Method for predicting accumulated plastic strain of roadbed soil under coupling action of freeze-thaw cycle and dynamic load

Abstract

The invention relates to the technical field of road construction, and discloses a roadbed soil cumulative plastic strain prediction method under the coupling action of freeze-thaw cycle and dynamic load, comprising the following steps: establishing a cumulative plastic strain prediction model; inputting the following parameters into the prediction model: freezing and thawing cycle times FT, water content W, dynamic stress amplitude sigma d, confining pressure sigma 3, compaction coefficient K, load vibration frequency f and vibration times N; and predicting an output cumulative plastic strain value of the model. The theoretical value of the prediction model provided by the invention is well matched with the experimental value, so that the method has a good application prospect, and provides an important reference basis for design and construction of the road in the seasonal frozen region and disease prevention.

Description

Technical Field

[0001] The invention relates to the technical field of road construction, and in particular to a method for predicting the accumulated plastic strain of roadbed soil under the coupling effect of freeze-thaw cycles and dynamic loads. Background Art

[0002] Seasonal frozen soil is widely distributed in most parts of my country. In recent years, with the country's vigorous development of the transportation industry, more and more highway lines have been extended to the frozen soil areas in northern China. Compared with permafrost areas, seasonal frozen soil areas experience freezing and thawing at least once a year. When the temperature drops, the water in the soil freezes into ice and the soil expands and bulges. When the temperature rises, the ice melts into water. The existence of ice-water phase transition makes frozen soil show strong temperature sensitivity and certain rheological properties. And due to the long-term repeated action of traffic loads, irreversible cumulative deformation occurs, resulting in different degrees of uneven settlement of the roadbed in the seasonal frozen area, making the road surface uneven. At the least, it will cause vehicles to bump during driving, affecting the driving comfort of vehicles; at the worst, it will cause excessive cracks on the road surface, damage the road, and seriously affect the safe operation of traffic.

[0003] At present, domestic and foreign scholars have established a large number of cumulative plastic deformation prediction models for the prediction of roadbed cumulative deformation in the non-freezing and thawing state, but there is a lack of research on the cumulative plastic strain prediction model under extreme climatic conditions such as freeze-thaw cycle coupling under dynamic load and water replenishment conditions, which cannot meet the increasingly complex engineering environment. Therefore, it is urgent to establish a responsive model to accurately and reliably predict the cumulative deformation of the roadbed under the coupling of freeze-thaw cycles and dynamic loads. Summary of the invention

[0004] In order to solve the technical problems raised in the background technology, the present invention provides a method for predicting the cumulative plastic strain of roadbed soil under the coupling effect of freeze-thaw cycles and dynamic loads.

[0005] The present invention adopts the following technical solution to achieve: a method for predicting the cumulative plastic strain of roadbed soil under the coupling of freeze-thaw cycles and dynamic loads, comprising the following steps:

[0006] Establish a cumulative plastic strain prediction model; input the following parameters into the prediction model: freeze-thaw cycle number FT, moisture content W, dynamic stress amplitude σ d , confining pressure σ 3 , compaction coefficient K and load vibration frequency f, vibration number N; output cumulative plastic strain value of the prediction model.

[0007] Specifically, the load vibration frequency of the roadbed v is the vehicle speed, which is 120km / h, and l = 17.5m.

[0008] Specifically, the confining pressure σ 3Take 20kPa, 40kPa or 60kPa.

[0009] Specifically, establishing the cumulative plastic strain prediction model includes the following steps:

[0010] Triaxial simulation experiments under freeze-thaw cycles were carried out to obtain experimental data between various parameters and plastic strain;

[0011] According to the test data obtained above, a range analysis table of the results of the 6-factor, 3-level non-standard orthogonal experiment was established. The significance and priority order of each factor affecting the mechanical properties of frozen soil were analyzed by using the orthogonal experiment, and the input parameters of the prediction model were finally determined. According to the orthogonal experiment, the range analysis results were used to express the influence of each factor on the cumulative plastic strain, and the contribution rate of each factor to the cumulative plastic strain was obtained.

