(1. School of Civil Engineering and Architecture, Central South University, Changsha, Hunan 4 10075.

2. Guizhou Provincial Traffic Planning Survey and Design Institute, Guiyang, Guizhou 55000 1)

As a medium coupling of soil and stone, soil-rock mixture has unique characteristics such as heterogeneity, discontinuity and difficulty in sample collection, which brings great difficulties to the research. Soil-rock mixture is a typical porous medium, and its permeability is closely related to particle size, void ratio and particle shape. The effects of gravel content, void ratio and particle shape on the permeability coefficient of different graded earth-rock mixtures are studied by indoor orthogonal test and self-made constant head permeameter. The influence order of three factors on the permeability coefficient of soil-rock mixture is determined by orthogonal test, and the significance level of each factor is determined. A formula for calculating the permeability coefficient of soil-rock mixture is put forward, and the correctness of the formula is verified by the test results, which provides a concise and useful calculation tool for the theoretical calculation of the permeability coefficient of soil-rock mixture.

Orthogonal test of permeability calculation formula of soil-rock mixture: porous medium

Earth-rock mixture is generally composed of gravel or block stone as aggregate and clay or sand as filler. It is a special geological body between soil and rock mass, and it is a medium coupling body of soil and stone [1]. Because of the unique characteristics of soil-rock mixture, such as the complexity of material composition, the irregularity of structural distribution and the difficulty of sample collection, it has brought great difficulties to the research, and the research on it is still in the exploratory stage [2]. Permeability, strength and deformation characteristics are the main mechanical properties to be studied in soil mechanics, which play an important role in various fields of civil engineering [3]. Soil-rock mixture is a typical heterogeneous porous medium [4], and its permeability is closely related to particle size, particle composition, void ratio and particle shape. The permeability coefficient of soil can be calculated by Darcy's theorem through laboratory tests, but it is difficult to determine the permeability coefficient of soil-rock mixture, mainly because: (1) sampling is difficult; It is difficult to carry out conventional penetration test; Large-scale penetration test not only has high cost and poor accuracy, but also has large dispersion of test results, so it is difficult to grasp its regularity. So far, there is no information about the permeability of soil-rock mixture in China. The existing research results are limited to the study of its deformation and mechanical characteristics through physical and numerical simulation tests, but the permeability has not been involved. Therefore, the formula for calculating the permeability coefficient of soil-rock mixture has important theoretical significance and engineering application value.

The influence of gravel content, void ratio (compactness) and particle shape on the permeability coefficient of earth-rock mixture at different levels is studied, the relationship between the three factors and the permeability coefficient of earth-rock mixture is found out, and the calculation formula of the permeability coefficient of earth-rock mixture is put forward.

Orthogonal test of permeability of 1 soil-rock mixture

1. 1 design of orthogonal test scheme

The effects of gravel content, void ratio (compactness) and particle shape on the permeability coefficient of soil-rock mixture are considered in the indoor test, and each factor considers three levels. For this experiment with three factors and three levels, if we consider the influence of different levels of each factor on the substrate, we can get 33 groups of experiments according to the combination, which wastes manpower, material resources and time, so it is more reasonable to study this problem with orthogonal experimental design. The orthogonal table chosen in this experiment is L9(34), which considers the influence of experimental errors, but does not consider the interaction between various factors (that is, assuming that they do not affect each other). * * * 9 groups of tests are required, with 3 parallel tests and 27 penetration tests in each group. See table 1 for the factors and corresponding grades used in this test, in which the coarse grain shape is divided into three grades: spherical, hexahedron and triangular pyramid, which are approximately replaced by pebbles, strong wind fossils and newly broken gravel respectively.

Table 1 orthogonal test factor level

Basic physical and mechanical properties of 1.2 sample

The soil sample used in the test is a typical soil-rock mixture at the exit of Qinglong Tunnel in Guizhou section of Shangrui Expressway under construction. See Table 2 and Figure 1 for the physical indexes and particle grading curves of soil in natural state. As can be seen from the figure 1, the inhomogeneity coefficient Cu of the soil sample retrieved from the site is 12.3 1, which indicates that there are many particle size series in the soil sample, and the coarse and fine particle sizes are quite different. The curvature coefficient Cc of particle grading curve is 1.59, and the grading is excellent.

