A method for predicting depth distribution of permeability coefficient of fly ash considering particle breakage effect

Abstract

The application discloses a kind of considering the deep distribution prediction method of gangue permeability coefficient of particle crushing effect, belong to geotechnical performance prediction technical field.The application carries out dynamic triaxial test to gangue sample, explores the dynamic evolution law of particle size distribution, crushing rate of gangue at different depth sites after different loading times.Meanwhile, through seepage erosion simulation test device, the gangue that is crushed after cyclic loading carries out permeation test, explores the critical hydraulic gradient of internal fine particle migration and structure damage of different size distribution gangue under seepage erosion, reveals its deterioration, damage mechanism, and with negative exponential continuous grading equation as pivot, constructs the prediction model of particle crushing index and permeability coefficient, reveals the internal mechanism of gangue subgrade particle crushing behavior and its permeation characteristic evolution under cyclic loading, so that the predicted permeability coefficient is more close to actual permeability coefficient, improves the precision of prediction.

Description

Technical Field

[0001] The present invention belongs to the technical field of rock and soil performance prediction, and in particular relates to a method for predicting the depth distribution of slag permeability coefficient taking into account particle crushing effect. Background Art

[0002] Slag is widely used as embankment fill due to its high strength, high compaction density, minimal settlement and deformation, strong permeability, high erosion resistance, and availability. Under cyclic vehicle loads, moderately to strongly weathered siliceous mudstone slag is susceptible to particle fragmentation. The resulting fine particles gradually fill the pores of the slag particles, redistributing the particle structure (pore channels and pore structure) within the roadbed, which in turn alters the permeability characteristics of the slag roadbed. The permeability characteristics of the roadbed are closely related to the internal water migration within it. Water accumulation can lead to subsidence or collapse, compromising the long-term stability of the roadbed.

[0003] In the existing technology, most of the research on the permeability mechanism of slag is based on experimentally obtained parameters such as water-soil characteristic curves, settlement deformation, and permeability coefficient. That is, the permeability coefficient of slag in the vertical or depth direction is regarded as a constant, and the internal mechanism of internal structural redistribution and spatiotemporal evolution of permeability characteristics caused by particle crushing is not considered. In addition, most of the existing technology conducts analysis on unit bodies, and rarely conducts research on the evolution of permeability characteristics at different locations of the overall roadbed structure. The roadbed is a structure with obvious layered characteristics. Due to different usage requirements, the requirements for the particle size, gradation, compaction degree, and moisture content of its filler are different in each layer. In addition, the confining pressure and cyclic dynamic stress at each point vary with depth, resulting in differences in the particle crushing situation inside the slag embankment and its corresponding permeability characteristics along the depth. The above two defects make the existing technology's prediction accuracy of the slag permeability coefficient insufficient and cannot truly reflect the permeability of the slag. Summary of the Invention

[0004] The present invention provides a method for predicting the depth distribution of slag permeability coefficient taking into account the particle crushing effect. It takes into account the influence of particle crushing effect and depth on the slag permeability coefficient, and can make the predicted permeability coefficient closer to the actual permeability coefficient, thereby improving the prediction accuracy, thereby solving at least one technical problem involved in the background technology.

[0005] In order to solve the above-mentioned technical problems, the present invention is achieved as follows:

[0006] A method for predicting the depth distribution of slag permeability coefficient considering particle crushing effect includes the following steps:

[0007] Step S1, preparing a slag sample, performing a triaxial test on the slag sample, screening the loaded slag sample to determine the percentage of slag samples with different particle sizes in the total weight of the slag sample, and drawing a gradation curve of the slag sample;

[0008] Step S2: Based on the shakedown theory, the gradation corresponding to the cumulative deformation convergence stage of the slag sample is defined as the final gradation, the area enclosed by the final gradation curve and the initial gradation curve is defined as the total crushing potential, the area enclosed by the final gradation curve and the initial gradation curve is defined as the potential crushing potential, and the ratio of the total crushing potential to the potential crushing potential is defined as the relative crushing potential. The relative crushing potential is used to characterize the crushing degree of the slag sample after loading;

[0009] Step S3, considering the effect of particle crushing on the porosity of the slag sample, the porosity of the slag sample under the current gradation is calculated by converting the volume change of the slag sample after loading, and fitting the relationship between the porosity under the current gradation and the relative crushing potential as the porosity expression;

