Method for determining shear strength parameter under consideration of earthquake action

Abstract

The invention discloses a shear strength parameter determination method considering earthquake action, which comprises the following steps: collecting a soil sample of a research area, air-drying, dispersing the soil sample into single particles, and sieving to obtain the stone content of the soil sample; the method comprises the following steps: preparing a compacted cylindrical sample from a soil sample, and placing the compacted cylindrical sample in a triaxial testing machine for a triaxial test to obtain static strength parameters of the soil sample; collecting seismic magnitude data of the research area, and determining the seismic magnitude of the research area; and according to the stone content, the static strength parameter and the earthquake magnitude, calculating the shear strength parameter of the research area under the earthquake action by adopting a shear strength damage cracking model. Based on PFC numerical simulation software, dynamic triaxial numerical simulation of the accumulation body is carried out and compared with an indoor test result, the change rule and numerical value of the numerical simulation result are close to those of the indoor test result, the parameter error is smaller than 50%, and the reasonability of the established accumulation body sample model and the calculated dynamic strength parameters is verified.

Description

Technical Field

[0001] The present invention relates to the field of geotechnical safety technology, and in particular to a method for determining shear strength parameters under earthquake action. Background Art

[0002] In geotechnical engineering, shear strength (internal friction and internal cohesion) is a key parameter that determines the soil's ability to resist shear failure. When the shear stress generated by external loads within the foundation reaches the soil's shear strength, the soil will be damaged. In severe cases, it may lead to landslides and loss of building foundation stability. Therefore, shear strength is a crucial parameter in engineering design. In geotechnical engineering, the impact of shear strength is mainly reflected in the following aspects: Foundation Stability: Shear strength directly impacts foundation stability. Excessively low shear strength can lead to foundation instability, triggering landslides and other geological hazards. Slope Design: When designing slopes, soil shear strength must be considered to ensure slope stability. Tunnel and Underground Space Development: In tunnel and underground space development, shear strength is a key indicator for assessing soil stability and construction safety.

[0003] To accurately determine shear strength and thus accurately estimate soil safety, researchers both domestically and internationally have conducted extensive research on the dynamic properties of soil (dynamic characteristics primarily refer to dynamic shear modulus, damping, vibration compaction, dynamic strength, and liquefaction, with shear strength being one indicator). Most research focuses on the dynamic elastic modulus and damping ratio of soil under cyclic loading, but little research has been conducted on dynamic strength properties, leading to divergent conclusions in many areas. Currently, research on soil dynamic strength primarily relies on laboratory testing, theoretical analysis, and numerical simulation. The following analysis examines the current state of research in these two areas.

[0004] (1) In terms of indoor testing, at present, the most commonly used method by domestic and foreign scholars to study the dynamic strength characteristics of soil is the dynamic triaxial apparatus. A large number of studies have been conducted based on the dynamic triaxial test and certain results have been achieved.

[0005] (2) In terms of theoretical calculation, soil, as a typical nonlinear material, has complex and variable mechanical responses under dynamic loads. Many scholars at home and abroad have conducted extensive research on the dynamic parameters that can describe soil. Currently, in terms of theoretical calculation, scholars mainly establish empirical strength fitting expressions based on experimental results.

[0006] (3) Numerical simulation: With the continuous development of computer technology, the method of using numerical simulation software to analyze the dynamic characteristics of soil has been favored by many scholars. For example, Xia Peng et al. (2022) carried out simulations of static and dynamic triaxial tests of binary medium mixtures based on the discrete element numerical method, obtained the distribution characteristics of the force chain structure of the binary medium mixture under the initial state and constructed a characterization method for the critical content. Based on the simulation results of the consolidation and drainage shear test, a characterization method for the equivalent skeleton porosity of the binary medium mixture was established. Liu Haoyu (2023) used particle flow discrete element software to establish a dynamic triaxial unit test numerical model and used the combined method of backbone curve and hysteresis curve to calibrate the microscopic parameters of the lightweight soil model, so that the numerical specimen can more realistically reflect the mechanical characteristics of the lightweight soil.

[0007] In summary, scholars have achieved certain research results on the dynamic strength of rock and soil. However, the method for determining its dynamic strength index parameters is mainly obtained through a large number of dynamic triaxial tests indoors. Due to the large amount of test work required and the high test failure rate, it is impossible to quickly and accurately obtain its dynamic strength index parameters (dynamic cohesion and dynamic internal friction angle), which makes it difficult to quickly apply it in actual engineering. In other words, it is difficult to quickly obtain the shear strength to evaluate the safety of specific projects. Summary of the Invention

[0008] In response to the above-mentioned deficiencies in the prior art, the method for determining shear strength parameters under earthquake action provided by the present invention solves the problem that the prior art requires a large number of indoor tests and has a high test failure rate, resulting in the inability to quickly and accurately obtain the dynamic strength index parameters of the soil.

