A humidity calculation method considering the compaction characteristics of subgrade

Abstract

The present invention provides a humidity calculation method considering the compaction characteristics of subgrade, comprising the following steps: S1: constructing a subgrade soil hydraulic characteristic model considering the degree of compaction and vertical load; S2: constructing a spatial distribution model of subgrade compaction degree considering randomness and decay; S3: calculating the subgrade humidity based on the subgrade soil hydraulic characteristic model considering the degree of compaction and vertical load and the spatial distribution model of subgrade compaction degree considering randomness and decay. To solve the problem that the existing humidity calculation methods cannot consider the randomness and decay of subgrade compaction degree, so as to achieve accurate calculation of the evolution and balance laws of subgrade humidity.

Description

Technical Field

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

[0002] The distribution of the subgrade humidity field is the key to determining the performance of the subgrade. It is crucial to accurately evaluate the evolution and balance laws of the subgrade humidity. The subgrade is compacted and formed according to a specific compaction degree; during the operation period, since the subgrade is in the atmospheric environment, it will be affected by natural conditions such as rainfall, evaporation, freeze-thaw, and vehicle loads, which will cause the attenuation of the soil compaction degree, especially significant in the humid and hot areas in the south of China. Through field investigations on expressways such as Lianzhu, Heliu, and Changzhang, after years of operation, the overall compaction degree has attenuated by about 10%, which will cause changes in the hydraulic properties such as the 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 compaction, natural environment, and vehicle loads, there is a great variability in the compaction degree in space, which will lead to differences in hydraulic properties at various positions of the subgrade. In the existing humidity calculation methods, these two characteristics existing in the subgrade are not considered, resulting in differences between the calculated subgrade humidity and the actual situation, which is not conducive to accurately obtaining the evolution and balance laws of the subgrade humidity, and thus unable to evaluate the evolution of the subgrade mechanical properties and ensure the durability of the subgrade. Summary of the Invention

[0003] The purpose of the embodiments of the present invention is to provide a humidity calculation method considering the compaction characteristics of subgrade to solve the problems that the existing humidity calculation methods do not conform to the actual situation, the calculation results are inaccurate, and the evolution and balance laws of the subgrade humidity cannot be accurately obtained.

[0004] To solve the above technical problems, the technical solution adopted by the present invention is

[0005] A humidity calculation method considering the compaction characteristics of subgrade includes the following steps:

[0006] S1: Construct a subgrade soil hydraulic property model considering the compaction degree and vertical load;

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

[0008] S3: Calculate the subgrade humidity field based on the subgrade soil hydraulic property model considering the compaction degree and vertical load and the subgrade compaction degree spatial distribution model considering randomness and decay.

[0009] Further, the S1 includes:

[0010] S11: Prepare soil samples according to the optimum water content;

[0011] S12: Press the soil sample to different compaction degrees;

[0012] S13: Set different vertical loads P on the soil samples in S12,

[0013] Obtain the relationship curves between the 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 degree and vertical load, as shown in Equation (1a);

[0015] Construct a permeability coefficient function equation considering compaction degree and vertical load, as shown in Equation (1b);

[0016]

[0017]

[0018] where θ, θ r , θ s are the water content, residual water content, and saturated water content respectively, and C represents the compaction degree; the calculation formula of θ s is: θ 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 the soil sample, and γ w is the unit weight of water; is the matrix suction; P a is the value of 1 atmospheric pressure; m2, m3, m4, m5 are fitting parameters; m1 = 1 - 1 / m2;

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

[0020] Furthermore, in the above S14, the saturated permeability coefficient k s is fitted by the following formula:

[0021]

[0022] In the formula: a·k0 is the saturated permeability coefficient in the initial state, that is, the k sThe value of; k0 is the base part when expressing the initial state saturated permeability coefficient in scientific notation, a is the 10^n part when expressing the initial state saturated permeability coefficient in scientific notation; k1, k2, and k3 are fitting parameters.