[0012] Since the accumulated plastic strain and the number of dynamic load cycles satisfy the following relationship:

[0013] ε p =AN B Formula (1)

[0014] In formula (1): ε p is the cumulative plastic strain; N is the number of dynamic load cycles; A and B are experimental fitting parameters related to stress conditions and soil properties;

[0015] When the soil dynamic stress is smaller than the critical dynamic stress, the cumulative plastic strain and the number of dynamic load cycles satisfy the following relationship:

[0016]

[0017] Where: ε p is the cumulative plastic strain; N is the number of load cycles; a, b, c are parameters related to stress conditions and soil properties;

[0018] It can be seen from the above formula (2) that when c = 0, formula (2) is equivalent to formula (1). When N is infinite, a / c is the limit value of the expression, which has the physical meaning of representing the deformation limit of the stable curve soil, while b can reflect the shape of the cumulative plastic strain curve and can be defined as a constant under certain circumstances.

[0019] Taking into account other factors that affect the accumulated plastic strain, the prediction model is expressed as follows:

[0020] ε p =ε p (F T ,σ d ,σ 3 ,W,K,f) Formula (3)

[0021] Where FT is the number of freeze-thaw cycles; σ d is the dynamic stress amplitude; σ 3 is the confining pressure; W is the initial water content; K is the compaction coefficient; f is the load frequency.

[0022] By performing nonlinear fitting on the experimental groups corresponding to the above 6-factor, 3-level orthogonal experimental table according to formula (2), the values ​​of parameters a, b and c can be obtained; then the parameters a, b and c obtained by fitting each factor with the experimental data are subjected to multivariate linear regression analysis, and the relationship expression between each factor and a, b and c can be obtained as follows:

[0023] a=A 1 +A 2 N FT +A 3 σ d -A 4 σ 3 -A 5 WA 6 KA 7 f Formula (4)

[0024] b=-B 1 -B 2 N FT -B 3 σ d +B 4 σ 3 +B 5 W+B 6 KB 7 f Formula (5)

[0025] c=C 1 -C 2 N FT +C 3 σ d -C 4 σ 3 -C 5 WC 6 KC 7 f Formula (6)

[0026] Then substitute equation (4), equation (5) and equation (6) into equation (3) to obtain the explicit expression of equation (3), namely equation (7):

[0027]

[0028] And in the formula: A1=13.04, A2=0.07, A3=0.22, A4=0.02, A5=0.12, A6=13.52, A7=-0.05, B1=4.10, B2=-0.065, B3=-0.03, B4=0.01, B5=0.001, B6=4.78, B7=-0.01, C1=7.00, C2=0.07, C3=0.02, C4=0.01, C5=0.006, C6=6.90, C7=0.03.

[0029] Compared with the prior art, the present invention has the following beneficial effects:

[0030] The present invention takes out samples that have experienced several freeze-thaw cycles and conducts indoor dynamic triaxial tests. The GCTS dynamic triaxial apparatus is used to execute the cumulative plastic strain program, and the influence of main factors such as dynamic stress amplitude, number of freeze-thaw cycles, confining pressure, loading frequency, etc. on the cumulative plastic strain and the degree of influence are analyzed. A cumulative plastic strain prediction model is proposed, and it is verified by experiments that the theoretical value of the prediction model proposed by the present invention is in good agreement with the experimental value. Therefore, the model has good application prospects, and provides an important reference basis for the design, construction and disease prevention of roads in seasonally frozen areas. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 a is the relationship curve between the cumulative plastic strain εp and the vibration number N under different freeze-thaw cycle numbers when the confining pressure is 20 kPa. Figure 1 It is the relationship curve between the cumulative plastic strain εp and the vibration number N under different freeze-thaw cycle numbers when the confining pressure is 40kpa;

[0032] Figure 2 c is the relationship curve between the cumulative plastic strain εp and the vibration number N under different freeze-thaw cycle numbers when the confining pressure is 60 kPa; Figure 2 d is the relationship curve between the cumulative plastic strain εp and the number of freeze-thaw cycles at different confining pressures when the vibration number is 10000 times;

[0033] Figure 3 Figure a is a curve diagram showing the relationship between the cumulative plastic strain εp of the roadbed and the number of cycles N under different dynamic stress amplitudes when the confining pressure is 20 kPa; Figure b is a curve diagram showing the relationship between the cumulative plastic strain εp of the roadbed and the number of cycles N under different dynamic stress amplitudes when the confining pressure is 40 kPa;

[0034] Figure 4 a is the relationship curve between the cumulative plastic strain εp of the roadbed and the number of cycles N under different confining pressures when the dynamic stress amplitude is 20 kPa; Figure 4 b is the relationship curve between the cumulative plastic strain εp of the roadbed and the number of cycles N under different confining pressures when the dynamic stress amplitude is 30 kPa;