[0009] In order to achieve the above-mentioned object of the invention, the technical solution adopted by the present invention is: A method for determining shear strength parameters under earthquake action is provided, comprising the steps of: S1. Collect soil samples from the study area and sieve them to obtain the rock content of the soil in the study area; S2. Conduct indoor triaxial tests on soil samples collected from the study area to calculate the static shear strength of the soil samples. The static shear strength includes cohesion and internal friction angle. S3. Collect earthquake magnitude data in the study area and determine the earthquake magnitude in the study area; S4. Based on the rock content, static shear strength, and earthquake magnitude, the dynamic cohesion and dynamic internal friction angle of the study area are calculated using the shear strength parameter degradation model. The expression of the shear strength parameter degradation model is: in, is dynamic cohesion; is the dynamic internal friction angle; e is the natural logarithm; Q is the rock content; M is the earthquake magnitude; is the static cohesion; is the static internal friction angle.

[0010] Furthermore, the step S1 further includes: S11. Soil samples collected from the study area were air-dried and hammered into dispersed single particles; S12, stacking the coarse sieve and the fine sieve in sequence and placing them on a vibrating sieve machine, weighing a single granular soil sample of a preset weight and placing it into the vibrating sieve machine, and weighing the mass of the soil sample on the sieve after vibrating for a preset time, and recording the mass; S13, repeating step S12 until the difference between the mass of the soil sample on the sieve after multiple screenings and the total mass of the single granular soil samples weighed before multiple screenings is less than 1% of the total mass of the single granular soil samples weighed before multiple screenings; S14. Based on the mass of the soil sample on the sieve with a pore size greater than 5 mm, calculate the mass proportion of particles with a particle size greater than 5 mm as the stone content of the soil.

[0011] Furthermore, the rock content of the soil is obtained with an accuracy of 1 g at each weighing.

[0012] Furthermore, the preset time is 15 minutes.

[0013] Furthermore, step S2 further includes: S21. Test the density of soil samples collected from the study area. Weigh the mass of the soil sample and the amount of water required for the test according to the pressure chamber volume of the triaxial testing machine, and mix them evenly. S22. Place a permeable plate and filter paper on the base of the pressure chamber in sequence, fix the rubber membrane and sample preparation cylinder on the base of the pressure chamber, load the material into the rubber membrane, and compact it layer by layer to obtain a cylindrical specimen; S22. Assemble the pressure chamber onto the triaxial testing machine, inject water into the pressure chamber to apply confining pressure, and perform a shear test on the cylindrical specimen. Stop the test when the total strain reaches 15%. S24. Based on the stress-strain curves under different confining pressures obtained from the test, draw the stress-strain relationship curve according to the Mohr-Coulomb theory, and draw the Mohr stress circle of each sample under different confining pressures respectively, draw the circle envelope, and obtain the static shear strength of the sample.

[0014] Furthermore, the method for constructing the shear strength parameter degradation model includes: S41. Using the static shear strength without vibration as the basis for evaluating the strength degradation of the pile, a shear strength degradation equation considering earthquake action is constructed: , Among them, A and B are the damage degradation coefficients of the accumulation body; S42. Triaxial tests were used to obtain the dynamic shear strength of the accumulation body under different earthquake magnitudes. The dynamic shear strength was then incorporated into the shear strength degradation equation to calculate the corresponding damage degradation coefficients under different earthquake magnitudes. S43. According to the damage degradation coefficients corresponding to different earthquake magnitudes, the magnitude and the damage degradation coefficients are fitted to obtain the fitting formula of the accumulation damage degradation coefficients A and B and the magnitude: ; S44. Conduct indoor triaxial tests to obtain the shear strength corresponding to different stone contents under natural conditions, and perform fitting to obtain the fitting formula for the shear strength of different stone contents: ; S45. Substitute the fitting formula of the accumulation damage degradation coefficient A and B and the earthquake magnitude and the fitting formula of the shear strength of different stone contents into the shear strength degradation relationship to obtain the shear strength parameter degradation model: .

[0015] Furthermore, the failure criterion during the triaxial test is the strain failure criterion, that is, when the soil does not liquefy, a limiting strain is specified as the failure criterion.

[0016] The beneficial effects of the present invention are as follows: when calculating the shear strength, this scheme only needs to obtain the stone content of the soil through indoor tests and the static shear strength of the land through triaxial indoor tests. Then, combined with the constructed shear strength parameter degradation model, the dynamic shear strength of the soil in the study area can be quickly and accurately obtained. There is no need to carry out a large number of indoor tests, and there is no need to worry about the failure of indoor tests affecting the accuracy of the dynamic shear strength calculation of the soil, thereby providing an accurate basis for the subsequent safety assessment of the soil in the study area. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 Flowchart of the method for determining shear strength parameters under earthquake action.

