freeze-thaw cycles. Through nonlinear regression analysis, a prediction model considering the effects of confining pressure and freeze-thaw cycles is obtained, thus yielding the normalized secant dynamic elastic modulus. This method improves prediction efficiency.

Description

Technical Field

[0001] This invention belongs to the field of road engineering technology, specifically relating to a method for predicting the dynamic elastic modulus of basalt fiber cement silt soil used in roadbeds in seasonally frozen areas. Background Technology

[0002] Compared with other fibers, basalt fiber possesses excellent properties such as high tensile strength, good chemical stability, high temperature resistance, and resistance to acid and alkali corrosion. Basalt fiber can effectively improve the brittle failure of cement-soil mixtures and enhance soil ductility. Simultaneously, basalt fiber cement-soil exhibits good freeze-thaw stability. As a road material, basalt fiber cement-soil will bear long-term dynamic loads from vehicles during its service life. Under freeze-thaw cycles, it is highly susceptible to roadbed deformation and other road defects, affecting road service life and driving safety. Research on the dynamic characteristics of basalt fiber cement-soil for roadbeds in seasonally frozen areas has significant practical implications and can provide a reliable reference for the design and construction of roadbeds in seasonally frozen regions.

[0003] The dynamic characteristics of subgrade soil are the main reference for subgrade design. At present, most scholars mainly focus on the dynamic stress-strain relationship, dynamic elastic modulus and cumulative plastic deformation of raw soil under dynamic load. However, systematic research on the dynamic characteristics of basalt fiber cement composite modified subgrade filler under dynamic load is still insufficient, and research on the influence of special geographical environmental factors in seasonally frozen areas is rarely reported.

[0004] In his paper, "Research on Mechanical Properties and Design Methods of Solidified Silt Subgrade under Cyclic Traffic Loads," Zhang Xiaobin systematically studied the effects of factors such as curing agent dosage, curing age, initial moisture content, and test confining pressure on the dynamic stress-strain, dynamic elastic modulus, and damping ratio characteristics of cement- and high-performance curing agents-solidified silt through cyclic triaxial tests with progressively increasing dynamic stress amplitudes. Simultaneously, based on the influence of each factor on the maximum dynamic elastic modulus, a predictive model for the maximum dynamic elastic modulus of solidified silt was established. However, the predictive model for the maximum dynamic elastic modulus of solidified silt studied in this paper did not consider the influence of freeze-thaw cycles, and the curing agent used was traditional cement, which reduced the applicability and accuracy of the model.

[0005] Chinese patent CN117078080A discloses a rapid evaluation method for the dynamic elastic modulus and compaction degree of roadbed based on an improved PFWD (Power Factor Dynamics Theory). This method establishes optimal regression equations for dynamic elastic modulus and compaction degree, and calculates the required compaction degree and dynamic elastic modulus based on field measured data of dynamic elastic modulus and compaction degree, respectively, using the optimal regression equations to evaluate road construction quality with dual indicators, thus improving efficiency and accuracy. However, this patent does not consider the influence of external environmental conditions on dynamic elastic modulus and compaction degree, and cannot accurately predict the dynamic elastic modulus of soil under different stress conditions of repeated cyclic loading. Summary of the Invention

[0006] In view of the shortcomings and deficiencies of the existing technology, the purpose of this invention is to provide a method for predicting the dynamic elastic modulus of basalt fiber cement silt used in roadbeds in seasonally frozen areas. This method considers the influence of confining pressure and the number of freeze-thaw cycles on the dynamic characteristics of basalt fiber cement silt used in roadbeds in seasonally frozen areas. Based on the Hardin-Drnevich hyperbolic model, through nonlinear least squares method and nonlinear regression analysis, a prediction model for the maximum dynamic elastic modulus and the final dynamic stress amplitude of basalt fiber cement silt under the combined influence of confining pressure and freeze-thaw cycles is established, which greatly improves the prediction efficiency and solves the problems of limited consideration of freeze-thaw cycle effects and complex and time-consuming prediction process in existing prediction methods.