[0035] Figure 5 c is the relationship curve between the cumulative plastic strain εp and the number of cycles N of the roadbed with different confining pressures when the dynamic stress amplitude is 40 kPa; Figure 5 d is the relationship curve between the cumulative plastic strain εp and the confining pressure for different dynamic stress amplitudes when the vibration number is 10000 times;

[0036] Figure 6 a is the relationship curve between the cumulative plastic strain εp and the number of cycles N at different frequencies when the dynamic stress amplitude is 20 kPa; Figure 6 b is the relationship curve between the cumulative plastic strain εp and the number of cycles N at different frequencies when the dynamic stress amplitude is 30 kPa;

[0037] Figure 7 c is the relationship curve between the cumulative plastic strain εp and the number of cycles N at different frequencies when the dynamic stress amplitude is 40 kPa. Figure 7 d is the relationship curve between the cumulative plastic strain εp and the vibration frequency for different dynamic stress amplitudes when the vibration number is 10000 times;

[0038] Figure 8 a is the relationship curve between the cumulative plastic strain and the load vibration times under different initial moisture contents when the number of freeze-thaw cycles is 0; Figure 8 b is the relationship curve between the cumulative plastic strain and the load vibration times under different initial moisture contents when the number of freeze-thaw cycles is 1;

[0039] Fig. 9 e is the relationship curve between the cumulative plastic strain and the load vibration times under different initial moisture contents when the number of freeze-thaw cycles is 7; Fig. 9 f is the relationship curve between the cumulative plastic strain and the initial function rate at different freeze-thaw cycles when the vibration number is 1000 times;

[0040] Fig.10 The relationship between the accumulated plastic strain εp and the number of cycles N of soil with different initial water contents in open and closed systems;

[0041] Fig.11 a is the relationship curve between the cumulative plastic strain and the load vibration times under different compaction coefficients when the initial water content is 12.6%; Fig.11 b is the relationship curve between the cumulative plastic strain and the load vibration times under different compaction coefficients when the initial water content is 14.6%

[0042] Fig.12 c is the relationship curve between the cumulative plastic strain and the load vibration times under different compaction coefficients when the initial water content is 16.6%; Fig.12 d is the relationship curve between the cumulative strain and compaction coefficient at different water contents with 1000 vibration times;

[0043] Fig.13 It is the factor effect trend chart;

[0044] Fig.14 It is a fitting curve diagram of the experimental value and calculated value of cumulative plastic strain under different freeze-thaw cycles and confining pressures. DETAILED DESCRIPTION

[0045] The present invention is further described below in conjunction with the accompanying drawings and specific implementation methods. It should be noted that, under the premise of no conflict, the various embodiments or technical features described below can be arbitrarily combined to form a new embodiment.

[0046] Embodiment 1:

[0047] Please combine Figure 1 , xxx of this embodiment, includes.

[0048] An implementation principle of XXX in the embodiment of the present application is:

[0049] Embodiment 2:

[0050] The method for predicting the accumulated plastic strain of roadbed soil under the coupling of freeze-thaw cycle and dynamic load is characterized by comprising the following steps:

[0051] Establish a cumulative plastic strain prediction model; input the following parameters into the prediction model: freeze-thaw cycle number FT, moisture content W, dynamic stress amplitude σ d , confining pressure σ 3 , compaction coefficient K and load vibration frequency f, vibration number N; output cumulative plastic strain value of the prediction model.

[0052] Specifically, the load vibration frequency of the roadbed v is the vehicle speed, which is 120km / h, and l = 17.5m.

[0053] Specifically, the confining pressure σ 3 Take 20kPa, 40kPa or 60kPa.

[0054] Specifically, establishing the cumulative plastic strain prediction model includes the following steps:

[0055] Triaxial simulation experiments under freeze-thaw cycles were carried out to obtain experimental data between various parameters and plastic strain;

[0056] According to the test data obtained above, a range analysis table of the results of the 6-factor, 3-level non-standard orthogonal experiment was established. The significance and priority order of each factor affecting the mechanical properties of frozen soil were analyzed by using the orthogonal experiment, and the input parameters of the prediction model were finally determined. According to the orthogonal experiment, the range analysis results were used to express the influence of each factor on the cumulative plastic strain, and the contribution rate of each factor to the cumulative plastic strain was obtained.