[0023] Further, the S2 includes:

[0024] S21: Construct a compaction degree decay function C(t); fill the soil sample into the container according to the set compaction degree, then replenish water, record the displacement change Δh of the top surface of the sample, convert it into dry density as shown in Equation (3), and calculate the compaction degree using the ratio of the dry density ρ of the soil sample at each time point d to its maximum dry density, obtain the time history curve of compaction degree decay, and fit the compaction degree decay function C(t);

[0025]

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

[0027] Further, the S2 also includes:

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

[0029] S221: Calculate the autocorrelation coefficient: Calculate the relative distance Δd(i,j) between data points according to the measured field compaction degree data, as shown in Equation (4a), to obtain the relative distance matrix of data points;

[0030]

[0031] In Equation (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 i-th data point, (x j ,y j ) is the spatial coordinate of the j-th data point;

[0032] Normalize and multiply the compaction degrees of data points with a relative distance of Δd k , then sum and average to obtain the autocorrelation coefficient of compaction degrees between data points with a relative distance of Δd k , as shown in Equation (4b):

[0033]

[0034] In Equation (4b), R(Δd k)Indicates the autocorrelation coefficient of compaction between data points with a relative distance of Δd k of the data points, represents the mean of the measured compaction data, C std is the variance of the measured compaction data, C ki 、C kj Indicates that for two data points with a relative distance of Δd k the compaction of the data points, n k is the relative distance of Δd k for the number of groups of data points;

[0035] S222: Construct the compaction autocorrelation model; According to the relative distance matrix and the corresponding compaction autocorrelation coefficient, select the autocorrelation function model in Equation (5), use the least squares method for fitting, select the optimal autocorrelation function type according to the fitting result, and determine the autocorrelation distance δ;

[0036]

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

[0038] Furthermore, the S22 also includes:

[0039] S223: Construct the compaction random field; Discretize the subgrade space, discretize the subgrade space into n discrete regions, and each discrete region represents a compaction value; At the same time, represent the compaction C as a set of spatially correlated and identically distributed random variables at each spatial position, calculate the relative distance between each discrete region and other discrete regions to obtain the relative distance matrix of the discrete space; Subsequently, substitute the discrete space relative distance matrix into the compaction autocorrelation model established in S222 to calculate the compaction autocorrelation coefficient matrix R(Δd) of data points with a relative distance of Δd in the discretized subgrade 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 Equation (6a); Finally, generate a set of random matrices U that are identically distributed with the compaction C variable, and multiply it by the matrix L to obtain the compaction random field C(x,y), as shown in Equation (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 covariance matrix decomposition, L Tis the transpose of matrix L, and U is a set of random variables that are identically distributed with the variables of the compaction degree C;

[0043] S23: Construct a spatial distribution model of subgrade compaction degree considering randomness and decay, and 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 subgrade compaction degree considering randomness and decay, and C(t) is the compaction degree decay function.

[0046] Furthermore, the said S3 includes:

[0047] In engineering software, add the seepage physical field and the custom physical field;

[0048] In the seepage physical 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 overburden 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 overburden 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 self-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 due to gravity; x represents the abscissa of the data point; y represents the vertical coordinate of the data point, ymin is the lower limit of the vertical coordinate value of the data point, ymax is the upper limit of the vertical coordinate value of the data point; L is the width of the road surface;

[0050] Couple the seepage physical field and the custom physical field and use them for subgrade moisture calculation.

[0051] The beneficial effects of the present invention are

[0052] 1. In the existing moisture calculation methods, the two characteristics of the compaction degree and stress influence in the subgrade are not considered. Based on the pore ratio, the present invention proposes a new model of the hydraulic characteristics of subgrade soil considering the compaction degree and stress influence, which can more accurately describe the hydraulic characteristics of subgrade soil and provides a constitutive model for subgrade moisture calculation.

[0053] 2. Set the mean value of the compaction degree as a time-history function that evolves over time. Based on the random field theory, construct a random field of compaction degree and combine it with a new hydraulic model. Establish a moisture migration model that takes into account the randomness and decay of compaction degree, making the humidity calculation more in line with the actual situation.