[0007] To achieve the above objectives, the present invention adopts the following technical solution:

[0008] A method for predicting the dynamic elastic modulus of basalt fiber-cement silt soil used in roadbeds in seasonally frozen zones, the method comprising the following steps:

[0009] S1: Prepare the specimens and conduct freeze-thaw cycle tests on the cured specimens with different numbers of freeze-thaw cycles;

[0010] S2: Perform staged loading dynamic triaxial tests on the samples after freeze-thaw cycles to obtain the dynamic stress of the soil under different confining pressures. and dynamic strain ,draw — The hysteresis curve, with its slope defined as the dynamic elastic modulus. , ;

[0011] S3: Fitting based on Hardin-Drnevich hyperbolic model and The relationship between them Where a and b are fitting parameters, the maximum dynamic elastic modulus of basalt fiber cement silt is obtained. and final dynamic stress amplitude Introducing reference dynamic strain , The normalized secant dynamic elastic modulus of basalt fiber cement silt was obtained. , ;

[0012] S4: Based on the nonlinear least squares method, statistical analysis was performed on the experimental data under different confining pressures and freeze-thaw cycles to obtain the maximum dynamic elastic modulus characterizing basalt fiber-cement silt. and final dynamic stress amplitude Prediction models related to confining pressure and number of freeze-thaw cycles;

[0013] S5: Based on the predicted model obtained in step S4, the maximum dynamic elastic modulus of basalt fiber cement silt under the combined effects of confining pressure and freeze-thaw cycles is obtained through nonlinear regression analysis. and final dynamic stress amplitude The prediction model;

[0014] S6: Based on the prediction model obtained in step S5, the maximum dynamic elastic modulus and the final dynamic stress amplitude of basalt fiber cement silt under the combined influence of confining pressure and freeze-thaw cycle can be obtained by substituting the required environmental conditions, confining pressure and freeze-thaw cycle number. Then, the normalized secant dynamic elastic modulus can be obtained.

[0015] Furthermore, step S1 specifically includes the following steps:

[0016] S11: Add water to silty sand to prepare a soil sample with a set moisture content;

[0017] S12: Incorporate cement and basalt fiber into the soil sample;

[0018] S13: For each mix proportion, m parallel samples are prepared by impact molding;

[0019] S14: Wrap the prepared sample in plastic wrap and place it in the curing room for curing;

[0020] S15: Conduct freeze-thaw cycle tests on the cured specimens with different numbers of freeze-thaw cycles.

[0021] Furthermore, in step S12, the cement content, basalt fiber content, and basalt fiber length are recorded. The cement content is the percentage of cement mass to the total mass of dry sand, and the basalt fiber content is the percentage of fiber mass to the total mass of cement and dry sand.

[0022] Furthermore, in step S13, a layered method is used in the impact molding process, and the surface of the upper layer of soil is roughened before the next layer of soil is placed.

[0023] Furthermore, in step S14, the prepared sample is wrapped in plastic wrap and placed in a curing room for 14 days. The curing conditions are a temperature of 20±2 ℃ and a relative humidity of more than 95%.

[0024] Furthermore, in step S15, the selection of the freeze-thaw cycle test temperature requires investigation of the extreme negative temperature values ​​of the project site over the past ten years, and in combination with the soil strength change characteristics under low temperature conditions, the test freezing temperature is selected, the absolute values ​​of the thawing positive temperature and the freezing negative temperature are equal, the freezing and thawing time are both set to 24 h, and the number of freeze-thaw cycles is set to 0, 1, 3, 6 and 10 times in a progressively increasing manner.

[0025] Furthermore, in step S2, the specimen after freeze-thaw cycles is subjected to a graded loading dynamic triaxial test. The waveform applied in the dynamic triaxial test is a half-sine wave; the axial dynamic load frequency is set to 1 Hz; the confining pressures selected for the dynamic triaxial test are 20 kPa, 50 kPa and 80 kPa respectively; and during the test, a confining pressure of 30 kPa is first applied to the specimen for 1000 pre-loading cycles. After the pre-loading is completed, the selected confining pressure is used to perform graded loading with an increment of 40 kPa, and each load level vibrates 12 times.

[0026] Furthermore, in step S4, the maximum dynamic elastic modulus of basalt fiber cement silt is constructed. When using prediction models related to confining pressure, since confining pressure is related to atmospheric pressure, atmospheric pressure is considered during data processing. P a The setting is 101 kPa.

[0027] Furthermore, in step S5, the maximum dynamic elastic modulus of basalt fiber cement silt soil under the combined influence of confining pressure and freeze-thaw cycles... Final dynamic stress amplitude The expression for the prediction model is:

[0028] ;

[0029] ;

[0030] In the formula: , Under the combined effects of confining pressure and freeze-thaw cycles and The parameters, and , and They are based on confining pressure and number of freeze-thaw cycles A model for predicting the maximum dynamic elastic modulus and the final dynamic stress amplitude.

