Humidity calculation method considering roadbed compaction characteristics

Abstract

The invention provides a humidity calculation method considering roadbed compaction characteristics. The humidity calculation method comprises the following steps: S1, constructing a roadbed soil hydraulic characteristic model considering compaction degree and vertical load; s2, constructing a roadbed compaction degree spatial distribution model considering randomness and decay; and S3, calculating the roadbed humidity based on the roadbed soil hydraulic characteristic model considering the compactness and the vertical load and the roadbed compactness spatial distribution model considering the randomness and the decay. The problem that the randomness and the decay property of the roadbed compactness cannot be considered in an existing humidity calculation method is solved, and therefore accurate calculation of the roadbed humidity evolution and balance rule is achieved.

Description

Technical Field

[0001] The invention belongs to the technical field of geotechnical engineering, and in particular relates to a humidity calculation method considering the compaction characteristics of a roadbed. Background Art

[0002] The distribution of subgrade humidity field is the key to determine the performance of the subgrade, and it is crucial to accurately evaluate the evolution and balance of subgrade humidity. The construction of the subgrade is rolled and formed according to a specific compaction degree; during the operation period, the subgrade is in the atmospheric environment and will be subjected to natural conditions such as rainfall, evaporation, freeze-thaw and vehicle loads, which will cause the soil compaction degree to decay, which is particularly significant in the humid and hot areas in southern my country. Through field surveys on highways such as Lianzhu, Heliu, and Changzhang, the overall compaction degree decays by about 10% after years of operation, which will cause changes in the hydraulic properties such as water holding characteristics and permeability characteristics of the soil, thereby affecting the migration and balance of humidity. At the same time, due to the influence of filling machinery rolling, natural environment and vehicle load, the compaction degree has a great variability in space, which will lead to differences in hydraulic properties at various locations of the subgrade. In the existing humidity calculation method, these two characteristics existing in the subgrade are not taken into account, resulting in differences between the subgrade humidity calculation and the actual situation, which is not conducive to accurately obtaining the evolution and balance law of subgrade humidity, and thus cannot evaluate the evolution of subgrade mechanical properties and ensure the durability of the subgrade. Summary of the invention

[0003] The purpose of the embodiment of the present invention is to provide a humidity calculation method that takes into account the compaction characteristics of the roadbed, so as to solve the problem that the existing humidity calculation method does not conform to the actual situation, the calculation results are inaccurate, and the evolution and balance law of the roadbed humidity cannot be accurately obtained.

[0004] In order to solve the above technical problems, the technical solution adopted by the present invention is:

[0005] The moisture calculation method considering the compaction characteristics of the roadbed includes the following steps:

[0006] S1: Construct a hydraulic characteristic model of subgrade soil considering compaction and vertical load;

[0007] S2: Construct a spatial distribution model of roadbed compaction considering randomness and decay;

[0008] S3: The subgrade moisture field is calculated based on the subgrade soil hydraulic characteristics model considering compaction and vertical load, and the subgrade compaction spatial distribution model considering randomness and decay.

[0009] Furthermore, the S1 includes:

[0010] S11: Prepare soil samples according to the optimal moisture content;

[0011] S12: Compressing the soil samples to different compaction degrees;

[0012] S13: Set different vertical loads P on the soil samples of S12.

[0013] Obtain the relationship curve between matrix suction and water content of soil samples with different compaction degrees under different vertical loads; obtain the saturated permeability coefficient k of soil samples with different compaction degrees under different vertical loads s ;

[0014] S14: Construct a soil-water characteristic curve model considering compaction and vertical load, as shown in formula (1a);

[0015] The permeability coefficient function equation considering compaction and vertical load is constructed as shown in formula (1b);

[0016]

[0017]

[0018] Among them, θ, θ r ,θ s are moisture content, residual moisture content, and saturated moisture content, respectively; C represents the degree of compaction; θ s The calculation formula is: s =1-C*ρ dmax *γ w / G s , ρ dmax is the maximum dry density of the soil sample, G s is the specific gravity of soil sample, γ w is the weight of water; is matrix suction; P a is the value of 1 atmosphere; m2, m3, m4, m5 are fitting parameters; m1 = 1-1 / m2;

[0019] k s are the unsaturated permeability coefficient and the saturated permeability coefficient respectively, S is the effective saturation,

[0020] Furthermore, in S14, the saturated permeability coefficient k s The following fitting formula is used:

[0021]

[0022] Where: a·k0 is the saturated permeability coefficient in the initial state, that is, k0 is the working condition with the lowest compaction degree and vertical load. sThe value of; k0 is the cardinality part when the initial state saturated permeability coefficient is expressed in scientific notation, a is the 10^n part when the initial state saturated permeability coefficient is expressed in scientific notation; k1, k2, k3 are fitting parameters.