[0057] Since the accumulated plastic strain and the number of dynamic load cycles satisfy the following relationship:

[0058] ε p =AN B Formula (1)

[0059] In formula (1): ε p is the cumulative plastic strain; N is the number of dynamic load cycles; A and B are experimental fitting parameters related to stress conditions and soil properties;

[0060] When the soil dynamic stress is smaller than the critical dynamic stress, the cumulative plastic strain and the number of dynamic load cycles satisfy the following relationship:

[0061]

[0062] Where: ε p is the cumulative plastic strain; N is the number of load cycles; a, b, c are parameters related to stress conditions and soil properties;

[0063] It can be seen from the above formula (2) that when c = 0, formula (2) is equivalent to formula (1). When N is infinite, a / c is the limit value of the expression, which has the physical meaning of representing the deformation limit of the stable curve soil, while b can reflect the shape of the cumulative plastic strain curve and can be defined as a constant under certain circumstances.

[0064] Taking into account other factors that affect the accumulated plastic strain, the prediction model is expressed as follows:

[0065] ε p =ε p (F T ,σ d ,σ 3 ,W,K,f) Formula (3)

[0066] Where FT is the number of freeze-thaw cycles; σ d is the dynamic stress amplitude; σ 3 is the confining pressure; W is the initial water content; K is the compaction coefficient; f is the load frequency.

[0067] By performing nonlinear fitting on the experimental groups corresponding to the above 6-factor, 3-level orthogonal experimental table according to formula (2), the values ​​of parameters a, b and c can be obtained; then the parameters a, b and c obtained by fitting each factor with the experimental data are subjected to multivariate linear regression analysis, and the relationship expression between each factor and a, b and c can be obtained as follows:

[0068] a=A 1 +A 2 N FT +A 3 σ d -A 4 σ 3 -A 5 WA 6 KA 7 f Formula (4)

[0069] b=-B 1 -B 2 N FT -B 3 σ d +B 4 σ 3 +B 5 W+B 6 KB 7 f Formula (5)

[0070] c=C 1 -C 2 N FT +C 3 σ d -C 4 σ 3 -C 5 WC 6 KC 7 f Formula (6)

[0071] Then substitute equation (4), equation (5) and equation (6) into equation (3) to obtain the explicit expression of equation (3), namely equation (7):

[0072]

[0073] And in the formula: A1=13.04, A2=0.07, A3=0.22, A4=0.02, A5=0.12, A6=13.52, A7=-0.05, B1=4.10, B2=-0.065, B3=-0.03, B4=0.01, B5=0.001, B6=4.78, B7=-0.01, C1=7.00, C2=0.07, C3=0.02, C4=0.01, C5=0.006, C6=6.90, C7=0.03.

[0074] In this embodiment:

[0075] The experimental plan is as follows:

[0076]

[0077] Effect of freeze-thaw cycles

[0078] Reference Figure 1 , 4.6 gives the relationship between the cumulative plastic strain of the soil and the number of vibrations when the initial water content is 14.6%, the loading frequency is 1 Hz, and the dynamic stress levels and confining pressures are different. Figure 4 .6(a)~(l) It can be seen that the freeze-thaw cycle has a significant effect on the cumulative plastic deformation of the soil. With the increase of the number of freeze-thaw cycles, the cumulative plastic strain of the soil sample tends to increase. When the number of freeze-thaw cycles is greater than 5 times, the soil strain tends to be stable.

[0079] Reference Figure 2 When the number of freeze-thaw cycles and confining pressure are constant, the accumulated plastic strain of the soil first increases rapidly with the increase of the number of vibrations, and then decreases rapidly with the continued increase of the number of vibrations, and finally the soil deformation tends to be stable.

[0080] When the confining pressure is small, the soil deformation increases sharply after the first freeze-thaw cycle compared with the non-freeze-thaw case. When the confining pressure is 20kPa and 40kPa, the soil that has not experienced freeze-thaw cycles quickly tends to stabilize under the condition of small dynamic load vibration, and the final cumulative plastic deformation εp = 0.08% and 0.06%, while after a freeze-thaw cycle, the final cumulative plastic strain εp = 0.3% and 0.16%, respectively, which increases by 275% and 167%. When the confining pressure is relatively large, after a freeze-thaw cycle, the soil deformation only increases by 46%, and with the increase of confining pressure, the final deformation of the soil decreases, indicating that the first freeze-thaw cycle has the greatest disturbance effect on the soil, and increasing the confining pressure can inhibit the deformation of the soil under dynamic load after the freeze-thaw cycle.