[0031] Compared with the prior art, the advantages and beneficial effects of the present invention are:

[0032] (1) This invention studies the dynamic stress-strain relationship, normalized dynamic elastic modulus, maximum dynamic elastic modulus, and final dynamic stress amplitude of basalt fiber cement silt under different confining pressures and different freeze-thaw cycles. At the same time, based on the Hardin-Drnevich hyperbola model, a prediction model for the maximum dynamic elastic modulus and final dynamic stress amplitude of basalt fiber cement silt that simultaneously considers the effects of confining pressure and freeze-thaw cycles is established through nonlinear least squares method and nonlinear regression analysis. This provides a quantitative basis for the dynamic characteristic analysis of basalt fiber cement silt used in roadbeds in seasonally frozen areas and provides a reliable reference for the design and construction of the project.

[0033] (2) Based on the prediction model obtained by the present invention, the maximum dynamic elastic modulus and the final dynamic stress amplitude of basalt fiber cement silt soil that are close to the actual test values ​​can be obtained by simply substituting the required environmental conditions, confining pressure and number of freeze-thaw cycles. Then, the normalized dynamic elastic modulus can be obtained, which provides an efficient and reliable method for characterizing the dynamic performance of basalt fiber cement silt soil subgrade in seasonally frozen areas.

[0034] (3) The prediction method provided by the present invention greatly improves the prediction efficiency and solves the problems of the existing prediction method having limited consideration of the effects of freeze-thaw cycles and the prediction process being complex and time-consuming. Attached Figure Description

[0035] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0036] Figure 1 This is a multi-stage axial load loading method.

[0037] Figure 2 The dynamic stress-strain curves of basalt fiber cement silt under different confining pressures during 6 freeze-thaw cycles are shown.

[0038] Figure 3 The dynamic stress-strain relationship curves of basalt fiber cement silt under different freeze-thaw cycles at a confining pressure of 50 kPa are shown.

[0039] Figure 4 The experimental values ​​and fitted curves show the relationship between the maximum dynamic elastic modulus and the final dynamic stress amplitude of basalt fiber cement silt and the confining pressure under six freeze-thaw cycles.

[0040] Figure 5The experimental values ​​and fitted curves show the relationship between the maximum dynamic elastic modulus and the final dynamic stress amplitude of basalt fiber cement silt under a confining pressure of 50 kPa and the number of freeze-thaw cycles.

[0041] Figure 6 The curves show the relationship between the normalized secant dynamic elastic modulus and dynamic strain of basalt fiber cement silt under different confining pressures during 6 freeze-thaw cycles.

[0042] Figure 7 The curves show the relationship between the normalized secant dynamic elastic modulus and dynamic strain of basalt fiber cement silt under different freeze-thaw cycles at a confining pressure of 50 kPa.

[0043] Figure 8 This is a comparison chart of the experimental and fitted values ​​of the final dynamic stress amplitude of basalt fiber cement silt under different confining pressures and freeze-thaw cycles.

[0044] Figure 9 This is a comparison chart of the experimental and fitted values ​​of the maximum dynamic elastic modulus of basalt fiber cement silt under different confining pressures and freeze-thaw cycles. Detailed Implementation

[0045] The technical solutions of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0046] This invention provides a method for predicting the dynamic elastic modulus of basalt fiber cement silt soil used in roadbeds in seasonally frozen areas, which is carried out according to the following steps:

[0047] S1: Cylindrical specimens with a cement content of 2%, a fiber content of 0.2%, and a fiber length of 12 mm were prepared by impact molding. At the same time, m parallel specimens were prepared. The prepared specimens were wrapped in plastic wrap and placed in the curing room for curing for 14 days. The cured specimens were subjected to 0 to 10 freeze-thaw cycle tests.