[0054] 3. Through the secondary development of finite elements, construct a method for calculating the subgrade humidity that takes into account the random distribution and decay characteristics of subgrade compaction degree, fully reflecting the unique characteristics of the subgrade, and providing a method for accurately revealing the mechanism of subgrade humidity evolution. Brief Description of the Drawings

[0055] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

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

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

[0058] Figure 3a It is the subgrade humidity evolution diagram obtained by the traditional method.

[0059] Figure 3b It is the subgrade humidity evolution diagram obtained by considering the influence of compaction degree and overlying stress.

[0060] Figure 3c It is the subgrade humidity evolution diagram obtained by considering the decay of compaction degree.

[0061] Figure 3d It is the subgrade humidity evolution diagram obtained by considering the randomness and decay of compaction degree.

[0062] Figure 4a It is the probability distribution diagram of the water content of the No. 1 observation point after 15 years under the condition of considering the random field and decay of compaction degree.

[0063] Figure 4b It is the probability distribution diagram of the water content of the No. 2 observation point after 15 years under the condition of considering the random field and decay of compaction degree.

[0064] Figure 4c It is the probability distribution diagram of the water content of the No. 3 observation point after 15 years under the condition of considering the random field and decay of compaction degree. Detailed Embodiment

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

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

[0067] Embodiment 1

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

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

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

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

[0072] S14: Considering that the compaction degree and overlying 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 the compaction degree and overlying stress on the saturated permeability coefficient, the permeability coefficient function equation (1b) can be obtained. In summary, a hydraulic characteristic model of subgrade soil considering the influence of compaction degree and vertical load is constructed.

[0073]

[0074]

[0075] In the formula: θ, θ r , θ s are the water content, residual water content, and saturated water content respectively, C represents the compaction degree; the calculation formula of θ s is: θ 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 the soil sample, γ w is the unit weight of water; is the matrix suction; Pa is 1 atmospheric pressure; m2, m3, m4, m5 are fitting parameters, and m1 = 1 - 1 / m2;

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

[0077]

[0078] In the formula: a·k0 is the saturated permeability coefficient in the initial state, that is, the value of k under the condition where both the compaction degree and the stress value in the test scheme are the lowest; To avoid poor fitting effect due to too small fitting data, a is the 10^n part when using scientific notation, and k0 is the base part; k1, k2, k3 are fitting parameters. s For the sake of avoiding poor fitting effect due to too small fitting data, a is the 10^n part when using scientific notation, k0 is the base part; k1, k2, k3 are fitting parameters.

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

[0080] S21: Construct a decay function. Fill the remolded soil sample into a container with a fixed volume according to the set compaction degree, then replenish water at the bottom, install a displacement meter at 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). Use the ratio of ρ d at each time point to its maximum dry density to calculate the compaction degree, form a time-history curve of compaction degree decay, and fit out the decay function C(t) of the compaction degree.

[0081]

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

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

[0084] S221: Calculate the autocorrelation coefficient. First, calculate the relative distance between the collected data points according to the measured field compaction degree data to obtain the relative distance matrix △d(i,j) of the data points, as shown in formula (4a). Subsequently, multiply the compaction degrees of two collected data points with a relative distance of △d k after normalization, and finally sum and average the products of the compaction degrees of the data points corresponding to the same relative distance to obtain the autocorrelation coefficient of the data points with a relative distance of △d k as shown in formula (4b),

[0085]

[0086]

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

[0088] In Equation (4b), R(Δd k ) represents the autocorrelation coefficient between data points with a relative distance of Δd k , represents the mean value of the measured compaction data, C std is the variance of the measured compaction data, C ki and C kj represent a set of compaction data with a relative distance of Δd k , that is, the compaction degrees of two data points with a relative distance of Δd k , and n k is the number of groups of data points with a relative distance of Δd k .

[0089] S222: Construct a compaction degree autocorrelation model. Based on the random field theory, substitute the relative distances and the corresponding autocorrelation coefficient results calculated above into the autocorrelation function model (5) and perform fitting using the least squares method. Then, select the optimal autocorrelation function type according to the fitting results and determine the corresponding undetermined parameter, the autocorrelation distance δ, so as to establish a compaction degree autocorrelation model inversed based on the on-site measured data.