[0081] Effect of dynamic stress amplitude

[0082] Reference Figure 3 Since the magnitude of dynamic stress is an important factor affecting the dynamic characteristics of roadbed soil, when considering the effect of cyclic dynamic stress amplitude on the cumulative plastic strain development of low liquid limit clay after freeze-thaw cycles, the dynamic stress amplitude is selected as 20kPa, 30kPa and 40kPa. The experimental results are as follows: Figure 3 Shown

[0083] Reference Figure 3The results show that, when other conditions are constant, the larger the dynamic stress amplitude, the greater the cumulative plastic deformation of low liquid limit clay. In the early stage of dynamic load vibration, the cumulative plastic deformation develops fastest, and a larger deformation occurs with fewer vibration times. Figure 4 .7(a)~(t), the accumulated plastic strain has reached about 80% of the total deformation when the load vibration N=2000 times, and then tends to be stable as the load vibration times increase. Figure 3 In the study, when the freeze-thaw cycle was 1 time, the confining pressure was 20 kPa, and the dynamic stress amplitude increased from 20 kPa to 40 kPa, the axial cumulative plastic strain increased from 0.31% to 1.73%. When the freeze-thaw cycle number increased from 1 to 3 times, the confining pressure was 20 kPa, and the dynamic stress amplitude was 40 kPa, the corresponding cumulative deformation increased from 1.73% to 2.3%, indicating that the dynamic stress amplitude has a significant promoting effect on the increase of the cumulative strain of the soil after the freeze-thaw cycle. Therefore, in order to reduce the uneven settlement of the roadbed during the operation period after the roadbed is built in the seasonal frozen soil area, the size of the dynamic stress acting on the roadbed should be strictly controlled to limit the overweight behavior of passing trucks.

[0084] Effect of confining pressure

[0085] During the experiment, the confining pressure applied in the consolidation stage and the dynamic triaxial stage remained consistent. Figure 4 The relationship between the cumulative plastic strain of soil and the number of vibrations is given under the conditions of an initial water content of 14.6%, a loading frequency of 1 Hz, different dynamic stress levels and freeze-thaw cycles. Figure 4 The relationship curve between the cumulative plastic strain of low liquid limit clay and the number of load vibrations under different consolidation confining pressures is given. The results show that under the same dynamic stress amplitude, with the increase of confining pressure, the cumulative plastic strain continues to decrease, and the amplitude of decrease continues to increase, that is, the development of the cumulative plastic strain is negatively correlated with the confining pressure. When the freeze-thaw cycle is 5 times, the dynamic stress amplitude is 20kPa, and the confining pressure is 60kPa, the cumulative plastic strain after 10,000 cycles is 0.047%; when the dynamic stress amplitude and confining pressure increase to 40kPa and 20kPa respectively, the corresponding cumulative plastic strain increases to 1.61%, that is, under the conditions of larger dynamic stress and lower confining pressure, the cumulative plastic strain will develop rapidly.

[0086] In order to more intuitively analyze the influence of confining pressure on the development of cumulative plastic deformation, Figure 5The relationship curve between the cumulative plastic strain and the confining pressure under the cyclic load number N = 10000 times was selected. The results show that when the confining pressure is constant, the greater the dynamic stress amplitude, the greater the final cumulative plastic deformation. Under the conditions of constant freeze-thaw cycle number, frequency, compaction coefficient, dynamic stress, etc., the cumulative plastic strain decreases approximately linearly with the increase of confining pressure, which further confirms that the confining pressure has a restraining effect on the deformation of the roadbed soil under dynamic load. In actual engineering, the size of the confining pressure reflects the lateral pressure that varies with depth at a certain point in the roadbed soil. The greater the depth, the greater the lateral pressure, that is, the greater the confining pressure. Compared with the deep roadbed, the shallow roadbed is in an environment with larger dynamic stress and smaller confining pressure. Therefore, during the construction and maintenance of the shallow roadbed, the construction quality and materials should be strictly controlled to meet the requirements of relevant specifications.