[0048] S2: Perform staged loading dynamic triaxial tests on the samples after freeze-thaw cycles to obtain the dynamic stress of the soil under different confining pressures. and dynamic strain ,draw — Relationship curve;

[0049] S3: Based on the Hardin-Drnevich hyperbolic model, the maximum dynamic elastic modulus of basalt fiber-cemented silt was obtained. and final dynamic stress amplitude Introducing reference dynamic strain The normalized secant dynamic elastic modulus of basalt fiber cement silt was obtained. The specific analysis process is as follows:

[0050] Drawing dynamic stress Dynamic strain Hysteresis curve, and the slope of the hysteresis curve is defined as the dynamic elastic modulus. :

[0051] (1)

[0052] Fitting with Hardin-Drnevich hyperbolic model and The relationship between them can be represented as:

[0053] (2)

[0054] Solving equations (1) and (2) simultaneously yields equation (3):

[0055] (3)

[0056] In particular, in formula (3) When, we get equation (4); when in equation (2) Then, we get equation (5):

[0057] (4)

[0058] (5)

[0059] In the formula: This is the maximum dynamic elastic modulus, in MPa. This represents the final dynamic stress amplitude.

[0060] Introducing reference dynamic strain Its expression is equation (6):

[0061] (6)

[0062] Combining equations (3), (4), and (6), we can obtain the expression for the normalized secant dynamic elastic modulus as follows:

[0063] (7)

[0064] In the formula: This is the normalized secant dynamic elastic modulus.

[0065] In particular, the dynamic elastic moduli analyzed in this invention are all normalized secant dynamic elastic moduli.

[0066] S4: Based on the nonlinear least squares method, statistical analysis was performed on the experimental data under different confining pressures and freeze-thaw cycles to obtain the maximum dynamic elastic modulus characterizing basalt fiber-cement silt. and final dynamic stress amplitude Prediction models related to confining pressure and number of freeze-thaw cycles;

[0067] S5: Based on the predicted model obtained in step S4, the maximum dynamic elastic modulus of basalt fiber cement silt under the combined effects of confining pressure and freeze-thaw cycles is obtained through nonlinear regression analysis. and final dynamic stress amplitude The prediction model was developed, and its effectiveness was verified.

[0068] S6: Based on the prediction model obtained in step S5, the maximum dynamic elastic modulus and the final dynamic stress amplitude of basalt fiber cement silt under the combined influence of confining pressure and freeze-thaw cycle can be obtained by substituting the required environmental conditions, confining pressure and freeze-thaw cycle number. Then, the normalized secant dynamic elastic modulus can be obtained.

[0069] Specifically, in this embodiment, silty sandy soil widely distributed in Songyuan City, Jilin Province, is used as raw material. Based on previous research, 42.5 grade ordinary Portland cement (PO 42.5) with an optimal admixture of 2% is selected to treat the soil. The basic physical parameters of the cement-soil are shown in Table 1. Short-cut basalt fiber produced by Jilin Huayang New Composite Materials Co., Ltd. is used as the modifying material. Its basic physical and mechanical parameters are shown in Table 2.

[0070] Table 1 Basic physical parameters of cement-soil

[0071] <![CDATA[Liquid limit w L (%)]]> <![CDATA[Plastic limit w P (%)]]> <![CDATA[Plasticity index I P (%)]]> <![CDATA[Optimum moisture content limit w opt (%)]]> <![CDATA[Maximum dry density ρ d max ( g / cm 3 )]]> 25.6 17.6 8.9 9.69 2.042

[0072] Table 2 Basic Properties of Basalt Fibers

[0073] Fiber type Diameter (μm) <![CDATA[Density (g / cm 3 ).]]> Tensile strength (MPa) Elastic modulus (GPa) Melting point (°C) Monofilament 7 ~ 15 2.63 3000 ~ 4800 91 ~ 110 1050

[0074] The following details the method for predicting the dynamic elastic modulus of basalt fiber cement silt soil used in roadbeds in seasonally frozen zones, specifically including the following steps:

[0075] S1: Sample preparation was conducted according to the specific requirements of the "Specifications for Geotechnical Testing of Highways" JTG 3430-2020. First, an appropriate amount of water was added to the silty sand and mechanically stirred. Then, the mixture was placed in a sealed container to retain moisture for 8 hours to ensure uniform internal moisture distribution. Next, cement and basalt fiber were added to the prepared silty sand, and water was added to the optimum moisture content of 9.69%, followed by mechanical stirring for 10 minutes. The cement content was 2%, and the basalt fiber content was 0.2%, with a fiber length of 12 mm. The cement content was the percentage of cement mass to the total dry silty sand mass, and the fiber content was the percentage of fiber mass to the total mass of cement and dry silty sand. Three parallel samples were prepared for each group. The samples were prepared using impact molding to form cylindrical specimens with a height of 100 mm, a diameter of 50 mm, and a compaction degree greater than 96%. The maximum dry density was 2.042 g / cm³. 3 As required, the samples were compacted by impact in layers, and the surface of the previous layer of soil was roughened before placing the next layer. After preparation, the samples were wrapped in plastic wrap and placed in a curing room at a temperature of 20 ± 2 ℃ and a relative humidity greater than 95% for 14 days, according to the "Test Procedure for Inorganic Binder Stabilized Materials in Highway Engineering" JTG E51-2009. Subsequently, the cured samples were subjected to 0, 1, 3, 6, and 10 freeze-thaw cycles, respectively. The specific test scheme is shown in Table 3.