[0023] Further, the S2 includes:

[0024] S21: Construct compaction decay function C(t); fill the soil sample into the container according to the set compaction degree, then add water, record the displacement change △h of the top surface of the sample, and convert it into dry density as shown in formula (3), using the soil sample dry density ρ at each time point d The compaction degree is calculated by the ratio of the maximum dry density, the time course curve of compaction degree decay is obtained, and the compaction degree decay function C(t) is fitted;

[0025]

[0026] ρ d is the dry density of soil sample, m s is the mass of soil particles, V0 is the initial soil sample volume, △V is the volume change rate, ΔV=πr 2 Δh, r is the radius of the soil sample.

[0027] Furthermore, the S2 further includes:

[0028] S22: Constructing a random function of compaction degree; including:

[0029] S221: Calculate the autocorrelation coefficient: Calculate the relative distance Δd(i,j) between data points based on the field compaction degree measured data, as shown in formula (4a), and obtain the data point relative distance matrix;

[0030]

[0031] In formula (4a), Δd(i,j) represents the relative distance between the i-th data point and the j-th data point, (x i ,y i ) is the spatial coordinate of the ith data point, (x j ,y j ) is the spatial coordinate of the jth data point;

[0032] The relative distance is Δd k The compaction degree of the data points is normalized and multiplied, and then added and averaged to obtain the relative distance Δd k The compaction degree autocorrelation coefficient between the data points is as follows:

[0033]

[0034] In formula (4b), R(Δd k) indicates the relative distance is Δd k The autocorrelation coefficient of compaction between the data points is, represents the mean value of the measured compaction data, C std is the variance of the measured compaction data, C ki , C kj Expressed as a relative distance Δd k The compaction degree of two data points, n k The relative distance is Δd k The number of groups of data points;

[0035] S222: constructing a compaction degree autocorrelation model; selecting the autocorrelation function model in formula (5) according to the relative distance matrix and the corresponding compaction degree autocorrelation coefficient, fitting it using the least squares method, selecting the optimal autocorrelation function type according to the fitting result, and determining the autocorrelation distance δ;

[0036]

[0037] Where: Δd represents the relative distance between two data points in the roadbed space, R(Δd) represents the autocorrelation coefficient of compaction between data points with a relative distance of Δd in the roadbed space, δ is the autocorrelation distance of compaction, and e is the base of the natural logarithm.

[0038] Furthermore, the S22 further includes:

[0039] S223: Construct a compaction random field; discretize the roadbed space into n discrete areas, each of which represents a compaction value; at the same time, the compaction C is represented as a set of random variables that are spatially correlated and identically distributed at each spatial position, and the relative distance between each discrete area and other discrete areas is calculated to obtain a relative distance matrix of the discrete space; then substitute the discrete space relative distance matrix into the compaction autocorrelation model established in S222, calculate the compaction autocorrelation coefficient matrix R(Δd) of the data points with a relative distance Δd in the discretized roadbed space, and decompose the compaction autocorrelation coefficient matrix R(Δd) according to the covariance matrix decomposition method to obtain the decomposed lower triangular matrix L, as shown in formula (6a); finally, generate a set of random matrices U identically distributed with the compaction C variable, and multiply them with the matrix L to obtain the random field C(x,y) of the compaction, as shown in formula (6b):

[0040] LL T =R(Δd)(6a)

[0041] C(x,y)=LU(6b)

[0042] Among them, Δd represents the relative distance matrix of the discrete space, L is the lower triangular matrix obtained after decomposition of the covariance matrix, and L Tis the transpose of the matrix L, U is a set of random variables with the same distribution as the variables of compaction degree C;

[0043] S23: Construct a spatial distribution model of roadbed compaction considering randomness and decay. The calculation formula is as follows:

[0044] C(x,y,t)=C(x,y)-C(x,y)*C(t) (7)

[0045] Among them, C(x, y, t) represents the compaction degree of the roadbed considering randomness and decay, and C(t) is the compaction degree decay function.

[0046] Further, the S3 includes:

[0047] In engineering software, add seepage physics and custom physics fields;

[0048] In the seepage physics field, add C(t), equation (7), equation (1a), and equation (1b);

[0049] In the custom physical field, set the independent variable u, where u represents the overlying stress, i.e. the vertical load, and define: ∫ Ω -(u-P1)*test(u)dΩ=0; where Ω is the calculation domain; P1 is the integral form of the overlying stress, test() is the trial function, P1=(abs(integrate(rho1*g_const,y,ymin,ymax))+P1P)*(x<=L)+(abs(integrate(rho1*g_const,y,ymin,ymax)))*(x>L), where P1P is the dead weight of the road surface; rho1 is the wet density of the soil; abs() represents the absolute value function; integrate() represents the integral function; g_const represents the acceleration of gravity; x represents the horizontal coordinate of the data point; y represents the vertical coordinate of the data point, ymin is the lower limit of the vertical coordinate of the data point, and ymax is the upper limit of the vertical coordinate of the data point; L is the road width;

[0050] The seepage physics field and the custom physics field are coupled and used to calculate the roadbed moisture.

