A prediction method based on maximum shear modulus of soil intergranular stress

Abstract

This invention relates to the field of soil testing technology, specifically to a method for predicting the maximum shear modulus of soil based on intergranular stress. The method first conducts pressure plate tests on soil samples to obtain soil-water characteristic curves; then, it fits the soil-water characteristic data of the samples using a VG model to obtain the matrix suction of the samples at different saturations; based on the concept of true pore pressure, it establishes a method for calculating intergranular stress of soil considering physicochemical effects, obtaining the variation law of intergranular stress with saturation during the soil dehydration process; and based on the test results of the maximum shear modulus during the soil dehydration process, it constructs a quantitative characterization and prediction method for the maximum shear modulus based on intergranular stress. This invention achieves quantitative characterization and prediction of the variation law of the maximum shear modulus during the soil dehydration process through conventional pressure plate tests and theoretical analysis.

Description

Technical Field

[0001] This invention relates to the field of soil testing technology, and specifically to a method for predicting the maximum shear modulus based on intergranular stress in soil. Background Technology

[0002] The maximum shear modulus of soil is a crucial parameter for accurately assessing soil deformation characteristics. In arid or semi-arid regions, relative humidity significantly impacts soil mechanical properties. Soil deformation under environmental influences alone is inseparable from the interaction of intergranular stresses within the soil itself, and the variation of intergranular stresses is directly reflected in the maximum shear modulus. The relationship between the maximum shear modulus of soil and its intergranular stresses is currently unclear, and the testing of the maximum shear modulus typically relies on high-end equipment, such as resonant columns and bending elements. Resonant column equipment is complex, difficult to operate, and the test results are severely limited by the equipment. While bending elements are simple to operate, the methods for accurately obtaining the shear wave arrival time are inconsistent, and high-end waveform generators, filters, and oscilloscopes are required to ensure the accuracy of the test results.

[0003] The deformation of soil under varying environmental humidity is not only closely related to the maximum shear modulus, but also directly related to the interparticle stress within the soil itself during the deformation process. By obtaining the variation law of interparticle stress during the soil dehumidification process through theoretical analysis and laboratory experiments, and predicting the maximum shear modulus of soil based on interparticle stress, it is inevitable that the limitations of complex testing equipment on the maximum shear modulus test can be avoided. If the maximum shear modulus of soil can be predicted using only conventional tests and theoretical models, it will help to quickly obtain the maximum shear modulus and empower the design and construction of geotechnical engineering related problems. Summary of the Invention

[0004] To address the aforementioned technical problems, the present invention aims to provide a method for predicting the maximum shear modulus of soil based on intergranular stress. The specific technical solution adopted is as follows: Pressure plate test was conducted on soil samples to obtain soil-water characteristic curves of the samples; The soil-water property data of the samples were fitted based on the VG model to obtain the matrix suction of the samples under different saturation levels. Based on the concept of real pore pressure, a method for calculating interparticle stress in soil considering physicochemical effects is established to obtain the variation law of interparticle stress with saturation during soil desaturation process. Based on the test results of the maximum shear modulus during the soil dehydration process, a quantitative characterization and prediction method for the maximum shear modulus based on intergranular stress is constructed.

[0005] Furthermore, obtaining the matrix suction of samples at different saturations includes: The water retention properties of the samples were tested to obtain the variation of matrix suction with saturation. The formula for calculating the matrix suction is: ; in, For matrix suction; Saturation; and These are the fitting parameters.

[0006] Furthermore, the formula for calculating the actual pore pressure is as follows: ; in, This represents the actual pore pressure. To balance the solution pressure; It refers to generalized osmotic pressure; Generalized osmotic pressure is caused by the physicochemical interactions between soil particles and pores, including: Donnan osmotic pressure, capillary and adsorption pressure, expressed as: ; in, The mass density of pure water is taken as 1 g / m3 under standard atmospheric pressure; The Donnan osmotic pressure is expressed as: ; Where R is the universal gas constant; The molar mass of water; To balance the mole fraction of water in the solution; This represents the mole fraction of water in the pore solution of the soil. This refers to the surface energy potential, which is related to the surface forces caused by the interaction between soil and water. It is temperature T and liquid volume fraction The constructed function, namely: (5) in, This represents the volume fraction of pore water when the soil is saturated. The pore solution mass density; The density of pure water is approximately equal to that of the pore solution when the pore solution is dilute. The matrix suction is the air pressure. With equilibrium solution pressure The difference, if known Then it can be determined by the soil-water characteristic curve. .