[0087] Effect of loading frequency

[0088] Figure 6 , Figure 7 The law of cumulative plastic strain changing with load times under different load vibration frequencies (1Hz, 3Hz, 5Hz), dynamic stress amplitudes and confining pressures is given. The experimental results show that the vibration frequency has a significant effect on the cumulative plastic deformation of the soil. With the increase of the vibration frequency, the cumulative plastic strain continues to decrease. When the freeze-thaw cycle is 5 times, the other environmental conditions of the soil are constant, the load vibration times are 10,000 times, and the cumulative plastic deformations corresponding to the frequencies of 1HZ, 3HZ, and 5HZ are 0.712%, 0.623%, and 0.122% respectively; and the greater the frequency, the fewer the vibration times required for the soil deformation to reach stability. The reason is that the higher the load frequency, the more obvious the vibration compaction effect on the soil, the faster the soil reaches density, and therefore the fewer the load vibration times required for the soil deformation to reach stability. Existing literature shows that there is no unified understanding of the influence of vibration frequency on the cumulative plastic strain of soil. The reason is that the deformation of soil under dynamic load has hysteresis, and the frequency has a significant effect on it. The greater the loading frequency, the shorter the vibration time under the same load vibration number, and the smaller the deformation of the soil. Conversely, the smaller the load loading frequency, the longer the vibration time under the same vibration number, the more sufficient the soil vibration, and the greater the corresponding cumulative plastic strain.

[0089] Effect of initial moisture content W

[0090] Reference Figure 8 , Fig. 9, which is the relationship curve between the cumulative plastic strain and the number of load vibrations under different initial moisture contents and different freeze-thaw cycles. It can be seen that in the first three freeze-thaw cycles, the greater the initial moisture content of the soil, the faster the cumulative plastic strain increases with the number of vibrations, the more vibrations are required to reach stability, and the greater the final stable deformation; after three freeze-thaw cycles, under different initial moisture contents and the same number of vibrations, the cumulative deformation of the roadbed is not much different, and the final stable cumulative deformation is close. In order to explore the reason, the relationship between the cumulative plastic strain and the number of load vibrations after freeze-thaw of samples with different initial moisture contents under closed and open system conditions was studied, as shown in the figure. Fig.10 shown.

[0091] Fig.10 The relationship between the cumulative stress and the number of vibrations is studied under the conditions of 3 freeze-thaw cycles, compaction coefficient 0.95, dynamic stress amplitude 20kPa, and confining pressure 20kPa. The experimental results show that when the sample is frozen and thawed under closed system conditions, the soil is in an unsaturated state after experiencing freeze-thaw cycles, and the water content has an important influence on the cumulative plastic deformation of the roadbed soil. When the sample is frozen and thawed under open system conditions, the soil reaches a saturated or even supersaturated state after 3 freeze-thaw cycles, and the soil changes from the initial unsaturated state to the saturated state. Compared with the closed system, under the same stress conditions, the cumulative plastic strain develops rapidly with the increase of the number of vibrations; while in the open system, the final stable value of the cumulative plastic deformation under different initial water contents tends to be close. The reason is that when the saturated soil is subjected to load, the pore water pressure increases rapidly, resulting in negative pore water pressure, which causes the effective stress in the soil to decrease, and thus the deformation develops rapidly. Therefore, during the actual roadbed construction, the moisture content in the soil should be strictly controlled, and drainage should be done well to ensure that the soil moisture content is close to the optimal moisture content, which is of great significance to the deformation stability of the roadbed.

[0092] Effect of compaction coefficient K

[0093] like Fig.11 It shows that the cumulative plastic strain decreases with the increase of compaction degree. When the compaction degree increases from 0.93 to 0.97, the cumulative plastic strain decreases from 0.93122% to 0.652423% after 10,000 load vibrations. This phenomenon is mainly due to the large porosity of silty clay under low compaction coefficient. When the compaction coefficient increases, the soil voids are compressed, and the soil particles are arranged more compactly and densely, resulting in the obstruction of the water migration channel when the soil is frozen, which reduces the disturbance of the freeze-thaw cycle on the soil to a certain extent, improves the soil's ability to resist external deformation, and reduces the cumulative plastic deformation, which meets the requirements of the minimum compaction degree of roads at all levels specified in the relevant road design specifications.

[0094] Through the above experiments, this scheme uses orthogonal tests to analyze the significance of the main factors affecting the mechanical properties of frozen soil. When fitting the experimental data, the orthogonal experimental table is used to analyze the order of factors, and the experimental data is fitted to determine the estimated model experimental parameters. The range analysis chart of the designed 6-factor, 3-level non-standard orthogonal experimental results.

[0095]

[0096] In the table, Ti represents the cumulative plastic strain ε corresponding to any column level number i (1, 2, 3) p Experimental indicators and average values ​​t i =T i / r; r is the number of times each level appears in any column. In the orthogonal experiment table of this paper, r=9.