[0051] The beneficial effects of the present invention are

[0052] 1. In the existing humidity calculation method, the two characteristics of compaction and stress in the roadbed are not considered. Based on the pore ratio, the present invention proposes a new hydraulic characteristic model of roadbed soil that considers the compaction and stress effects. It can more accurately describe the hydraulic characteristics of roadbed soil and provide a constitutive model for roadbed humidity calculation.

[0053] 2. The mean value of compaction degree is set as a time-history function that evolves over time. A compaction degree random field is constructed based on random field theory and combined with a new hydraulic model. A moisture migration model that considers the randomness and decay of compaction degree is established to make the humidity calculation more in line with actual conditions.

[0054] 3. Through the secondary development of finite element method, a roadbed moisture calculation method considering the random distribution and decay characteristics of roadbed compaction was constructed, which fully reflects the unique characteristics of the roadbed and provides a method for accurately revealing the evolution mechanism of roadbed moisture. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0056] Figure 1 It is a schematic diagram of the geometric model for calculating roadbed moisture.

[0057] Figure 2 is the random distribution of compaction at the initial moment and at the end of decay.

[0058] Figure 3a This is the roadbed moisture evolution diagram obtained by traditional methods.

[0059] Figure 3b This is the roadbed moisture evolution diagram considering the influence of compaction degree and overlying stress.

[0060] Figure 3c This is the roadbed moisture evolution diagram obtained by considering the compaction degree decay.

[0061] Figure 3d This is the roadbed moisture evolution diagram obtained by considering the randomness and decay of compaction degree.

[0062] Figure 4a This is the probability distribution diagram of the moisture content at observation point 1 15 years later, considering the random field and decay of compaction degree.

[0063] Figure 4b This is the probability distribution diagram of the moisture content at observation point 2 15 years later, considering the random field and decay of compaction degree.

[0064] Figure 4c This is the probability distribution diagram of moisture content at observation point No. 3 15 years later, considering the random field and decay of compaction degree. DETAILED DESCRIPTION

[0065] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0066] The complete steps of the embodiment of the present invention are as follows:

[0067] Example 1

[0068] S1: Construct the soil-water characteristic curve and permeability coefficient model of the roadbed soil.

[0069] S11: Prepare soil samples according to the optimum moisture content.

[0070] S12: Compress soil samples to different compaction degrees to simulate soil density under different construction conditions.

[0071] S13: Set different vertical loads P to simulate the upper pressure under different working conditions. Then, under different vertical loads P, use the stress-related pressure plate instrument to obtain the relationship curve between the matrix suction and moisture content of soil samples with different compaction degrees. Under different vertical loads, use the stress-related saturated permeameter to obtain the saturated permeability coefficient k of soil samples with different compaction degrees. s .

[0072] S14: Considering that compaction and overburden stress mainly affect the void ratio, the following soil-water characteristic curve model (1a) is proposed based on the traditional soil-water characteristic curve model considering the void ratio. At the same time, based on the Mualem statistical model and considering the influence of compaction and overburden stress on the saturated permeability coefficient, the permeability coefficient function equation (1b) can be obtained. In summary, a subgrade soil hydraulic characteristic model considering the influence of compaction and vertical load is constructed.

[0073]

[0074]

[0075] Where: θ, θ r ,θ s are moisture content, residual moisture content, and saturated moisture content, respectively; C represents the degree of compaction; θ s The calculation formula is: s =1-C*ρ dmax *γ w / G s , ρ dmax is the maximum dry density of the soil sample, G s is the specific gravity of soil sample, γ w is the weight of water; is matrix suction; Pa is 1 atmosphere; m2, m3, m4, m5 are fitting parameters, m1 = 1-1 / m2;

[0076] k s are the unsaturated permeability coefficient and the saturated permeability coefficient respectively, S is the effective saturation, The saturated permeability coefficient k s The following model is fitted:

[0077]

[0078] Where: a·k0 is the saturated permeability coefficient in the initial state, that is, k0 is the working condition with the lowest compaction degree and stress value in the test scheme. s To avoid poor fitting effect due to too small fitting data, a is the 10^n part when using scientific notation, k0 is the cardinality part; k1, k2, k3 are fitting parameters.