[0010] Step S4, considering the effect of depth on the porosity of the slag sample, determining the stable porosity of the slag sample at different depths, fitting a relationship between the stable porosity and depth, and then substituting the relationship into the porosity expression to correct the porosity expression, wherein the stable porosity of the slag sample represents the porosity under the final gradation;

[0011] Step S5, substitute the porosity ratio expression corrected in step S4 into the Kozeny-Carman formula to construct a prediction model for the permeability coefficient of the slag. The prediction model takes the relative crushing potential and depth of the slag as input and outputs the distribution prediction results of the permeability coefficient of the slag at different depth points.

[0012] As a preferred improvement, the total crushing potential B t (N) and relative crushing potential B r *(N) represents:

[0013]

[0014] Where P(N) is the mass percentage of slag sample with particle size smaller than a certain value, which is obtained from the gradation curve; d maxN Indicates the maximum particle size of the slag sample under the current gradation; d max0 The maximum particle size of the slag sample under the initial gradation; d maxM Indicates the maximum particle size of the slag sample under the final gradation; a N 、b N represents the fitting parameters of the current gradation curve; a0 and b0 represent the fitting parameters of the initial gradation curve; a M 、b M Represents the fitting parameters of the final gradation curve.

[0015] As a preferred improvement, after the Nth loading, the porosity ratio ε of the slag sample is N Expressed as:

[0016]

[0017] Where V0 represents the initial volume of the slag sample; ΔV represents the volume change of the slag sample after the Nth loading, which is obtained by monitoring the displacement of the pressure chamber in the triaxial test; ε0 represents the initial porosity of the slag sample, where:

[0018]

[0019] Where, ρ dmax is the maximum dry density of the slag sample; G s is the relative density of the slag sample; ρ w is the water density; w opt is the optimal moisture content of the slag sample.

[0020] As a preferred improvement, the void ratio ε N and relative crushing potential B r *(N) is expressed as:

[0021]

[0022] Where, ε M represents the porosity ratio of the slag sample under the final gradation; β represents the material constant.

[0023] As a preferred improvement, the modified porosity ratio expression is expressed as:

[0024]

[0025] Where, ε M (0) represents the stable porosity of the site with a depth of 0 in the slag sample; h represents the depth of the site in the slag sample; ξ represents the fitting parameter.

[0026] As a preferred improvement, the prediction model is expressed as:

[0027]

[0028] Where, represents the permeability coefficient; It represents a constant related to the specific surface area of ​​slag and fluid properties; γ is the density of water; C is a constant; α is the dynamic viscosity of water; S0 is the specific surface area of ​​slag.

[0029] The beneficial effects of the present invention are:

[0030] (1) The present invention conducts dynamic triaxial tests on a certain slag, and explores the dynamic evolution of particle gradation and crushing rate of slag at different depths of the roadbed after different vibration loadings. At the same time, a permeability test is conducted on the slag crushed by cyclic loading through a seepage erosion simulation test device, and the critical hydraulic gradient of fine particle migration and structural damage in slag with different gradations under the action of seepage erosion is explored, revealing its degradation and destruction mechanism, and using the negative exponential continuous gradation equation as the hub, constructing a prediction model of particle crushing index and permeability coefficient, revealing the internal mechanism of the particle crushing behavior of slag roadbed under cyclic loading and the evolution of its permeability characteristics, making the predicted permeability coefficient closer to the actual permeability coefficient, and improving the accuracy of the prediction;

[0031] (2) The method for predicting the depth distribution of the permeability coefficient of slag proposed in the present invention has greatly improved the current situation of empirical and extensive calculation of the permeability coefficient of slag filling materials, and significantly enhanced the scientificity and reliability of the prediction of the permeability coefficient of slag filling materials under actual working conditions (vehicle cyclic load and rainwater erosion). It provides a reference for the stability assessment and long-term service performance improvement of slag roadbed / embankment in mountainous areas, which will help to further promote the resource utilization of slag and the high-quality development of roadbed construction in mountainous areas. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 Schematic diagram showing the loading method in triaxial test;

[0033] Figure 2 It represents the gradation curve of the slag sample under working conditions A1-A4;