[0090]

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

[0092] S223: Construct the compactness random field. First, discretize the subgrade space. Represent the compactness C as a set of spatially correlated and identically distributed random variables at each spatial position, and discretize the subgrade space into multiple small regions, with each region representing a compactness value. Calculate the relative distance between each discrete region and other discrete regions to obtain the relative distance matrix of the discrete space. Subsequently, substitute the calculated relative distance matrix of the discrete space into the compactness autocorrelation model established above to calculate the autocorrelation coefficient matrix R(Δd) of the compactness on the discretized subgrade space, and decompose the autocorrelation coefficient matrix R(Δd) according to the covariance matrix Cholesky decomposition method to obtain the lower triangular matrix L after decomposition, as shown in Equation (6a). Finally, generate a random matrix U that is identically distributed with the compactness C variable, and multiply it by the decomposed lower triangular matrix L to obtain the simulated random field C(x,y) of the compactness, as shown in Equation (6b):

[0093] LL T =R(Δd)(6a)

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

[0095] where: Δd represents the relative distance coordinate matrix of the discrete space, R(Δd) is the autocorrelation matrix of the compactness on the subgrade space, L is the lower triangular matrix obtained after the Cholesky matrix decomposition, L T is the transpose of the matrix L, and U is a set of random variables that are identically distributed with the variables of the compactness C.

[0096] Use Matlab software to inversely obtain the probability parameters, namely the mean value of the compactness and the standard deviation, as well as the autocorrelation distance δ of the compactness random field from the measured field compactness data. Then, build the compactness random field model based on the exponential autocorrelation function, and subsequently generate the compactness random field according to the covariance matrix Cholesky decomposition method (Equation 6).

[0097] S23: Consider the spatial distribution of compactness with randomness and decay. Construct a compactness 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 compactness decay function, and C(x,y,t) represents the subgrade compactness considering randomness and decay.

[0100] S3: Calculate the subgrade moisture field.

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

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

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

[0104] Using the variable module, define the compaction degree function considering randomness and decay, Equation (7);

[0105] Define each parameter in Equations (1a) and (1b) and incorporate them into the calculation program in sequence.

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

[0107] Define: ∫ Ω -(u - P1)*test(u)dΩ = 0; where, Ω is the calculation domain; P1 is the integral form of the overburden 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 self-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 due to gravity; x represents the abscissa of the data point; y represents the vertical coordinate of the data point, ymin is the lower limit of the vertical coordinate value of the data point, ymax is the upper limit of the vertical coordinate value of the data point; L is the width of the road surface; The coupling of the two physical fields is realized through the continuous self-reconstruction of the trial function test().

[0108] Calculate the subgrade moisture field and analyze the evolution law of the subgrade moisture field. Through the secondary development of finite element calculation by COMSOL Multiphysics, a loop program is compiled in the MATLAB development environment. Based on the Monte Carlo simulation method, random data of compaction degree is automatically generated according to the random field model, and the evolution law of subgrade moisture considering the decay of compaction degree under different random distributions is calculated. The posterior probability distribution of subgrade moisture can be obtained according to the calculation results, so as to realize the analysis of the evolution law of subgrade moisture based on the inversion of field measured data and considering the randomness and decay of compaction degree.

[0109] Example 2

[0110] Taking typical silt in the south of China as an example for illustration, the steps are as follows:

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

[0112] Table 1 Hydraulic model parameters

[0113]

[0114] S2: Determine the spatial distribution of subgrade compaction degree considering randomness and decay.

[0115] S21: Construct the decay function. According to the decay range of compaction degree measured on site from 0 to 10%, only the influence of decay is explained here, so a simplified function is adopted, that is, it is stipulated that the compaction degree in each area decays by 5% within 3 years and remains stable.

[0116] S22: Use more than 1000 groups of measured compaction degrees of the subgrades of Changzhang, HeLiu and other expressways as the sample library, calculate the correlation coefficient by using formulas (4a) and (4b), and then fit by using the autocorrelation model (5). 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 - 1.53.