[0079] S2: Construct a spatial distribution model of roadbed compaction considering randomness and decay.

[0080] S21: Construct decay function. Fill the remolded soil sample into a container of fixed volume according to the set compaction degree, then add water at the bottom, install a displacement meter on the top to record the displacement change △h of the top surface of the sample, and convert it into dry density as shown in formula (3), using ρ at each time point d The compaction degree is calculated by the ratio of the maximum dry density to form a time course curve of compaction degree decay, and the compaction degree decay function C(t) is fitted.

[0081]

[0082] ρ d is the dry density of soil sample, m s is the mass of soil particles, V0 is the initial soil sample volume, △V is the volume change rate, ΔV=πr 2 Δh, r is the radius of the soil sample.

[0083] S22: Construct a randomness function. The specific steps are as follows:

[0084] S221: Calculate the autocorrelation coefficient. First, calculate the relative distance between the collected data points based on the field compaction measured data to obtain the data point relative distance matrix Δd(i,j), as shown in formula (4a). Then, the relative distance Δd k The compaction degrees of the two collected data points are normalized and then multiplied. Finally, the compaction degree products of the data points corresponding to the same relative distance are added and averaged to obtain the relative distance Δd. k The autocorrelation coefficient of the data point is as follows:

[0085]

[0086]

[0087] In formula (4a), Δd(i,j) represents the relative distance matrix between the i-th data point and the j-th data point, (x i ,y i ) is the spatial coordinate of the ith data point, (x j ,y j ) is the spatial coordinate of the jth data point;

[0088] In formula (4b), R(Δd k ) indicates the relative distance is Δd k The autocorrelation coefficient between the data points is It is expressed as the mean of the measured compaction data, C std is the variance of the measured compaction data, C ki and C kj Expressed as a relative distance Δd k A set of compaction data, that is, the relative distance is Δd k The compaction degree of two data points, n k The relative distance is Δd k The number of groups of data points.

[0089] S222: Constructing a compaction degree autocorrelation model. Based on the random field theory, the relative distance and the corresponding autocorrelation coefficient obtained by the above calculation are substituted into the autocorrelation function model (5) and fitted using the least squares method. The optimal autocorrelation function type is selected based on the fitting result, and the corresponding undetermined parameter autocorrelation distance δ is determined, thereby establishing a compaction degree autocorrelation model based on the inversion of the field measured data.

[0090]

[0091] Where: Δd represents the relative distance between two points in the roadbed space, R(Δd) represents the autocorrelation coefficient of compaction degree with a relative distance of Δd in the roadbed space, δ is the autocorrelation distance of compaction degree, and e is the base of the natural logarithm.

[0092] S223: Construct a random field of compaction. First, discretize the roadbed space, express the compaction C as a set of random variables that are spatially correlated and identically distributed at each spatial position, and discretize the roadbed space into multiple small areas, each of which represents a compaction value. Calculate the relative distance between each discrete area and other discrete areas to obtain the relative distance matrix of the discrete space; then substitute the calculated discrete space relative distance matrix into the compaction autocorrelation model established above, calculate the autocorrelation coefficient matrix R (Δd) of the compaction in the discretized roadbed space, and decompose the autocorrelation coefficient matrix R (Δd) according to the covariance matrix Cholesky decomposition method to obtain the decomposed lower triangular matrix L, as shown in formula (6a); finally, generate a random matrix U identically distributed to the compaction C variable, and multiply it with the decomposed lower triangular matrix L to obtain the simulated random field C (x, y) of compaction, as shown in formula (6b):

[0093] LL T =R(Δd)(6a)

[0094] C(x,y)=LU(6b)

[0095] Where: Δd represents the relative distance coordinate matrix in discrete space, R(Δd) is the autocorrelation matrix of compaction degree in roadbed space, L is the lower triangular matrix obtained by Cholesky matrix decomposition, and L T is the transpose of the matrix L, and U is a set of random variables with the same distribution as the compaction degree C.

[0096] Matlab software is used to invert the compaction degree measured data on site to obtain the probability parameter, that is, the compaction degree mean value. The compaction random field model is then built based on the exponential autocorrelation function, and then the compaction random field is generated according to the covariance matrix Cholesky decomposition method (Formula 6).

[0097] S23: Spatial distribution of compaction considering randomness and decay. Construct a compaction function considering randomness and decay:

[0098] C(x,y,t)=C(x,y)- C(x,y)*C(t) (7)

[0099] Where: C(x,y) is the random field function generated above, C(t) represents the compaction decay function, and C(x,y,t) represents the roadbed compaction considering randomness and decay.

[0100] S3: Calculate the roadbed humidity field.