[0034] Figure 3 It represents the gradation curve of the slag sample under working conditions B1-B4;

[0035] Figure 4 It represents the gradation curve of the slag sample under working conditions C1-C4;

[0036] Figure 5 Schematic diagram showing total crushing potential and relative crushing potential;

[0037] Figure 6 A graph showing the variation of total crushing potential with the number of cyclic loading;

[0038] Figure 7 A graph showing the change of relative crushing potential with the number of cyclic loading;

[0039] Figure 8 A graph showing the relationship between void ratio and relative crushing potential;

[0040] Figure 9 A graph showing the relationship between site depth and stable porosity ratio;

[0041] Figure 10 A schematic diagram showing the prediction model provided by this application;

[0042] Figure 11 A comparison chart showing the predicted values ​​and measured values ​​of different relative crushing potential prediction models. DETAILED DESCRIPTION

[0043] The following will be combined with the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the embodiments described are 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 making any creative efforts shall fall within the scope of protection of the present invention.

[0044] Please refer to Figures 1-11 The present invention provides a method for predicting the depth distribution of slag permeability coefficient taking into account the particle crushing effect, comprising the following steps:

[0045] Step S1, preparing a slag sample, performing a triaxial test on the slag sample, screening the loaded slag sample to determine the percentage of slag samples with different particle sizes in the total weight of the slag sample, and drawing a gradation curve of the slag sample.

[0046] Before the test begins, a slag sample must be prepared. The specific process is as follows: the slag is mixed at the optimal moisture content, allowed to stand and sealed for 24 hours, and then compacted in six layers to form the slag sample. The top surface of each layer is roughened before compaction, and the final layer is leveled. The relative density of the slag sample is controlled by controlling the mass and height of each layer. The compaction degree of all slag samples is controlled at around 95%.

[0047] The tests were conducted using a DYNTTS servo-controlled dynamic triaxial testing system developed by GDS (UK). The loading frequency range was 0-5 Hz, the axial load range was 0-10 kN, and the rated confining pressure was 0-2000 kPa. The slag specimens were 100 mm in diameter and 150 mm in height. The ratio of the slag specimen diameter to the maximum soil particle size was 6.67 (greater than 5), essentially eliminating size effects.

[0048] A total of 48 slag samples were prepared for the test. The slag samples were first isotropically consolidated to a set confining pressure value σ3, and then cyclic dynamic deviatoric stress σ d The unsaturated drainage cyclic load test was carried out. The first cycle of all slag samples was slow loaded with a frequency of 0.01 Hz to eliminate the irregularities of the upper and lower parts of the slag samples and thus eliminate the deformation of the slag samples in the initial stage. The test was loaded with a sinusoidal wave, such as Figure 1 shown.

[0049] The theoretical calculation process of confining pressure σ3 is as follows:

[0050] σ3=K0(σ0+γh);

[0051] Where K0 is the lateral earth pressure coefficient, which can be calculated as K0 = μ / (1-μ), μ is the Poisson's ratio, and its value range is 0.2 to 0.45; σ0 is the cover weight of the asphalt surface layer and the water-stabilized macadam base layer, the thickness of the asphalt surface layer is 0.12 to 0.32 m, and the value is 23.3 to 24.6 kN / m 3 The thickness of the water-stable crushed stone base is 0.44~0.77m, and the weight is 22~25kN / m 3 ), γ is the average bulk density of the slag, and h is the depth from the top of the roadbed. The greater the confining pressure σ3, the more obvious the particle crushing. To achieve obvious crushing, the most unfavorable load value that maximizes σ3 is selected, namely: μ is 0.45; the asphalt surface layer thickness is 0.32m, and the gravity is 24.6kN / m 3 The thickness of the water-stabilized gravel layer is 0.77m, and the weight is 25kN / m 3 .

[0052] Combine the theoretical calculation formula of confining pressure σ3 and the empirical value to set the confining pressure σ3 value selected for loading, and set the cyclic dynamic deviator stress σ according to the empirical value. d The value of the roadbed frequency is generally 0.1 to 10 Hz, so the loading frequency is proposed to be 5 Hz. d , confining pressure σ3 and number of cyclic loading N are divided into 12 groups of working conditions, and the loading plan is shown in Table 1.