Table 2 Basic physical indexes of natural soil

Figure 1 natural soil particle grading curve

Development of 1.3 large armor-piercing projectile

According to the Code for Geotechnical Test (SL 237- 1999), the indoor permeability coefficient of coarse-grained soil should be tested by constant-head permeameter, and the commonly used constant-head permeameter in China is Model 70. The inner diameter of the cylinder of Model 70 permeameter is 9.44 cm, and the maximum particle size of the test material is 2 cm. Specification [5] requires that the inner diameter of the cylinder should be 8 ~ 10 times of the maximum particle size. Therefore, the inner diameter of the cylinder of Model 70 permeameter is too small, so it is necessary to develop a large-size permeameter. The inner diameter and sample height of the self-made permeameter should be at least 8 times of the maximum particle size, that is, at least 16cm. In addition, considering the boundary effect, the upper and lower ends of the sample are increased by 2cm respectively, so the inner diameter and sample height of the self-made permeameter are 16cm and 20cm respectively. Considering the strong permeability of earth-rock mixture, the diameter of inlet and outlet pipes is 2cm. The self-made large constant head permeameter is shown in Figure 2 and Figure 3.

Fig. 2 Schematic diagram of constant head permeameter

The data unit is centimeters.

Fig. 3 Self-made permeameter

2 Analysis of test results

2. 1 test results

According to the arrangement of orthogonal test table L9(34), * * * needs to do 9 groups of tests, and each group of tests needs to be conducted in parallel for 3 times. Take the average value of three measurements and multiply it by the temperature correction coefficient to obtain the permeability coefficient of each group of tests at 20℃. See Table 3 for the measurement results of permeability coefficient.

Table 3 Determination Results of Permeability Test

sequential

2.2 test analysis

Using the intuitive analysis method and variance analysis method of orthogonal test, this paper analyzes the primary and secondary order of each factor's influence on the permeability coefficient of soil-rock mixture, draws the trend diagram of each factor's influence level, and finds out the significance level of each factor.

2.2. 1 intuitive analysis

Through orthogonal test, the range analysis of permeability coefficient of soil-rock mixture obtained from the test is carried out, and the horizontal influence trend diagram of each factor is drawn. The range analysis table of orthogonal test is shown in Table 4, and the relationship between three factors and permeability coefficient is shown in Figure 4.

Table 4 Scope Analysis Table

Fig. 4 Relationship between various factors and permeability coefficient

A- gravel content; B—— porosity ratio; Coarse particle shape

From the range analysis table of orthogonal test, it can be seen that the order of influence on the permeability coefficient of earth-rock mixture is A→B→C, that is, gravel content → void ratio → particle shape. It can be seen from the diagram of the relationship between various factors and permeability coefficient that the more gravel content, the greater void ratio, the greater permeability coefficient, the greater particle roundness and the smaller permeability coefficient. In subgrade engineering and dam engineering, the permeability coefficient needed by engineering can be obtained by adjusting the content, compactness and particle shape of coarse particles.

Variance analysis

In order to determine whether the difference of test results corresponding to different levels of factors is caused by different levels of factors or by test errors, and to give an accurate quantitative evaluation of the significance level of various factors affecting the permeability coefficient of soil-rock mixture, it is necessary to analyze the test data by variance analysis of orthogonal test, and the analysis results are shown in Table 5.

Table 5 Results of ANOVA

The results of variance analysis show that:

(1) The difference of test results corresponding to each level of factors is caused by different levels of factors, not by test errors;

(2) Gravel content has a very significant effect on the permeability coefficient of soil-rock mixture, and void ratio has a significant effect on the permeability coefficient of soil-rock mixture, but particle shape has no significant effect.

3 permeability coefficient of soil-rock mixture

3. 1 Relationship between permeability coefficient and gravel content

As we all know, the permeability coefficient of soil-rock mixture is related to particle size and gradation. In this paper, equivalent particle size d20 and curvature coefficient Cc are selected to represent the particle size and gradation of soil, because literature [3] thinks that equivalent particle size d20 can represent the particle size more accurately than other particle size characteristic coefficients, while the coefficients related to particle gradation are uneven coefficient Cu and curvature coefficient Cc, which only reflect the dispersion degree of soil particle composition, and curvature coefficient Cc can reflect the characteristics of particle composition curve to some extent. The grain grading curves of different gravel contents are shown in Figure 5. The grain size characteristic coefficient of each curve can be obtained from Figure 5, as shown in Table 6.