[0117] Table 2 Autocorrelation distance of each engineering 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 Subgrade Moisture Field Calculation Model

[0120] Based on a typical subgrade structure, a geometric model is established. The foundation is 1 m high and 25 m wide, the subgrade is 6 m high, the top width of the subgrade is 13 m, and the slope ratio is 1:1.5; Thickness: 0.8 m in Zone 96, 0.6 m in Zone 94, and the structure is as Figure 1 shown. The hydraulic model parameters are shown in Table 1. The calculation time is 15 years. Observation points ①(6.5, 6.6) in Zone 96 of the subgrade, ②(6.5, 5.85) in Zone 94, and ③(6.5, 3.25) in Zone 93 are set. As Figure 1 shown.

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

[0122] Construction of seepage physical field. Based on the Richards saturated-unsaturated seepage equation, the constructed hydraulic model and the compaction degree random and decay models 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, define the compaction degree function C(x, y, t)=μ(x, y)+σ*C(x, y)-μ(x, y)*C(t) considering randomness and decay. σ is the standard deviation of the compaction degree random variable, taking 0.0466, and C(x, y) is the generated random field function; μ(x, y) takes 0.93, 0.94, and 0.96 in Zones 93, 94, and 96 respectively.

[0125] Define each parameter in Equation (1) and compile them into the calculation program in turn.

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

[0127] Analysis of the evolution law of the subgrade moisture field. Through secondary development of the finite element calculation by COMSOL Multiphysics, a loop program is compiled in the MATLAB development environment. Based on the Monte Carlo simulation method, 1000 groups of random field models are generated to generate random data of the compaction degree, and the evolution law of the subgrade moisture considering the decay of the compaction degree under different random distributions is automatically calculated. According to the calculation results, the probability distribution of the subgrade moisture can be obtained.

[0128] The results are analyzed as follows:

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

[0130] Figure 3a Figure 3a is the subgrade moisture evolution map obtained by the traditional method, i.e., the method that does not consider the compaction degree and the overburden stress. Figure 3b is the subgrade moisture evolution map considering the influence of the compaction degree and the overburden stress. Figure 3c is the subgrade moisture evolution map considering the decay of the compaction degree. Figure 3d is the subgrade moisture evolution map considering the randomness and decay of the compaction degree;

[0131] From Figure 3a 、 3b 、Figure 3c, and Figure 3d, it can be seen that after the subgrade is filled, the moisture content of the subgrade increases under the influence of rainfall, evaporation, and the groundwater level, and the moisture content becomes stable after about 4 years. Among them, see Figure 3a, Point 3 at the center of Area 93 shows an increase in moisture content in the first year because it is close to the groundwater level. Around two years later, the moisture content at Monitoring Points 2 and 1 in Areas 94 and 96 also starts to increase, and the moisture content reaches equilibrium after the fourth year; the overall equilibrium moisture content of the roadbed increases with depth. When the influence of compaction degree and overlying stress is considered in the calculation method, see Figure 3b , the initial moisture contents of each observation point are different because the initial condition is a fixed matrix suction value. After considering the overlying stress and compaction degree, it can be seen from Equation (1a) that the initial moisture contents of each observation point are different. Comparing with the results of the traditional method ( Figure 3a ), it can be found that the starting time of moisture change at each location is advanced to about one year for Points 1 and 2, and the equilibrium time is also advanced to about three years; the equilibrium moisture contents of Point 3 under the two calculation methods are close, while the equilibrium moisture contents of Points 1 and 2 increase, and the difference in the equilibrium moisture contents of Points 1 and 2 also increases. This is because the hydraulic parameters of the traditional method are for the test conditions without compaction degree and without load, while there are differences in hydraulic parameters after considering the compaction degree and overlying stress. Figure 3c To further consider the evolution results when the compaction degree decays, it can be found that the equilibrium time of moisture at each point is slightly advanced, and the most significant change is that the equilibrium moisture content has increased significantly. For example, for Monitoring Point 3, the results of the first two methods are about 0.40 cm 3 / cm 3 , while the moisture content increases to 0.42 cm 3 / cm 3 by this method. This is because the compaction degree decays, increasing the pore volume and resulting in an increase in moisture content. Figure 3d In