[0053] Table 1 Loading schedule

[0054]

[0055]

[0056] After loading, thoroughly mix the four parallel slag samples from each working condition. The slag samples are then spread into a thin layer and air-dried for 1–2 days to evaporate the moisture in the soil. After air-drying, the soil lumps are poured into a magnetic bowl and ground with a rubber-tipped pestle with appropriate force until the lumps are separated into individual particles. Finally, all slag samples are sieved on a vibrating screen. The pass rate of the slag samples at each sieve size is calculated. This pass rate represents the percentage of slag samples of different particle sizes relative to the total weight of the slag samples. Finally, a coordinate system is constructed, with the abscissa representing particle size and the ordinate representing the mass percentage of soil below a certain particle size. The measured data sets are plotted in the coordinate system, and each point is connected sequentially to form a gradation curve. The gradation curve is then fitted using a negative exponential continuous gradation equation to smooth the curve.

[0057] Under different loading conditions, the particle gradation curve of the crushed slag material changes as shown below: Figure 2-Figure 4 As shown in the figure, based on the grading curve, the negative exponential continuous grading equation under different cycle numbers N is established, which is expressed as:

[0058]

[0059] Where P(N) is the mass percentage of slag sample with particle size smaller than a certain value; d is the particle size; d max Maximum particle size; a N 、b N are the fitting parameters that control the shape and slope of the curve respectively.

[0060] Depend on Figure 2-Figure 4 It can be seen that the particle size distribution P(N) under a certain loading number N can be obtained by a unique array (d max , a N , b N ) is determined. Under different vibration times, the fitting determination coefficient R of the particle size distribution of the slag sample under each working condition is 2 All of them are greater than 0.9, which meets the requirements of fitting accuracy. Therefore, within a reasonable error range, the particle gradation characteristics of the slag sample under various loading conditions can be determined by fitting the negative exponential gradation equation.

[0061] Step S2, based on the stability theory, the gradation corresponding to the cumulative deformation convergence stage of the slag sample is defined as the final gradation, the area enclosed by the final gradation curve and the initial gradation curve is defined as the total crushing potential, the area enclosed by the final gradation curve and the initial grading curve is defined as the potential crushing potential, the ratio of the total crushing potential to the potential crushing potential is defined as the relative crushing potential, and the relative crushing potential is used to characterize the degree of crushing of the slag sample after loading.

[0062] Total crushing potential B t (N) and relative crushing potential B r *(N) represents:

[0063]

[0064] Where, d maxN Indicates the maximum particle size of the slag sample under the current gradation curve; d max0 The maximum particle size of the slag sample under the initial gradation curve; d maxM Indicates the maximum particle size of the slag sample under the final gradation curve; a N 、b N represents the fitting parameters of the current gradation curve; a0 and b0 represent the fitting parameters of the initial gradation curve; a M 、b M Represents the fitting parameters of the final gradation curve.

[0065] The total crushing potential and potential crushing potential are expressed as follows: Figure 5As shown. According to the total crushing potential B t (N) and relative crushing potential B t *(N) expression plots B t (N)-N and B r *(N)-N curve, such as Figure 6-Figure 7 As shown. Figure 6 and Figure 7 It can be seen that the total crushing potential B t (N), relative crushing potential B r *(N) growth rate decreases with the number of cycles N. In this embodiment, the gradation corresponding to N=20000 is taken as the final gradation, and the total crushing potential B t (N), relative crushing potential B r *(N) did not converge at N=20000, and continued to increase. r *(N) is slightly larger than that of the deep site, and increases with the depth and the number of cyclic loading. r *(N)The difference is narrowing.

[0066] Step S3, considering the effect of particle crushing on the porosity of the slag sample, the volume change of the slag sample after loading is converted to obtain the porosity of the slag sample under the current grading, and the relationship between the porosity under the current grading and the relative crushing potential is fitted as the porosity expression.

[0067] During cyclic loading, the crushing of slag particles leads to a decrease in the porosity ratio. This is because the crushing process produces more small particles that can fill the larger pores, and the compaction effect during the crushing process further reduces the pore space.