Fig. 5 Particle grading curve of samples

Table 6 Particle size characteristics of different coarse particle contents

It can be seen from Figure 6 that, under the same other conditions, the permeability coefficient k of soil-rock mixture has a linear relationship with the function f(d20, Cc), where,

Fig. 6 k20-f(d20, Cc) curve

3.2 Relationship between permeability coefficient and compactness

According to the analysis of variance of orthogonal test, the influence of porosity e on permeability coefficient is not as great as that of coarse particle content, but it is also very significant. Other conditions being the same, k has a linear relationship with, as shown in Figure 7.

Soil-rock mixture

3.3 Relationship between permeability coefficient and particle shape

In 1938, Tikell and Hiatt discussed the influence of "angularity" and "roundness" of particles on the permeability coefficient, and pointed out that the greater the angularity of particles, the greater the permeability coefficient [6]. According to the orthogonal test analysis table, CS1:CS2: CS3 = 0.9 ∶1:1.2, and the experimental data are regressed, and the results are related to the shape coefficient CS 1 = 0. 18, and CS 2 = 0.2.

3.4 Permeability coefficient of soil-rock mixture

From the above analysis, it can be seen that the permeability coefficient of soil-rock mixture is related to particle size, particle gradation, particle shape and void ratio, and osmotic fluid also has a certain influence on permeability, mainly due to the dynamic viscosity η of liquid. A large number of research results show that the permeability coefficient K is proportional to g/η [3,4,7]. Therefore, the formula for calculating the permeability coefficient of soil-rock mixture is

Soil-rock mixture

Where: k is the permeability coefficient of soil-rock mixture, cm/s; Cs is the shape coefficient of particles, m-3; D20 is equivalent particle size, and the soil weight less than this particle size accounts for 20% of the total soil weight, m; Cc is the curvature coefficient of particle gradation; E is porosity; G is the acceleration of gravity, 9.8n；; ; η is the dynamic viscosity of liquid, kPa s (10-6), η 20 =1.01×10-6 kpa s.

See Table 7 for the permeability coefficient k20 of earth-rock mixture calculated by formula (1) at 20℃. Compared with other physical and mechanical parameters, the variation range of permeability of soil-rock mixture is much larger. At the same time, influenced by the complexity of macro-structure and micro-structure, its permeability is extremely uneven [8]. In order to further verify the correctness of the formula (1), the measured value is compared with the calculated value obtained by the formula (1), as shown in Figure 8. It can be seen from Figure 8 that the permeability coefficient calculated by formula (1) is basically consistent with the measured value, and the average relative error of nine groups of samples is 2 1%, which is accurate enough for the permeability coefficient of soil-rock mixture with strong discreteness.

Table 7 Correspondence between calculated values and measured values

Fig. 8 Relationship between calculated value and measured value

4 conclusion

(1) Through orthogonal test, the primary and secondary order of the influence of gravel content, void ratio and particle shape on the permeability coefficient of earth-rock mixture is obtained, and the significance level of each factor is obtained. In engineering design, the permeability of soil-rock mixture can be controlled by reasonably adjusting the gravel content, void ratio (compactness) and particle shape.

(2) The permeability coefficient of soil-rock mixture is proportional to the function composed of equivalent particle size d20 and curvature coefficient Cc, and to the porosity ratio function.

(3) The formula for calculating the permeability coefficient of soil-rock mixture is put forward, and the correctness of the formula is verified by the test results, which provides a concise and useful calculation tool for quantitative prediction of the permeability coefficient of soil-rock mixture.

refer to

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Liu Jie. Seepage stability and seepage control of soil. Beijing: Water Conservancy and Electric Power Press, 1992: 1 ~ 20.

Physics of seepage in porous media. Beijing: Petroleum Industry Press,1984:141~173.

[5] People's Republic of China (PRC) and the Ministry of Water Resources. Code for geotechnical test (SL 237- 1999). Beijing: China Water Resources and Hydropower Press,1999:114 ~120.

[6] Tickell FG, Hiatt WN. Effect of particle angularity on porosity and permeability of unconsolidated sandstone. Announcement of AAPG,1938,22 (9):1272 ~1274

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