[0101] Add two physical fields: seepage and custom. In the seepage physical field, Richards equation is used to solve the seepage problem; in the custom physical field, the overlying stress state of each point is solved.

[0102] Construct the seepage physical field. Based on Richards saturated-unsaturated seepage equation, write the constructed hydraulic model and compaction random and decay model, as follows:

[0103] Write the decay function of compaction degree C(t) into the program as an analytical function;

[0104] Using the variable module, define the compaction function (7) that takes into account randomness and decay;

[0105] The various parameters in equations (1a) and (1b) are defined and incorporated into the calculation program in sequence.

[0106] Customize the physical field. Because the influence of stress needs to be considered, there is a cyclic variable in the seepage calculation, namely the water content. Therefore, it is customized using the weak form partial differential equation. The details are as follows: Select the weak form partial differential equation module in the software and set 1 independent variable: u is the overburden stress,

[0107] Definition: ∫ Ω -(u-P1)*test(u)dΩ=0; where Ω is the calculation domain; P1 is the integral form of the overlying stress, test() is the trial function, P1=(abs(integrate(rho1*g_const,y,ymin,ymax))+P1P)*(x<=L)+(abs(integrate(rho1*g_const,y,ymin,ymax)))*(x>L), where P1P is the dead weight of the road surface; rho1 is the wet density of the soil; abs() represents the absolute value function; integrate() represents the integral function; g_const represents the acceleration of gravity; x represents the horizontal coordinate of the data point; y represents the vertical coordinate of the data point, ymin is the lower limit of the vertical coordinate of the data point, and ymax is the upper limit of the vertical coordinate of the data point; L is the road width; the coupling of the two physical fields is realized through the continuous self-reconstruction of the trial function test();

[0108] Calculate the roadbed humidity field and analyze the evolution of the roadbed humidity field. Use COMSOL Multiphysics to perform secondary development of finite element calculations, compile a loop program in the MATLAB development environment, and automatically generate random compaction data based on the random field model based on the Monte Carlo simulation method. Calculate the evolution of roadbed humidity under different random distributions considering the decay of compaction. According to the calculation results, the posterior probability distribution of roadbed humidity can be obtained to achieve the analysis of the evolution of roadbed humidity based on the inversion of field measured data and considering the randomness and decay of compaction.

[0109] Example 2

[0110] Take typical silt soil in southern my country as an example to illustrate the steps as follows:

[0111] S1: Acquisition of hydraulic characteristic parameters. Configure soil samples under the optimal water content state, set four groups of soil-water characteristic curve tests under different compaction degrees of 90, 93, 96, and 99 and four groups of vertical loads of 0kPa, 40kPa, 80kPa, and 120kPa, and the matrix suction is loaded step by step according to 0kPa, 1kPa, 5kPa, 10kPa, 25kPa, 50kPa, 100kPa, 200kPa, and 300kPa; at the same time, the saturated permeability coefficient is tested using a stress-related saturated permeameter according to the above compaction degree and stress state. The specific gravity is obtained by the specific gravity bottle method, and the maximum dry density is obtained by the compaction test (Table 1). Then, the various parameters can be obtained by fitting according to the above formula (1) as shown in Table 1.

[0112] Table 1 Hydraulic model parameters

[0113]

[0114] S2: Determination of the spatial distribution of roadbed compaction considering randomness and decay.

[0115] S21: Construction of decay function. According to the field test, the decay range of compaction is 0-10%. Here, only the decay effect is explained, so a simplified function is used, that is, the compaction of each area decays by 5% within 3 years and remains stable.

[0116] S22: More than 1000 groups of measured compaction degrees of the roadbed of Changzhang, Heliu and other expressways were used as the sample library. The correlation coefficient was calculated using formula (4a) (4b), and then the autocorrelation model (5) was used for fitting. The results are shown in Table 2. It can be seen from the table that the distribution range of the autocorrelation coefficient is 1.28 to 1.53.

[0117] Table 2 Autocorrelation distance of each project section

[0118] Changzhang Section 1 Changzhang Section 2 Heliu Section 1 Heliu Section 3 1.42 1.28 1.51 1.53

[0119] S3: Construction of roadbed humidity field calculation model

[0120] Based on the typical roadbed structure, a geometric model is established, with a foundation height of 1m and a width of 25m, a roadbed height of 6m, a roadbed top width of 13m, a slope ratio of 1:1.5, thickness: 0.8m in 96 areas, 0.6m in 94 areas, and a structure such as Figure 1 The hydraulic model parameters are shown in Table 1. The calculation time is 15 years. Observation point ① (6.5, 6.6) in area 96 of the roadbed, observation point ② (6.5, 5.85) in area 94, and observation point ③ (6.5, 3.25) in area 93 are set. Figure 1 shown.