[0068] The calculation process of the initial porosity ratio ε0 of the slag sample is as follows:

[0069]

[0070] Where, ρ dmax is the maximum dry density of the slag sample; G s is the relative density of the slag sample; ρ w is the water density; w opt is the optimal moisture content of the slag sample.

[0071] The porosity ratio ε of the slag sample loaded for the Nth time N The conversion is based on the volume change of the slag sample, which is monitored by the displacement of the triaxial pressure chamber. N The calculation process is as follows:

[0072]

[0073] Where V0 represents the initial volume of the slag sample; ΔV represents the volume change of the slag sample.

[0074] (B r *(N), ε N ) The data points are marked in the coordinate system, and multiple groups of data points are fitted to obtain ε N -B r *(N) relationship curve, such as Figure 8 As shown. Figure 8 It can be seen that during the initial cyclic loading process, the void ratio ε decreases significantly, and the relative crushing potential B r * Increased significantly; During the mid-cycle loading process, the void ratio ε continued to decrease, but the rate of decrease gradually decreased, and the relative crushing potential B r * Rapidly increase; in the later cyclic loading process, the porosity ratio ε tends to be stable, and the relative crushing potential B r * also tends to be stable. Based on the above rules, the porosity ratio ε is obtained N The expression:

[0075]

[0076] Where, ε M represents the stable porosity, i.e. the porosity under the final gradation, and β represents the material constant, with a value range of 0.0652 to 0.1283. N -B r *(N) Relationship fitting determination coefficient R 2 When it exceeds 0.9, the fitting accuracy requirement is met.

[0077] Step S4, considering the influence of depth on the porosity of the slag sample, determines the stable porosity of the slag sample at different depths, fits the relationship between the stable porosity and depth, and then substitutes it into the porosity expression to correct the porosity expression, wherein the stable porosity of the slag sample represents the porosity under the final grading.

[0078] In actual engineering applications, the stable void ratio ε of the corresponding specimens at different locations of the embankment under cyclic loading is M and external loads (confining pressure σ3, cyclic dynamic deviatoric stress σ d ) is closely related to the distribution of confining pressure σ3 and cyclic dynamic deviatoric stress σ d The attenuation is a function of the depth h, and the fitting curve is as follows Figure 9 As shown. Then the distribution relationship of stable porosity along depth can be constructed, which is expressed as:

[0079] ε M (h)=ε M (0)·exp(ξh);

[0080] Where, εM (h) represents the stable porosity ratio of the site at depth h in the slag sample; ε M (0) represents the stable porosity at the site with a depth of 0 in the slag sample; ξ represents the fitting parameter.

[0081] ε M Substitute (h) into the porosity ratio expression to obtain the corrected porosity ratio expression:

[0082]

[0083] Step S5, substitute the porosity ratio expression corrected in step S4 into the Kozeny-Carman formula to construct a prediction model for the permeability coefficient of the slag. The prediction model takes the relative crushing potential and depth of the slag as input and outputs the distribution prediction results of the permeability coefficient of the slag at different depth points.

[0084] The original expression of the Kozeny-Carman formula is as follows:

[0085]

[0086] Where K is the permeability coefficient of the slag; γ is the density of water; C is a constant; α is the dynamic viscosity of water; S0 is the specific surface area of ​​the slag (cm 2 / cm 3 ); n is the porosity of the slag sample;

[0087] The above formula shows that when other factors affecting the permeability coefficient remain unchanged, K and n 3 / (1-n) 2 There is a linear relationship between the porosity n and the porosity ratio ε N The following relationship is satisfied:

[0088]

[0089] The permeability coefficient K can be converted into the following formula:

[0090]

[0091] Where, It represents a constant related to the specific surface area of ​​slag and fluid properties, with a value ranging from 0.67412 to 0.71984.

[0092] The constructed prediction model is expressed as:

[0093]

[0094] In this embodiment, A = 0.68101, ξ = 0.41543, β = 0.10723, and the function graph of the prediction model is as follows: Figure 10As shown. The depth h is 0.0m, 0.5m, 1.0m, different relative crushing potential B r *Comparison between model predictions and measured values ​​is as follows Figure 11 As shown in the figure, the relative error between the two is 2.29% to 33.83%. The predicted value and the measured value are in the same order of magnitude, and the relative error is less than 35%. Therefore, the prediction model K[B r *(N),h] has good applicability.