[0132] Figure 4a , considering the compaction degree decay and randomness, the evolution result diagram of the roadbed moisture content under a certain random distribution of compaction degree can be found. The distribution of moisture content shows randomness, and the moisture content distribution at each monitoring point no longer follows the rule of increasing with depth. Figure 4b Figure 4b is the probability distribution diagram of the moisture content at Observation Point 1 after 15 years considering the compaction degree random field and decay,

[0133] Figure 4c is the probability distribution diagram of the moisture content at Observation Point 3 after 15 years considering the compaction degree random field and decay. It can be seen that the equilibrium moisture contents at each location conform to the normal distribution, and the normal fitting accuracy reaches 0.99. For Observation Point 1, the mean value is 0.406 cm 3 / cm 3 ; for Observation Point 2, the mean value is 0.413 cm 3 / cm 3; For the observation point No. 3, the mean value is 0.420 cm 3 / cm 3 . It can be found by comparison that the equilibrium moisture content generally increases along the depth direction. In summary, through the probability analysis of the equilibrium moisture content, it can be concluded that the calculation method of subgrade moisture considering the randomness and decay of compaction degree can provide a basis for the reliability design of the performance of the entire subgrade structure.

[0134] Each embodiment in this specification is described in a related manner. For the same and similar parts between the embodiments, reference can be made to each other. 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 reference can be made to the partial description of the method embodiment for the relevant parts.

[0135] The above 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 humidity calculation method considering the compaction characteristics of subgrade, characterized in that, It includes the following steps: S1: Construct a hydraulic characteristic model of subgrade soil considering compaction degree and vertical load; S2: Construct a spatial distribution model of subgrade compaction degree considering randomness and decay; S3: Calculate the subgrade moisture field based on the hydraulic characteristic model of subgrade soil considering compaction degree and vertical load and the spatial distribution model of subgrade compaction degree considering randomness and decay; The S2 includes: S21: Construct the compaction degree decay function C(t); Fill the soil sample into the container according to the set compaction degree, then add water, record the displacement change Δh of the top surface of the sample, convert it into dry density as shown in Equation (3), and calculate the compaction degree using the ratio of the dry density ρ of the soil sample at each time point to its maximum dry density, obtain the time history curve of the compaction degree decay, and fit the compaction degree decay function C(t); d Calculate the compaction degree by using the ratio of the dry density ρ of the soil sample at each time point to its maximum dry density, obtain the time history curve of the compaction degree decay, and fit the compaction degree decay function C(t); ρ d is the dry density of the soil sample, m s is the mass of soil particles, V0 is the initial volume of the soil sample, ΔV is the volume change rate, ΔV = πr 2 Δh, r is the radius of the soil sample; S22: Construct a compaction degree random function; including: S221: Calculate the autocorrelation coefficient: Calculate the relative distance Δd between data points according to the measured field compaction degree data to obtain the relative distance matrix of data points; Normalize and multiply the compaction degrees of data points with the same relative distance, and then sum and average to obtain the autocorrelation coefficient of compaction degrees between data points with the same relative distance; S222: Construct an autocorrelation model of compaction degree; According to the relative distance matrix and the corresponding autocorrelation coefficient of compaction degree, select an autocorrelation function model, perform fitting using the least squares method, select the optimal autocorrelation function type according to the fitting result, and determine the autocorrelation distance δ; S223: Construct a compactness random field; discretize the subgrade space, discretize the subgrade space into n discrete regions, and each discrete region represents a compactness value; at the same time, represent the compactness C as a set of spatially correlated and identically distributed random variables at each spatial position, calculate the relative distance between each discrete region and other discrete regions, and obtain the relative distance matrix of the discrete space; subsequently, substitute the discrete space relative distance matrix into the compactness autocorrelation model established in S222 to calculate the compactness autocorrelation coefficient matrix of data points with a relative distance of Δd in the discretized subgrade space And decompose the compactness autocorrelation coefficient matrix according to the covariance matrix decomposition method Perform decomposition to obtain the decomposed lower triangular matrix L, as shown in Equation (6a); finally, generate a random matrix U that is identically distributed with the compactness C variable, and multiply it by the matrix L to obtain the random field C(x, y) of compactness, as shown in Equation (6b): C(x,y)=LU(6b) where L is the lower triangular matrix obtained after the covariance matrix decomposition, and L T is the transpose of matrix L, and U is a set of random variables that are identically distributed with the variables of the compaction degree C; S23: Construct a spatial distribution model of subgrade compaction degree considering randomness and decay, and 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 subgrade compaction degree considering randomness and decay, and C(t) is the compaction degree decay function.