[0097] According to the orthogonal experiment, the influence of each factor on the cumulative plastic strain is expressed by the range analysis results. The contribution rate of each factor to the cumulative plastic strain is:

[0098]

[0099] In the formula, is the contribution rate of the ith factor; is the range of the i-th factor; ΣR is the sum of the ranges. From the above formula, we can get the contribution rate of the number of freeze-thaw cycles to the cumulative plastic strain as ζ FT =0.5961 / 2.4632×100%=24.20%; Similarly, the contribution rates of other factors are From the contribution rate of each factor, it can be seen that the importance of the influence on the accumulated plastic strain of the low liquid limit clay is: dynamic stress amplitude > number of freeze-thaw cycles > confining pressure > compaction > frequency > initial water content. According to the orthogonal experimental table, the effect diagram of each factor can be obtained as follows Fig.13 shown.

[0100] Combination Fig.13 It can be seen that the cumulative plastic strain of low liquid limit clay increases significantly with the increase of freeze-thaw cycles and dynamic stress amplitude, and is negatively correlated with confining pressure, compaction degree and frequency. When the dynamic stress amplitude increases from 20Kp to 30kPa, the cumulative plastic strain increases from 0.3595% to 0.5757%, and when it increases from 30kPa to 40kPa, the cumulative plastic strain increases from 0.5757% to 1.0534%, indicating that when the dynamic stress amplitude increases to more than a certain value, the cumulative plastic strain will increase sharply, indicating that there is a critical dynamic stress that causes the soil deformation to transition from stable to destructive type.

[0101] In order to verify the accuracy of the prediction model proposed in this scheme, a large number of confirmation experiments were carried out. Fig.14The relationship curve between the experimental value of the accumulated plastic strain and the calculated value of the model when the load vibration number is 10,000 times is shown in the following figure for a batch of samples with an initial moisture content of 14.6% after 2, 4, 6 and 8 freeze-thaw cycles, under the conditions of dynamic load loading frequency of 1Hz, dynamic stress of 20kPa and 40kPa respectively, and dynamic triaxial loading parameters. Fig.14 It can be seen that when the prediction model proposed in this scheme is used to fit the cumulative plastic strain curve, although there is a certain deviation from the measured value, the fitting effect is generally good, indicating that the cumulative plastic strain prediction model established in this paper can estimate and fit the stable cumulative plastic strain curve of low liquid limit clay under the comprehensive influence of multiple factors, and can meet the actual engineering accuracy requirements.

[0102] In this scheme, samples that have undergone several freeze-thaw cycles are taken out for indoor dynamic triaxial tests. The GCTS dynamic triaxial apparatus is used to execute the cumulative plastic strain program. The influence of main factors such as dynamic stress amplitude, number of freeze-thaw cycles, confining pressure, and loading frequency on the cumulative plastic strain and the degree of influence are analyzed. A cumulative plastic strain prediction model is proposed, and after experimental verification, the theoretical value of the prediction model is in good agreement with the experimental value.

[0103] The following conclusions were drawn:

[0104] The freeze-thaw cycle has a significant effect on the cumulative plastic deformation of the soil. With the increase of the number of freeze-thaw cycles, the cumulative plastic strain of the soil sample tends to increase. When the number of freeze-thaw cycles is greater than 5, the soil strain tends to be stable.

[0105] When other conditions are constant, the greater the dynamic stress amplitude, the greater the cumulative plastic deformation of the roadbed soil. In the early stage of dynamic load vibration, the cumulative plastic deformation develops fastest, and a smaller number of vibrations will cause a larger deformation. When the load vibration is about N = 2000 times, the cumulative plastic strain has reached about 80% of the total deformation, and then tends to stabilize with the increase of the load vibration times.

[0106] The accumulated plastic strain decreases approximately linearly with the increase of confining pressure, which further confirms that the confining pressure has a restraining effect on the deformation of the roadbed soil under dynamic load.

[0107] The smaller the load frequency, the longer the vibration time under the same vibration frequency, the more fully the soil vibrates, and the greater the corresponding cumulative plastic strain. When the sample undergoes freeze-thaw cycles under open system conditions, the soil reaches a saturated or even supersaturated state after three freeze-thaw cycles, and the soil changes from an initial unsaturated state to a saturated state. Compared with a closed system, under the same stress conditions, the cumulative plastic strain develops rapidly with the increase in the number of vibrations; while under an open system, the final stable values ​​of the cumulative plastic deformation under different initial water contents tend to be close. Improving the compaction degree can effectively reduce the cumulative plastic strain of the soil.

[0108] The results of orthogonal test analysis show that in an open system, the importance of the influence on the cumulative plastic strain of the soil used in this paper is: dynamic stress amplitude > number of freeze-thaw cycles > confining pressure > compaction degree > frequency > initial moisture content.