[0007] Furthermore, the formula for calculating the intergranular stress of the soil is as follows: (6) in, It is the intergranular stress tensor; 1 represents the total stress tensor; 1 represents the unit tensor. To account for capillary, adsorption, and Donnan effect stress absorption; when the soil sample is fully saturated, , ; The pore solution mass density; It represents the liquid volume fraction; For matrix suction; Therefore, the formula for calculating intergranular stress in soil can be transformed into: (7) in, Porosity; To balance the solution pressure; It refers to generalized osmotic pressure; For effective stress tensor; From formula (7), the expression for intergranular stress during soil shrinkage can be obtained as follows: (8) When the sample is saturated with pure water, neglecting the influence of inherent salt ions in the soil pores, the Donnan osmotic pressure... Let the initial surface potential be... Based on the relationship between saturation and liquid volume fraction ; The surface potential under different saturation levels can be expressed by formula (5): (9) in, ε represents saturation; e represents void ratio. (10) This leads to the functional relationship between intergranular stress and saturation: (11); in, Mass density of pure water; For temperature.

[0008] Furthermore, the quantitative characterization and prediction method for the maximum shear modulus based on intergranular stress is as follows: (12) in, Maximum shear modulus; This represents the maximum shear modulus of the tested soil sample. This represents the maximum shear modulus corresponding to the soil air intake value. The initial void ratio; Standard atmospheric pressure; This is the intergranular stress tensor.

[0009] The embodiments of the present invention have at least the following beneficial effects: This invention obtains matrix suction at different saturation levels through conventional pressure plate tests and VG models. It then uses theoretical analysis to calculate interparticle stress during the dehydration process and proposes a quantitative characterization and prediction model for the maximum shear modulus based on interparticle stress. This model establishes the correspondence between interparticle stress and the maximum shear modulus during soil dehydration, enabling quantitative characterization and prediction of the variation law of the maximum shear modulus during soil dehydration using only conventional pressure plate tests and theoretical analysis. This avoids the drawbacks of existing equipment, such as complex operation and high cost, in obtaining the maximum shear modulus of soil. This model is applicable to fine-grained soils such as cohesive soils and silt, and is of great significance for analyzing the deformation mechanism of soil caused by environmental humidity. Attached Figure Description

[0010] To more clearly illustrate the technical solutions and advantages in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0011] Figure 1 This is a flowchart of a method for predicting the maximum shear modulus of soil based on intergranular stress, provided in one embodiment of the present invention. Figure 2 This is a schematic diagram of the soil-water characteristic curve of sample 1 provided in an embodiment of the present invention; Figure 3 This is a schematic diagram of the soil-water characteristic curve of sample 2 provided in an embodiment of the present invention; Figure 4 This is a schematic diagram of the soil-water characteristic curve of sample 3 provided in an embodiment of the present invention; Figure 5 This is a schematic diagram illustrating the variation of intergranular stress and maximum shear modulus with saturation for three types of soil samples provided in an embodiment of the present invention. Figure 6 This is a schematic diagram showing the fitting results of the prediction model and experimental data for sample 1 provided in one embodiment of the present invention; Figure 7 This is a schematic diagram showing the fitting results between the prediction model and experimental data for sample 2 provided in one embodiment of the present invention; Figure 8 This is a schematic diagram showing the fitting results of the prediction model and experimental data for sample 3 provided in an embodiment of the present invention. Detailed Implementation

[0012] To further illustrate the technical means and effects adopted by the present invention to achieve its intended purpose, the following, in conjunction with the accompanying drawings and preferred embodiments, details the specific implementation, structure, features, and effects of a method for predicting the maximum shear modulus based on intergranular stress in soil according to the present invention. In the following description, different "one embodiment" or "another embodiment" do not necessarily refer to the same embodiment. Furthermore, specific features, structures, or characteristics in one or more embodiments can be combined in any suitable form.