[0121] Add two physical fields: seepage and custom. In the seepage physical field, Richards equation is used to solve the seepage problem; in the custom physical field, the self-weight stress state of each point is solved.

[0122] Seepage physical field construction. Based on the Richards saturated-unsaturated seepage equation, the constructed hydraulic model and the random and decay models of compaction are written as follows:

[0123] The decay function C(t) of the compaction degree is written into the program as an analytical function, according to c(t) = (1-0.05 / 3*t)(t<=3)+(0.05)(t>3).

[0124] Using the variable module, the compaction function C(x,y,t)=μ(x,y)+σ*C(x,y)-μ(x,y)*C(t) is defined taking into account randomness and decay. σ is the standard deviation of the compaction random variable and is taken as 0.0466. C(x,y) is the generated random field function. μ(x,y) is taken as 0.93, 0.94 and 0.96 according to areas 93, 94 and 96 respectively.

[0125] Define each parameter in equation (1) and then compile it into the calculation program.

[0126] Customize the physical field. Select the weak form partial differential equation module in the software and set 1 independent variable; u is the overburden stress, and define: ∫ Ω-(u-P1)*test(u)dΩ=0; where Ω is the calculation domain; P1 is the integral form of the overlying stress, test() is the trial function, P1=(abs(integrate(rho1*g_const,y,ymin,ymax))+P1P)*(x<=L)+(abs(integrate(rho1*g_const,y,ymin,ymax)))*(x>L), where P1P is the road weight, which is 14.28kPa; rho1 is the wet density of the soil; Abs() represents the absolute value function; integrate() represents the integral function; g_const represents gravity, 9.81m / s 2 ; x represents the horizontal coordinate of the data point; y represents the vertical coordinate of the data point, ymin is the lower limit of the vertical coordinate of the data point, ymax is the upper limit of the vertical coordinate of the data point; L is the road width, which is 13m.

[0127] Analysis of the evolution law of roadbed moisture field. Through COMSOL Multiphysics, the finite element calculation was secondary developed, and a loop program was compiled in the MATLAB development environment. Based on the Monte Carlo simulation method, 1,000 sets of random field models were generated to generate random compaction data. The evolution law of roadbed moisture considering the compaction decay under different random distributions was automatically calculated. The probability distribution of roadbed moisture can be obtained based on the calculation results.

[0128] The results are analyzed as follows:

[0129] Figure 2 is the random field distribution diagram of compaction degree at the initial moment and the end of decay. Among them, a is the random field distribution diagram of compaction degree at the initial moment, i.e. t=0a, i.e. the 0th year, and b is the random field distribution diagram of compaction degree at the end of decay, i.e. t=3a, i.e. the third year.

[0130] Figure 3a 3a is the roadbed moisture evolution diagram obtained by the traditional method, i.e., the method without considering the compaction degree and overlying stress; 3b is the roadbed moisture evolution diagram obtained by considering the compaction degree and overlying stress; 3c is the roadbed moisture evolution diagram obtained by considering the compaction degree decay; 3d is the roadbed moisture evolution diagram obtained by considering the compaction degree randomness and decay;

[0131] Depend on Figure 3a , 3b , 3c, and 3d show that after the roadbed was filled, the moisture content of the roadbed increased due to the influence of rainfall, evaporation, and groundwater level, and the moisture content stabilized after about 4 years. Figure 3aThe moisture content of point 3, located in the center of area 93, increased in the first year due to its proximity to the groundwater level. The moisture content of monitoring points 2 and 1, located in areas 94 and 96, also began to increase in about 2 years. After the fourth year, the moisture content was balanced. The overall equilibrium moisture content of the roadbed increases with depth. When the compaction degree and overburden stress are considered in the calculation method, see Figure 3b , the initial water content of each observation point is different. This is because the initial condition is a fixed matrix suction value. After considering the overburden stress and compaction degree, it can be seen from formula (1a) that the initial water content of each observation point is different. Compared with the results of the traditional method ( Figure 3a ) It can be found that the starting time of moisture changes at each location is advanced to about 1 year for No. 1 and No. 2, and the equilibrium time is also advanced to about 3 years; the equilibrium moisture content of point 3 is close under the two calculation methods, and the equilibrium moisture content of points 1 and 2 increases, while the difference in equilibrium moisture content between No. 1 and No. 2 increases. This is because the hydraulic parameters of the traditional method are test conditions under no compaction and no load, while the hydraulic parameters are different after considering the compaction and overlying stress. Figure 3c To further consider the evolution of compaction decay, it can be found that the equilibrium time of moisture at each point is slightly advanced. The most significant change is that the equilibrium moisture content has increased significantly. For example, at monitoring point No. 3, the results of the first two methods are about 0.40 cm 3 / cm 3 , and this method increases the moisture content to 0.42cm 3 / cm 3 This is because the compaction degree has decreased, which increases the pore volume and leads to an increase in water content. Figure 3d In the figure, after considering the decay and randomness of compaction degree, the evolution result of the moisture content of the roadbed under a certain random distribution of compaction degree is shown. It can be found that the distribution of moisture content is random, and the moisture content distribution of each monitoring point no longer follows the law of increasing along the depth.