[0095] The embodiments of the present invention are described above in conjunction with the accompanying drawings, but the present invention is not limited to the above-mentioned specific implementation methods. The above-mentioned specific implementation methods are merely illustrative and not restrictive. Under the guidance of the present invention, ordinary technicians in this field can also make many forms without departing from the scope of protection of the present invention and the claims, all of which are protected by the present invention.

Claims

1. A method for predicting the depth distribution of slag permeability coefficient considering particle crushing effect, characterized in that: The steps include: Step S1, preparing a slag sample, performing a triaxial test on the slag sample, screening the loaded slag sample to determine the percentage of slag samples with different particle sizes in the total weight of the slag sample, and drawing a gradation curve of the slag sample; Step S2: Based on the shakedown theory, the gradation corresponding to the cumulative deformation convergence stage of the slag sample is defined as the final gradation, the area enclosed by the final gradation curve and the initial gradation curve is defined as the total crushing potential, the area enclosed by the final gradation curve and the initial gradation curve is defined as the potential crushing potential, and the ratio of the total crushing potential to the potential crushing potential is defined as the relative crushing potential. The relative crushing potential is used to characterize the crushing degree of the slag sample after loading; Step S3, considering the effect of particle crushing on the porosity of the slag sample, the porosity of the slag sample under the current gradation is calculated by converting the volume change of the slag sample after loading, and fitting the relationship between the porosity under the current gradation and the relative crushing potential as the porosity expression; Step S4, considering the effect of depth on the porosity of the slag sample, determining the stable porosity of the slag sample at different depths, fitting a relationship between the stable porosity and depth, and then substituting the relationship into the porosity expression to correct the porosity expression, wherein the stable porosity of the slag sample represents the porosity under the final gradation; Step S5, substituting the porosity ratio expression corrected in step S4 into the Kozeny-Carman formula to construct a prediction model for the permeability coefficient of the slag, wherein the prediction model takes the relative crushing potential and depth of the slag as input and outputs a distribution prediction result of the permeability coefficient of the slag at different depths; The prediction model is expressed as: ； Where, represents the permeability coefficient; B r * ( N ) indicates relative crushing potential; h Indicates the depth of the point in the slag sample; , represents a constant related to the specific surface area of ​​slag and fluid properties; γ is the weight of water; C is a constant; α is the dynamic viscosity of water; S 0 is the specific surface area of ​​slag; Indicates the N After the first loading, the porosity ratio of the slag sample; represents the initial porosity of the slag sample; It represents the stable porosity ratio of the site with a depth of 0 in the slag sample; represents the fitting parameters; Represents the material constant.

2. The method for predicting the depth distribution of slag permeability coefficient considering particle crushing effect according to claim 1 is characterized in that: Total crushing potential B t ( N ) and relative crushing potential B r * ( N ) are respectively expressed as: ； ； Where, P ( N ) is the mass percentage of slag sample with particle size smaller than a certain size, obtained through the gradation curve; It indicates the maximum particle size of the slag sample under the current gradation; The maximum particle size of the slag sample under the initial gradation; Indicates the maximum particle size of the slag sample under the final gradation; Indicates the fitting parameters of the current gradation curve; represents the fitting parameters of the initial grading curve; Represents the fitting parameters of the final gradation curve.

3. The method for predicting the depth distribution of slag permeability coefficient considering particle crushing effect according to claim 2 is characterized in that: No. N After the first loading, the porosity ratio of the slag sample is Expressed as: ； Where, Indicates the initial volume of the slag sample; Indicates the N The volume change of the slag sample after the first loading is obtained by monitoring the displacement of the pressure chamber outside the triaxial test; ； Where, is the maximum dry density of the slag sample; is the relative density of the slag sample; is the water density; is the optimal moisture content of the slag sample.

4. The method for predicting the depth distribution of slag permeability coefficient considering particle crushing effect according to claim 3 is characterized in that: Porosity Relative crushing potential B r * ( N ) is expressed as: ； Where, It represents the porosity ratio of the slag sample under the final gradation.

5. The method for predicting the depth distribution of slag permeability coefficient considering particle crushing effect according to claim 4 is characterized in that: The corrected porosity ratio expression is expressed as: 。

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