[0013] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0014] The following description, in conjunction with the accompanying drawings, details a specific scheme for predicting the maximum shear modulus of soil based on intergranular stress, provided by this invention.

[0015] Please see Figure 1 The diagram illustrates a flowchart of a method for predicting the maximum shear modulus of soil based on intergranular stress, provided by an embodiment of the present invention. The method includes the following steps: Step S100: Conduct a pressure plate test on the soil sample to obtain the soil-water characteristic curve of the sample.

[0016] First, conduct soil-water characteristic curve tests: 1. Sample preparation: Test the initial moisture content ω0 of the sample, given the dry density ρ. d The compacted sample was prepared by calculating the soil mass based on the size of the ring cutter. The remolded compacted sample was 20 mm high and 45 mm in diameter, and the static compaction method was used for sample preparation.

[0017] 2. The prepared compacted sample and the clay slab are placed in a vacuum cylinder and vacuumed for 10 hours. Then distilled water is added to completely immerse the soil sample, and vacuuming continues for another 20 hours to saturate the soil sample.

[0018] 3. For the soil-water characteristic test of the sample using a pressure plate apparatus, after weighing the saturated sample, place it on the saturated clay plate in the pressure plate apparatus. In order to ensure the continuity of the dehydration process of the sample in the pressure plate apparatus, it is necessary to ensure good contact between the ring sample and the clay plate. Different suction paths are given to obtain the soil-water characteristic curve of the sample dehydration process.

[0019] 4. The pressure plate apparatus regulates the matrix suction by controlling the air pressure. When a predetermined matrix suction is applied, the pressure chamber is sealed, and the mass of the specific gravity bottle connected to the clay plate is weighed to determine whether the soil sample has reached equilibrium under that level of suction.

[0020] 5. After the pressure plate instrument has stabilized at each stage of drainage and the suction has reached equilibrium, open the pressure chamber, take out the sample, and weigh it. Use this information to calculate the saturation of the soil under different matrix suction.

[0021] 6. After weighing, immediately put the sample back into the pressure chamber, seal it, and apply the next level of suction. When the suction is less than 500 kPa, use a clay plate with an intake value of 500 kPa; when the suction is greater than 500 kPa, use a clay plate with a suction of 1.5 MPa.

[0022] Please see Figures 2-4 , Figure 2 This is a schematic diagram of the soil-water characteristic curve of sample 1; Figure 3 This is a schematic diagram of the soil-water characteristic curve of sample 2; Figure 4 This is a schematic diagram of the soil-water characteristic curve of sample 3; Figures 2-4 middle and R² is the correlation coefficient in the fitting result. When the correlation coefficient is equal to 1, it means that the fit is complete. The closer the correlation coefficient is to 1, the better the fitting effect is. Sample 1 is Sanmenxia clay; Sample 2 is Denver claystone; Sample 3 is Zhengzhou silt.

[0023] Step S200: Fit the soil-water property data of the sample based on the VG model to obtain the matrix suction of the sample under different saturation levels.

[0024] Water retention capacity tests were conducted on the samples to obtain the variation of matrix suction with saturation. The main desiccation curve was obtained by fitting the Van Genuchten model (VG model). The functional relationship between saturation and matrix suction in the VG model is as follows: (1) in, For matrix suction; Saturation; and These are the fitting parameters. In this embodiment of the invention, the fitting parameters are obtained by fitting experimental data, specifically by fitting the matrix suction and saturation as experimental data.

[0025] Step S300: Based on the concept of real pore pressure, establish a method for calculating interparticle stress in soil that considers physicochemical effects, and obtain the variation law of interparticle stress with saturation during soil desaturation process.