[0132] Figure 4a This is the probability distribution diagram of the moisture content at observation point 1 15 years later, considering the random field and decay of compaction degree. Figure 4b 4a is the probability distribution diagram of the moisture content at observation point 2 15 years later, considering the random field and decay of compaction degree. 4b is the probability distribution diagram of the moisture content at observation point 3 15 years later, considering the random field and decay of compaction degree.

[0133] It can be seen that the equilibrium moisture content at each location conforms to the normal distribution, and the normal fitting accuracy reaches 0.99. For observation point 1, the mean is 0.406cm 3 / cm 3 ; For observation point 2, the mean is 0.413cm 3 / cm 3; For observation point 3, the mean is 0.420cm 3 / cm 3 By comparison, it can be found that the overall equilibrium moisture content increases along the depth direction. In summary, through the probabilistic analysis of the equilibrium moisture content, it can be concluded that the calculation method of the roadbed moisture considering the randomness and decay of the compaction degree can provide a basis for the reliability design of the entire roadbed structure performance.

[0134] Each embodiment in this specification is described in a related manner, and the same or similar parts between the embodiments can be referred to each other, and each embodiment focuses on the differences from other embodiments. In particular, for the system embodiment, since it is basically similar to the method embodiment, the description is relatively simple, and the relevant parts can be referred to the partial description of the method embodiment.

[0135] The above description is only a preferred embodiment of the present invention and is not intended to limit the protection scope of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention are included in the protection scope of the present invention.

Claims

1. A moisture calculation method considering the compaction characteristics of the roadbed, characterized in that: The following steps are involved: S1: Construct a hydraulic characteristic model of subgrade soil considering compaction and vertical load; S2: Construct a spatial distribution model of roadbed compaction considering randomness and decay; S3: The subgrade moisture field is calculated based on the subgrade soil hydraulic characteristics model considering compaction and vertical load, and the subgrade compaction spatial distribution model considering randomness and decay.

2. The humidity calculation method considering the roadbed compaction characteristics according to claim 1 is characterized in that: The S1 includes: S11: Prepare soil samples according to the optimal moisture content; S12: Compressing the soil samples to different compaction degrees; S13: Set different vertical loads P on the soil samples of S12. Obtain the relationship curve between matrix suction and water content of soil samples with different compaction degrees under different vertical loads; obtain the saturated permeability coefficient k of soil samples with different compaction degrees under different vertical loads s ; S14: Construct a soil-water characteristic curve model considering compaction and vertical load, as shown in formula (1a); The permeability coefficient function equation considering compaction and vertical load is constructed as shown in formula (1b); Among them, θ, θ r ,θ s are moisture content, residual moisture content, and saturated moisture content, respectively; C represents the degree of compaction; θ s The calculation formula is: s =1-C*ρ dmax *γ w / G s , ρ dmax is the maximum dry density of the soil sample, G s is the specific gravity of soil sample, γ w is the weight of water; is matrix suction; P a is the value of 1 atmosphere; m2, m3, m4, m5 are fitting parameters; m1 = 1-1 / m2; k s are the unsaturated permeability coefficient and the saturated permeability coefficient respectively, S is the effective saturation, 3. The humidity calculation method considering the roadbed compaction characteristics according to claim 1, characterized in that: In S14, the saturated permeability coefficient k s The following fitting formula is used: Where: a·k0 is the saturated permeability coefficient in the initial state, that is, k0 is the working condition with the lowest compaction degree and vertical load. s The value of; k0 is the cardinality part when the initial state saturated permeability coefficient is expressed in scientific notation, a is the 10^n part when the initial state saturated permeability coefficient is expressed in scientific notation; k1, k2, k3 are fitting parameters.

4. The method for calculating humidity considering roadbed compaction characteristics according to claim 1, characterized in that: The S2 includes: S21: Construct compaction decay function C(t); fill the soil sample into the container according to the set compaction degree, then add water, record the displacement change △h of the top surface of the sample, and convert it into dry density as shown in formula (3), using the soil sample dry density ρ at each time point d The compaction degree is calculated by the ratio of the maximum dry density, the time course curve of compaction degree decay is obtained, and the compaction degree decay function C(t) is fitted; ρ d is the dry density of soil sample, m s is the mass of soil particles, V0 is the initial soil sample volume, △V is the volume change rate, ΔV=πr 2 Δh, r is the radius of the soil sample.