[0076] Table 3 Test Protocol

[0077] Cement admixture (%) Fiber content (%) Fiber length (mm) Maintenance time (days) Freeze-thaw cycle count 2 0.2 12 14 0，1，3，6，10

[0078] S2: Dynamic triaxial tests were conducted using a multi-functional servo dynamic and static triaxial testing machine manufactured by Wille GmbH, Germany, to obtain the dynamic stress and dynamic strain of the specimens under different confining pressures and different freeze-thaw cycles. The dynamic and static triaxial testing machine features a cyclic cooling system, a fully automatic CNC and data acquisition system, a maximum axial load of 25 kN, a confining pressure control range of 0 ~ 2 MPa, a test frequency range of 0 ~ 10 Hz, a maximum axial displacement of 100 mm, and a temperature control range of -20 ℃ ~ 60 ℃. It can load different waveforms such as half-sine waves and sine waves. During the test, the dynamic load was simulated using a vehicle load. Field tests showed that the dynamic stress waveform within the roadbed under vehicle load is approximately a half-sine wave. Therefore, during the test, a dynamic stress waveform was applied such as... Figure 1 The axial stress of the dynamic load on the half-sine wave shown is... ;in, Representing the i Axial stress of a level load, Representing the i Level 1 load relative to Level 2 i- Stress increase for Level 1 load, The confining pressure represents the load. Since the typical speed of a road vehicle is 40-60 km / h, the axial dynamic load frequency was set to 1 Hz. During the test, a confining pressure of 30 kPa was first applied to the specimen for 1000 pre-loading cycles. After the pre-loading, a graded loading method as shown in Table 4 was used, with the load increasing in increments of 40 kPa. Each load level was subjected to 12 vibrations, and the axial dynamic strain under different dynamic stresses was measured.

[0079] Table 4 Dynamic Stress Amplitude Loading Scheme

[0080]

[0081] Depend on Figure 2 The dynamic stress-strain curves of basalt fiber-cement silt under different confining pressures during six freeze-thaw cycles show that under low confining pressure, the dynamic stress-strain curve is relatively flat, while it becomes steeper with increasing confining pressure. This indicates that under the same strain level, the greater the confining pressure, the greater the dynamic stress the soil can withstand. Under the same stress level, the greater the confining pressure, the smaller the dynamic strain of the soil, indicating that the soil's load-bearing capacity increases with increasing confining pressure. Figure 3 The dynamic stress-strain curves of basalt fiber cement silt under different freeze-thaw cycles at a confining pressure of 50 kPa show that the dynamic stress-strain curve is relatively steep before freezing and thawing. As the number of freeze-thaw cycles increases, the curve gradually flattens, indicating that under the same stress level, freeze-thaw cycles increase soil deformation. After 6 freeze-thaw cycles, the soil can withstand the minimum load for the same deformation, indicating that the soil strength is at its lowest under 6 freeze-thaw cycles, representing the most unfavorable stress state. Therefore, the mechanical properties under 6 freeze-thaw cycles can be used as a construction reference.

[0082] S3: Based on the Hardin-Drnevich hyperbolic model, the maximum dynamic elastic modulus of basalt fiber-cemented silt was obtained. and final dynamic stress amplitude Introducing reference dynamic strain The normalized secant dynamic elastic modulus of basalt fiber cement silt was obtained. The specific analysis process is as follows:

[0083] Drawing dynamic stress Dynamic strain Hysteresis curve, and the slope of the hysteresis curve is defined as the dynamic elastic modulus. :

[0084] (1)

[0085] Fitting with Hardin-Drnevich hyperbolic model and The relationship between them can be represented as:

[0086] (2)

[0087] Solving equations (1) and (2) simultaneously yields equation (3):

[0088] (3)

[0089] In particular, in formula (3) When, we get equation (4); when in equation (2) Then, we get equation (5):

[0090] (4)

[0091] (5)

[0092] In the formula: This is the maximum dynamic elastic modulus, in MPa. This represents the final dynamic stress amplitude.