[0026] To calculate pore water pressure, connect a unit soil mass to a container already filled with a certain solution. The entire system is in thermal equilibrium. The pressure of the solution in the container is then defined as the equilibrium solution pressure of the soil. The equilibrium solution is a solution that is not affected by the pore medium, is connected to the pore solution, and has the same physical quantities as the pore solution, such as concentration, pressure, composition, and temperature.

[0027] The actual pore pressure in the soil can be expressed as: (2) in, This represents the actual pore pressure. To balance the solution pressure; It refers to generalized osmotic pressure; Generalized osmotic pressure is caused by the physicochemical interactions between soil particles and pores, including: Donnan osmotic pressure, capillary and adsorption pressure, expressed as: (3) in, The mass density of pure water is taken as 1 g / m3 under standard atmospheric pressure; The Donnan osmotic pressure is expressed as: (4) Where R is the universal gas constant; The molar mass of water; To balance the mole fraction of water in the solution; This represents the mole fraction of water in the pore solution of the soil. This refers to the surface energy potential, which is related to the surface forces caused by the interaction between soil and water. It is temperature T and liquid volume fraction The constructed function, namely: (5) in, This represents the volume fraction of pore water when the soil is saturated. The pore solution mass density; The density of pure water is given by the formula. When the pore solution is a dilute solution, the density of the pore solution and the density of pure water are approximately equal. The matrix suction is the air pressure. With equilibrium solution pressure The difference, if known Then it can be determined by the soil-water characteristic curve. .

[0028] Based on the concept of true pore pressure, a formula for calculating interparticle stress in unsaturated soil that considers physicochemical effects can be established as follows: (6) in, It is the intergranular stress tensor; 1 represents the total stress tensor; 1 represents the unit tensor, meaning that all components of the tensor are equal to 1. To account for capillary, adsorption, and Donnan effect stress absorption; when the soil sample is fully saturated, , ; The pore solution mass density; It represents the liquid volume fraction; For matrix suction; Therefore, the formula for calculating intergranular stress in soil can be transformed into: (7) in, Porosity; To balance the solution pressure; It refers to generalized osmotic pressure; For effective stress tensor; The shrinkage test process only controlled the relative humidity of the environmental chamber to dehydrate and deform the soil sample, without applying any other external loads. From formula (7), the expression for the interparticle stress during the soil sample shrinkage process can be obtained as follows: (8) When the sample is saturated with pure water, if the influence of inherent salt ions in the soil within the pores is ignored, the Donnan osmotic pressure... Assume the initial surface potential is Based on the relationship between saturation and liquid volume fraction, i.e. ; The surface potential under different saturation levels can be expressed by formula (5): (9) in, ε represents saturation; e represents void ratio. (10) This leads to the functional relationship between intergranular stress and saturation: (11).

[0029] in, Mass density of pure water; For temperature.

[0030] Please see Figure 5 , Figure 5 A schematic diagram showing the variation of intergranular stress and maximum shear modulus with saturation for three types of soil samples is presented. The three soil samples... The effect of intergranular stress on the change of saturation degree is significant.

[0031] Step S400: Based on the test results of the maximum shear modulus during the soil dehydration process, construct a quantitative characterization and prediction method for the maximum shear modulus based on intergranular stress.

[0032] The change in stress state of soil due to variations in water content has a significant impact on low-stress stiffness. To more accurately predict the effect of intergranular stress on the maximum shear modulus... Based on experimental data and theoretical models, an empirical formula is proposed to quantitatively describe the relationship between the two factors: (12) in, Maximum shear modulus; This represents the maximum shear modulus of the tested soil sample. This represents the maximum shear modulus corresponding to the soil air intake value. The initial void ratio; Standard atmospheric pressure; This is the intergranular stress tensor.

[0033] Please see Figures 6-8 , Figure 6 A schematic diagram showing the fitting results between the prediction model and the experimental data for sample 1 is provided; Figure 7 A schematic diagram showing the fitting results between the prediction model and the experimental data for sample 2 is provided; Figure 8 A schematic diagram showing the fitting results between the prediction model and the experimental data for sample 3 is provided.