[0109] The above-mentioned embodiments are only preferred embodiments of the present invention and cannot be used to limit the scope of protection of the present invention. Any non-substantial changes and substitutions made by technicians in this field on the basis of the present invention shall fall within the scope of protection required by the present invention.

Claims

1. A method for predicting the cumulative plastic strain of roadbed soil under the coupling of freeze-thaw cycles and dynamic loads, characterized in that: The steps include: Establish a cumulative plastic strain prediction model; input the following parameters into the prediction model: freeze-thaw cycle number FT, moisture content W, dynamic stress amplitude σ d , confining pressure σ3, compaction coefficient K and load vibration frequency f, vibration number N; the output cumulative plastic strain value of the prediction model.

2. The method for predicting the cumulative plastic strain of roadbed soil under the coupling of freeze-thaw cycles and dynamic loads as claimed in claim 1, characterized in that: The load vibration frequency of the roadbed v is the vehicle speed, which is 120km / h, and l = 17.5m.

3. The method for predicting the cumulative plastic strain of roadbed soil under the coupling of freeze-thaw cycles and dynamic loads as claimed in claim 1, characterized in that: The confining pressure σ3 is 20 kPa, 40 kPa or 60 kPa.

4. The method for predicting the cumulative plastic strain of roadbed soil under the coupling of freeze-thaw cycles and dynamic loads as claimed in claim 1, characterized in that: Establishing the cumulative plastic strain prediction model includes the following steps: Triaxial simulation experiments under freeze-thaw cycles were carried out to obtain experimental data between various parameters and plastic strain; According to the test data obtained above, a range analysis table of the results of the 6-factor, 3-level non-standard orthogonal experiment was established. The significance and priority order of each factor affecting the mechanical properties of frozen soil were analyzed by using the orthogonal experiment, and the input parameters of the prediction model were finally determined. According to the orthogonal experiment, the range analysis results were used to express the influence of each factor on the cumulative plastic strain, and the contribution rate of each factor to the cumulative plastic strain was obtained. Since the accumulated plastic strain and the number of dynamic load cycles satisfy the following relationship: ε p =THE B formula (1) In formula (1): ε p is the cumulative plastic strain; N is the number of dynamic load cycles; A and B are experimental fitting parameters related to stress conditions and soil properties; When the soil dynamic stress is smaller than the critical dynamic stress, the cumulative plastic strain and the number of dynamic load cycles satisfy the following relationship: Where: ε p is the cumulative plastic strain; N is the number of load cycles; a, b, c are parameters related to stress conditions and soil properties; It can be seen from the above formula (2) that when c = 0, formula (2) is equivalent to formula (1). When N is infinite, a / c is the limit value of the expression, which has the physical meaning of representing the deformation limit of the stable curve soil, while b can reflect the shape of the cumulative plastic strain curve and can be defined as a constant under certain circumstances. Taking into account other factors affecting the accumulated plastic strain, the prediction model is expressed as follows: e p =e p (F T ,s d ,σ3,W,K,f) formula (3) Where FT is the number of freeze-thaw cycles; σ d is the dynamic stress amplitude; σ3 is the confining pressure; W is the initial water content; K is the compaction coefficient; f is the load frequency. By performing nonlinear fitting on the experimental groups corresponding to the above 6-factor, 3-level orthogonal experimental table according to formula (2), the values ​​of parameters a, b and c can be obtained; then the parameters a, b and c obtained by fitting each factor with the experimental data are subjected to multivariate linear regression analysis, and the relationship expression between each factor and a, b and c can be obtained as follows: a = A1 + A2N FT + A3σ d - A4σ3 - A5W - A6K - A7f Equation (4) b = -B1 - B2N FT -B3σ d +B4σ3 + B5W + B6K - B7f Equation (5) c = C1 - C2N FT + C3σ d - C4σ3 - C5W - C6K - C7f Equation (6) Then substitute equation (4), equation (5) and equation (6) into equation (3) to obtain the explicit expression of equation (3), namely equation (7): And in the formula: A1=13.04, A2=0.07, A3=0.22, A4=0.02, A5=0.12, A6=13.52, A7=-0.05, B1=4.10, B2=-0.065, B3=-0.03, B4=0.01, B5=0.001, B6=4.78, B7=-0.01, C1=7.00, C2=0.07, C3=0.02, C4=0.01, C5=0.006, C6=6.90, C7=0.03.

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