[0093] Introducing reference dynamic strain Its expression is equation (6):

[0094] (6)

[0095] Combining equations (3), (4), and (6), we can obtain the expression for the normalized secant dynamic elastic modulus as follows:

[0096] (7)

[0097] In the formula: This is the normalized secant dynamic elastic modulus.

[0098] Depend on Figure 2 and Figure 3 It can be seen that the nonlinear characteristics of the dynamic stress-strain relationship curve of soil under dynamic load are very significant. The Hardin-Drnevich hyperbola model of equation (2) is used to fit the dynamic stress-strain data of soil under different confining pressure conditions after freeze-thaw cycles. The fitting effect is good, and the dynamic constitutive relationship model parameters shown in Table 5 are obtained.

[0099] Table 5. Triaxial test conditions and fitting parameters for dynamic stress-strain curves.

[0100]

[0101] By using equations (4) and (5) and combining them with Table 5, the maximum dynamic elastic modulus of basalt fiber cement silt can be obtained under different confining pressures and different freeze-thaw cycles. and final dynamic stress amplitude .Depend on Figure 4 The experimental values ​​and fitted curves of the relationship between the maximum dynamic elastic modulus and the final dynamic stress amplitude of basalt fiber-reinforced cement silt and confining pressure after six freeze-thaw cycles show that both the maximum dynamic elastic modulus and the final dynamic stress amplitude increase with increasing confining pressure. The increase in the maximum dynamic elastic modulus with increasing confining pressure is due to the cement-soil skeleton structure generated by the hydration reaction significantly enhancing soil strength, and the bridging effect of the fibers effectively enhancing soil stiffness. The increase in the final dynamic stress amplitude is due to the good toughness and high tensile strength of the fibers, which improve the ductility of the cement-soil and enhance its bearing capacity. Figure 5 Under a confining pressure of 50 kPa, the experimental values ​​and fitted curves of the relationship between the maximum dynamic elastic modulus and the final dynamic stress amplitude of basalt fiber cement silt and the number of freeze-thaw cycles show that both the maximum dynamic elastic modulus and the final dynamic stress amplitude decrease with the increase of the number of freeze-thaw cycles. The maximum decrease in the maximum dynamic elastic modulus after freeze-thaw cycles is 44.96%, and the maximum decrease in the final dynamic stress amplitude is 31.45%. The decrease in the maximum dynamic elastic modulus and the final dynamic stress amplitude after freeze-thaw cycles is because the freeze-thaw cycle causes the migration of water in the soil, which weakens the interparticle bonding ability and causes some fibers to break or be pulled out.

[0102] Introducing reference dynamic strain The normalized secant dynamic elastic modulus of basalt fiber cement silt under different confining pressures and different freeze-thaw cycles was obtained by equation (7). .Depend on Figure 6 The normalized secant dynamic elastic modulus versus dynamic strain curves of basalt fiber-cement silt under different confining pressures after six freeze-thaw cycles show that the normalized secant dynamic elastic modulus increases with increasing confining pressure, and is more sensitive to low confining pressures. With increasing dynamic strain, the normalized secant dynamic elastic modulus exhibits a significant decreasing trend. The slope of the normalized secant dynamic elastic modulus versus dynamic strain curve is slightly greater at low confining pressures than at high confining pressures, indicating a faster decay rate of the normalized secant dynamic elastic modulus at low confining pressures. This is because at high confining pressures, the dynamic load on the soil decreases, resulting in benign displacement and reduced open porosity, thus enhancing the structural strengthening effect. Figure 7The normalized secant dynamic elastic modulus versus dynamic strain curves of basalt fiber-cement silt under different freeze-thaw cycles at 50 kPa confining pressure show that the normalized secant dynamic elastic modulus decreases with increasing freeze-thaw cycles, indicating a gradual decrease in soil stiffness. The first freeze-thaw cycle has the most detrimental effect on the normalized secant dynamic elastic modulus. The slope of the secant dynamic elastic modulus versus dynamic strain curve after freeze-thaw cycles is greater than that before freezing and thawing, indicating a rapid decrease in the normalized secant dynamic elastic modulus after freeze-thaw cycles. However, the fibers have a binding effect on the damaged soil, allowing it to maintain good integrity and preventing immediate brittle failure, thus enhancing the soil's ductility and freeze-thaw resistance.