[0034] The measured data points showed good agreement with the model predictions, with correlation coefficients all greater than 0.98. Due to the influence of adsorption terms in the intergranular stress during the residual stage, the model's prediction of small-strain shear modulus is relatively reliable at low moisture content.

[0035] It should be noted that the order of the above embodiments of the present invention is merely for descriptive purposes and does not represent the superiority or inferiority of the embodiments. The processes depicted in the accompanying drawings do not necessarily require a specific or sequential order to achieve the desired result. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0036] The various embodiments in this specification are described in a progressive manner. The same or similar parts between the various embodiments can be referred to each other. Each embodiment focuses on describing the differences from other embodiments.

Claims

1. A prediction method based on the maximum shear modulus of intergranular stress of soil mass, characterized in that, The method includes the following steps: Pressure plate test was conducted on soil samples to obtain soil-water characteristic curves of the samples; The soil-water property data of the samples were fitted based on the VG model to obtain the matrix suction of the samples under different saturation levels. Based on the concept of real pore pressure, a method for calculating interparticle stress in soil considering physicochemical effects is established to obtain the variation law of interparticle stress with saturation during soil desaturation process. Based on the test results of the maximum shear modulus during the soil dehydration process, a quantitative characterization and prediction method for the maximum shear modulus based on intergranular stress is constructed. The formula for calculating the actual pore pressure is as follows: ； wherein, is the true pore pressure; is the balanced solution pressure; is the generalized osmotic pressure; Generalized osmotic pressure is caused by the physicochemical interactions between soil particles and pores, including: Donnan osmotic pressure, capillary and adsorption pressure, expressed as: ； wherein Pure water mass density, taken as 1 g / m3 at standard atmospheric pressure; is the Donnan osmotic pressure, expressed by the formula: ； where R is the universal gas constant; is the molar mass of water; is the mole fraction of water in the bulk solution; is the mole fraction of water in the soil pore solution; is the surface energy potential, which is related to the surface forces induced by the soil-water interaction, is the temperature T and the liquid volume fraction is the constructed function, i.e.: （5） in, This represents the volume fraction of pore water when the soil is saturated. The pore solution mass density; The density of pure water is approximately equal to that of the pore solution when the pore solution is dilute. The matrix suction is the air pressure. With equilibrium solution pressure The difference, if known Then it can be determined from the soil-water characteristic curve. ; The formula for calculating the interparticle stress in the soil is as follows: (6) in, It is the intergranular stress tensor; 1 represents the total stress tensor; 1 represents the unit tensor. To account for capillary, adsorption, and Donnan effect stress absorption; when the soil sample is fully saturated, , ; The pore solution mass density; It represents the liquid volume fraction; For matrix suction; Therefore, the formula for calculating intergranular stress in soil can be transformed into: （7） in, Porosity; To balance the solution pressure; It refers to generalized osmotic pressure; For effective stress tensor; From formula (7), the expression for intergranular stress during soil shrinkage can be obtained as follows: （8） When the sample is saturated with pure water, neglecting the influence of inherent salt ions in the soil pores, the Donnan osmotic pressure... Let the initial surface potential be... Based on the relationship between saturation and liquid volume fraction ; The surface potential under different saturation levels can be expressed by formula (5): (9) in, ε represents saturation; e represents void ratio. (10) This leads to the functional relationship between intergranular stress and saturation: (11)； in, Mass density of pure water; For temperature; The quantitative characterization and prediction method for the maximum shear modulus based on intergranular stress is as follows: （12） in, Maximum shear modulus; This represents the maximum shear modulus of the tested soil sample. This represents the maximum shear modulus corresponding to the soil air intake value. The initial void ratio; Standard atmospheric pressure; This is the intergranular stress tensor.

2. The method for predicting the maximum shear modulus of soil based on intergranular stress according to claim 1, characterized in that, The method of obtaining the matrix suction of samples at different saturations includes: The water retention properties of the samples were tested to obtain the variation of matrix suction with saturation. The formula for calculating the matrix suction is: ; in, For matrix suction; Saturation; and These are the fitting parameters.

Images