2. The humidity calculation method considering the subgrade compaction characteristics according to claim 1, characterized in that, The S1 includes: S11: Prepare soil samples according to the optimum moisture content; S12: Press the soil samples to different compaction degrees; S13: Set different vertical loads P on the soil samples in S12; Obtain the relationship curves between the matric 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 degree and vertical load, as shown in formula (1a); Construct a permeability coefficient function equation considering compaction degree and vertical load, as shown in formula (1b); Among them, θ, θ r , θ s are the water content, residual water content, and saturated water content respectively, and C represents the degree of compaction; the calculation formula of θ s is: θ 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 the soil sample, γ w is the unit weight of water; is the matric suction; P a is the value of 1 atmospheric pressure; m1, m2, m3, m4, m5 are fitting parameters; m1 = 1 - 1 / m2; k s are the unsaturated hydraulic conductivity and the saturated hydraulic conductivity respectively, and S is the effective saturation, 3. The humidity calculation method considering the subgrade compaction characteristics according to claim 2, characterized in that, In S14, the saturated permeability coefficient k s is fitted by the following formula: a·k0 is the saturated permeability coefficient in the initial state, that is, the value of k under the condition of the lowest compaction degree and vertical load; where: k0 is the base part when expressing the saturated permeability coefficient in the initial state by scientific notation, and a is the power of 10 part when expressing the saturated permeability coefficient in the initial state by scientific notation; k1, k2, and k3 are fitting parameters. s value; In the formula: k0 is the base part when expressing the saturated permeability coefficient in the initial state by scientific notation, and a is the power of 10 n part; k1, k2, and k3 are fitting parameters.

4. The humidity calculation method considering the subgrade compaction characteristics according to claim 1, characterized in that In the S221, obtain the relative distance matrix of data points, as shown in formula (4a): In formula (4a), Δd(i,j) represents the relative distance between the i-th data point and the j-th data point, forming a relative distance matrix. (x i , y i ) are the spatial coordinates of the i-th data point, and (x j , y j ) are the spatial coordinates of the j-th data point; Obtain the autocorrelation coefficient of compaction degrees between data points with the same relative distance, as shown in formula (4b): In Equation (4b), R(Δd) represents the compaction autocorrelation coefficient between data points with a relative distance of Δd, represents the mean value of the measured compaction data, C std is the variance of the measured compaction data, C ki 、C kj represent the compaction degrees of two data points with a relative distance of Δd, n k is the number of groups of data points with a relative distance of Δd; In the S222, the autocorrelation function model is as shown in formula (5): In the formula: δ is the autocorrelation distance of compaction degree, and e is the base of the natural logarithm.

5. The humidity calculation method considering the subgrade compaction characteristics according to claim 2, characterized in that The S3 includes: In engineering software, add a seepage physical field and a custom physical field; In the seepage physical field, add C(t), formula (7), formula (1a), and formula (1b); In the custom physical field, the independent variable u is set, where u represents the overlying stress, i.e., the vertical load, and it is defined as: ∫ Ω -(u - P1)*test(u)dΩ = 0; where Ω is the computational 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 self-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 due to gravity; x represents the abscissa of the data point; y represents the vertical coordinate of the data point, ymin is the lower limit of the value of the vertical coordinate of the data point, ymax is the upper limit of the value of the vertical coordinate of the data point; L is the width of the road surface; Couple the seepage physical field and the custom physical field and use them to calculate the subgrade moisture.

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