[0103] S4: Based on the nonlinear least squares method, statistical analysis was performed on the experimental data under different confining pressures and freeze-thaw cycles to obtain the maximum dynamic elastic modulus characterizing basalt fiber-cement silt. and final dynamic stress amplitude Prediction models related to confining pressure and freeze-thaw cycle count:

[0104] (7)

[0105] (8)

[0106] (9)

[0107] (10)

[0108] In the formula: This is the maximum dynamic elastic modulus, in MPa. The confining pressure is expressed in kPa. P a The value is atmospheric pressure, usually taken as 101 kPa (because the confining pressure is related to atmospheric pressure, atmospheric pressure will affect the confining pressure and thus the data, so atmospheric pressure is taken into account in data processing). The final dynamic stress amplitude is expressed in MPa. This represents the number of freeze-thaw cycles.

[0109] S5: Considering that both confining pressure and the number of freeze-thaw cycles affect the maximum dynamic elastic modulus and the final dynamic stress amplitude, the maximum dynamic elastic modulus and the final dynamic stress amplitude can be expressed by equations (11) and (12):

[0110] (11)

[0111] (12)

[0112] In the formula: , Under the combined effects of confining pressure and freeze-thaw cycles and The parameters (the parameter values ​​are obtained through regression analysis). and , and These are prediction models for the maximum dynamic elastic modulus and the final dynamic stress amplitude, respectively, based on confining pressure and the number of freeze-thaw cycles.

[0113] Based on equations (7) to (12), regression analysis was performed on the experimental data to obtain the prediction models for the maximum dynamic elastic modulus and final dynamic stress of basalt fiber cement silt under the combined influence of confining pressure and freeze-thaw cycles:

[0114] (13)

[0115] (14)

[0116] To verify the rationality and effectiveness of the established model, and based on experimental data, comparative graphs were plotted showing the experimental values ​​and predicted model-fitted values ​​of the final dynamic stress amplitude and maximum dynamic elastic modulus of basalt fiber-cement silt under different confining pressures and different freeze-thaw cycles. Figure 8 , 9 As shown. By Figure 8 and Figure 9 As can be seen, the predicted model fit values ​​are similar to the experimental values, and the fitting effect is good, which verifies the effectiveness of the predicted model.

[0117] S6: Based on the prediction model obtained in step S5, the maximum dynamic elastic modulus and the final dynamic stress amplitude of basalt fiber cement silt under the combined influence of confining pressure and freeze-thaw cycle can be obtained by substituting the required environmental conditions, confining pressure and freeze-thaw cycle number. Then, the normalized secant dynamic elastic modulus can be obtained.

[0118] The various embodiments in this specification are described in a related manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments. In particular, the system embodiments are basically similar to the method embodiments, so the description is relatively simple; relevant parts can be referred to the descriptions of the method embodiments.

[0119] 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 for predicting the dynamic elastic modulus of basalt fiber cement silt soil used in roadbeds in seasonally frozen areas, characterized in that... The method includes the following steps: S1: Prepare the specimens and conduct freeze-thaw cycle tests on the cured specimens with different numbers of freeze-thaw cycles; S2: Perform staged loading dynamic triaxial tests on the samples after freeze-thaw cycles to obtain the dynamic stress of the soil under different confining pressures. and dynamic strain ,draw — The hysteresis curve, with its slope defined as the dynamic elastic modulus. , ; S3: Fitting based on Hardin-Drnevich hyperbolic model and The relationship between them Where a and b are fitting parameters, the maximum dynamic elastic modulus of basalt fiber cement silt is obtained. and final dynamic stress amplitude Introducing reference dynamic strain , The normalized secant dynamic elastic modulus of basalt fiber cement silt was obtained. , ; S4: Based on the nonlinear least squares method, statistical analysis was performed on the experimental data under different confining pressures and freeze-thaw cycles to obtain the maximum dynamic elastic modulus characterizing basalt fiber-cement silt. and final dynamic stress amplitude Prediction models related to confining pressure and number of freeze-thaw cycles; S5: Based on the predicted model obtained in step S4, the maximum dynamic elastic modulus of basalt fiber cement silt under the combined effects of confining pressure and freeze-thaw cycles is obtained through nonlinear regression analysis. and final dynamic stress amplitude The prediction model; S6: Based on the prediction model obtained in step S5, the maximum dynamic elastic modulus and the final dynamic stress amplitude of basalt fiber cement silt under the combined influence of confining pressure and freeze-thaw cycle can be obtained by substituting the required environmental conditions, confining pressure and freeze-thaw cycle number. Then, the normalized secant dynamic elastic modulus can be obtained.