5. The method for calculating humidity considering roadbed compaction characteristics according to claim 1, characterized in that: The S2 further includes: S22: Constructing a random function of compaction degree; including: S221: Calculate the autocorrelation coefficient: Calculate the relative distance Δd(i,j) between data points based on the field compaction degree measured data, as shown in formula (4a), and obtain the data point relative distance matrix; In formula (4a), Δd(i,j) represents the relative distance between the i-th data point and the j-th data point, (x i ,y i ) is the spatial coordinate of the ith data point, (x j ,y j ) is the spatial coordinate of the jth data point; The relative distance is Δd k The compaction degree of the data points is normalized and multiplied, and then added and averaged to obtain the relative distance Δd k The compaction degree autocorrelation coefficient between the data points is as follows: In formula (4b), R(Δd k ) indicates the relative distance is Δd k The autocorrelation coefficient of compaction between the data points is, represents the mean value of the measured compaction data, C std is the variance of the measured compaction data, C ki , C kj Expressed as a relative distance Δd k The compaction degree of two data points, n k The relative distance is Δd k The number of groups of data points; S222: constructing a compaction degree autocorrelation model; selecting the autocorrelation function model in formula (5) according to the relative distance matrix and the corresponding compaction degree autocorrelation coefficient, fitting it using the least squares method, selecting the optimal autocorrelation function type according to the fitting result, and determining the autocorrelation distance δ; Where: Δd represents the relative distance between two data points in the roadbed space, R(Δd) represents the autocorrelation coefficient of compaction between data points with a relative distance of Δd in the roadbed space, δ is the autocorrelation distance of compaction, and e is the base of the natural logarithm.

6. The method for calculating humidity considering roadbed compaction characteristics according to claim 5, characterized in that: The S22 further includes: S223: Construct a compaction random field; discretize the roadbed space into n discrete areas, each of which represents a compaction value; at the same time, the compaction C is represented as a set of random variables that are spatially correlated and identically distributed at each spatial position, and the relative distance between each discrete area and other discrete areas is calculated to obtain a relative distance matrix of the discrete space; then substitute the discrete space relative distance matrix into the compaction autocorrelation model established in S222, calculate the compaction autocorrelation coefficient matrix R(Δd) of the data points with a relative distance Δd in the discretized roadbed space, and decompose the compaction autocorrelation coefficient matrix R(Δd) according to the covariance matrix decomposition method to obtain the decomposed lower triangular matrix L, as shown in formula (6a); finally, generate a set of random matrices U identically distributed with the compaction C variable, and multiply them with the matrix L to obtain the random field C(x,y) of the compaction, as shown in formula (6b): LL T =R(Δd)(6a) C(x,y)=LU(6b) Among them, Δd represents the relative distance matrix of the discrete space, L is the lower triangular matrix obtained after decomposition of the covariance matrix, and L T is the transpose of the matrix L, U is a set of random variables with the same distribution as the variables of compaction degree C; S23: Construct a spatial distribution model of roadbed compaction considering randomness and decay. The calculation formula is as follows: C(x,y,t)=C(x,y)-C(x,y)*C(t) (7) Among them, C(x, y, t) represents the compaction degree of the roadbed considering randomness and decay, and C(t) is the compaction degree decay function.

7. The method for calculating humidity considering roadbed compaction characteristics according to claim 2, 4 or 6, characterized in that: The S3 includes: In engineering software, add seepage physics and custom physics fields; In the seepage physics field, add C(t), equation (7), equation (1a), and equation (1b); In the custom physical field, set the independent variable u, where u represents the overlying stress, i.e. the vertical load, and define: ∫ Ω -(u-P1)*test(u)dΩ=0; where Ω is the calculation domain; P1 is the integral form of the overlying stress, test() is the trial function, P1=(abs(integrate(rho1*g_const,y,ymin,ymax))+P1P)*(x<=L)+(abs(integrate(rho1*g_const,y,ymin,ymax)))*(x>L), where P1P is the dead weight of the road surface; rho1 is the wet density of the soil; abs() represents the absolute value function; integrate() represents the integral function; g_const represents the acceleration of gravity; x represents the horizontal coordinate of the data point; y represents the vertical coordinate of the data point, ymin is the lower limit of the vertical coordinate of the data point, and ymax is the upper limit of the vertical coordinate of the data point; L is the road width; The seepage physics field and the custom physics field are coupled and used to calculate the roadbed moisture.

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