2. The method for predicting the dynamic elastic modulus of basalt fiber cement silt soil for roadbeds in seasonally frozen areas according to claim 1, characterized in that, Step S1 specifically includes the following steps: S11: Add water to silty sand to prepare a soil sample with a set moisture content; S12: Incorporate cement and basalt fiber into the soil sample; S13: For each mix proportion, m parallel samples are prepared by impact molding; S14: Wrap the prepared sample in plastic wrap and place it in the curing room for curing; S15: Conduct freeze-thaw cycle tests on the cured specimens with different numbers of freeze-thaw cycles.

3. The method for predicting the dynamic elastic modulus of basalt fiber cement silt soil for roadbeds in seasonally frozen areas according to claim 2, characterized in that, In step S12, the cement content, basalt fiber content, and basalt fiber length are recorded. The cement content is the percentage of cement mass to the total mass of dry sand, and the basalt fiber content is the percentage of fiber mass to the total mass of cement and dry sand.

4. The method for predicting the dynamic elastic modulus of basalt fiber cement silt soil for roadbeds in seasonally frozen areas according to claim 2, characterized in that, In step S13, a layered method is used in the impact molding process, and the surface of the upper layer of soil is roughened before the next layer of soil is placed.

5. The method for predicting the dynamic elastic modulus of basalt fiber cement silt soil for roadbeds in seasonally frozen areas according to claim 2, characterized in that, In step S14, the prepared sample is wrapped in plastic wrap and placed in a curing room for 14 days. The curing conditions are a temperature of 20±2 ℃ and a relative humidity of more than 95%.

6. The method for predicting the dynamic elastic modulus of basalt fiber cement silt soil for roadbeds in seasonally frozen areas according to claim 2, characterized in that, In step S15, the selection of the freeze-thaw cycle test temperature requires investigation of the extreme negative temperature values ​​of the project site over the past ten years, and in combination with the soil strength change characteristics under low temperature conditions, the test freezing temperature is selected, the absolute values ​​of the thawing positive temperature and the freezing negative temperature are equal, the freezing and thawing time are both set to 24 h, and the number of freeze-thaw cycles is set to 0, 1, 3, 6 and 10 times in a progressively increasing manner.

7. The method for predicting the dynamic elastic modulus of basalt fiber cement silt soil for roadbeds in seasonally frozen areas according to claim 2, characterized in that, In step S2, the specimen after freeze-thaw cycles is subjected to a graded loading dynamic triaxial test. The waveform applied in the dynamic triaxial test is a half-sine wave. The axial dynamic load frequency is set to 1 Hz. The confining pressures selected for the dynamic triaxial test are 20 kPa, 50 kPa and 80 kPa. During the test, a confining pressure of 30 kPa is first applied to the specimen for 1000 pre-loading cycles. After the pre-loading is completed, the selected confining pressure is used to perform graded loading with an increment of 40 kPa. Each load level vibrates 12 times.

8. The method for predicting the dynamic elastic modulus of basalt fiber cement silt soil for roadbeds in seasonally frozen areas according to claim 2, characterized in that, In step S4, the maximum dynamic elastic modulus of basalt fiber cement silt is constructed. When using prediction models related to confining pressure, since confining pressure is related to atmospheric pressure, atmospheric pressure is considered during data processing. P a The setting is 101 kPa.

9. The method for predicting the dynamic elastic modulus of basalt fiber cement silt soil for roadbeds in seasonally frozen areas according to claim 2, characterized in that, In step S5, the maximum dynamic elastic modulus of basalt fiber cement silt soil under the combined effects of confining pressure and freeze-thaw cycles is determined. Final dynamic stress amplitude The expression for the prediction model is: ; ； In the formula: , Under the combined effects of confining pressure and freeze-thaw cycles and The parameters, and , and They are based on confining pressure and number of freeze-thaw cycles A model for predicting the maximum dynamic elastic modulus and the final dynamic stress amplitude.

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