[0018] Figure 2 Are stress-strain curves and strength envelopes, (a) is the stress-strain curve, (b) is the strength envelope.

[0019] Figure 3 Schematic diagram of the model domain constrained by the force-displacement criterion.

[0020] Figure 4 Schematic diagram of using wall simulation unit.

[0021] Figure 5Schematic diagram of the soil particle and rock sample models generated for the PFC numerical model.

[0022] Figure 6 Comparison diagram of the model before and after preload and confining pressure are applied, (a) the model after initial sample generation, (b) the model after preload and confining pressure are applied. DETAILED DESCRIPTION

[0023] The specific embodiments of the present invention are described below to facilitate understanding of the present invention by those skilled in the art. However, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the appended claims, these changes are obvious, and all inventions and creations utilizing the concepts of the present invention are protected.

[0024] refer to Figure 1 , Figure 1 The flowchart of the method for determining shear strength parameters under earthquake action is shown; Figure 1 As shown, the method S includes steps S1 to S4.

[0025] A method for determining shear strength parameters under earthquake action is provided, comprising the steps of: In step S1, soil samples are collected from the study area and sieved to obtain the rock content of the soil in the study area; During implementation, the preferred step S1 of this solution further includes: S11. Soil samples collected from the study area were air-dried and hammered into dispersed single particles; S12, stacking the coarse sieve and the fine sieve in sequence and placing them on a vibrating sieve machine, weighing a single granular soil sample of a preset weight and placing it into the vibrating sieve machine, and weighing the mass of the soil sample on the sieve after vibrating for a preset time, and recording the mass; S13, repeating step S12 until the difference between the mass of the soil sample on the sieve after multiple screenings and the total mass of the single granular soil samples weighed before multiple screenings is less than 1% of the total mass of the single granular soil samples weighed before multiple screenings; S14. Based on the mass of the soil sample on the sieve with a pore size greater than 5 mm, calculate the mass proportion of particles with a particle size greater than 5 mm as the stone content of the soil.

[0026] When obtaining the stone content, each weighing of the soil body is accurate to 1g, and the preset time is 15 minutes.

[0027] In step S2, indoor triaxial tests are carried out on soil samples collected from the study area to calculate the static shear strength of the soil samples. The static shear strength includes cohesion and internal friction angle.

[0028] During implementation, the preferred step S2 of this solution further includes: S21. Test the density of soil samples collected from the study area. Weigh the mass of the soil sample and the amount of water required for the test according to the pressure chamber volume of the triaxial testing machine, and mix them evenly. S22. Place a permeable plate and filter paper on the base of the pressure chamber in sequence, fix the rubber membrane and sample preparation cylinder on the base of the pressure chamber, load the material into the rubber membrane, and compact it layer by layer to obtain a cylindrical specimen; S22. Assemble the pressure chamber onto the triaxial testing machine, inject water into the pressure chamber to apply confining pressure, and perform a shear test on the cylindrical specimen. Stop the test when the total strain reaches 15%. S24. Based on the stress-strain curves under different confining pressures obtained from the test, draw the stress-strain relationship curve according to the Mohr-Coulomb theory, and draw the Mohr stress circle of each sample under different confining pressures respectively, draw the circle envelope, and obtain the static shear strength of the sample.

[0029] The circle envelope in S24 is drawn as follows: According to the Mohr-Coulomb theory, the 𝜏-𝜎 relationship curve is drawn, with the normal stress 𝜎 as the horizontal coordinate and the shear stress 𝜏 as the vertical coordinate. The Mohr stress circles of each specimen under different confining pressures are drawn on the horizontal coordinate to draw the circle envelope, as shown in the figure. Figure 2 shown.

[0030] In step S3, earthquake magnitude data of the study area is collected and the earthquake magnitude of the study area is determined; In step S4, the dynamic cohesion and dynamic internal friction angle of the study area are calculated using the shear strength parameter degradation model based on the rock content, static shear strength, and earthquake magnitude. The expression of the shear strength parameter degradation model is: in, is dynamic cohesion; is the dynamic internal friction angle; e is the natural logarithm; Q is the rock content; M is the earthquake magnitude; is the static cohesion; is the static internal friction angle.

[0031] In one embodiment of the present invention, a method for constructing a shear strength parameter degradation model includes: S41. Using the static shear strength without vibration as the basis for evaluating the strength degradation of the pile, a shear strength degradation equation considering earthquake action is constructed: , Among them, A and B are the damage degradation coefficients of the accumulation body; S42. Triaxial tests were used to obtain the dynamic shear strength of the accumulation body under different earthquake magnitudes. The dynamic shear strength was then incorporated into the shear strength degradation equation to calculate the corresponding damage degradation coefficients under different earthquake magnitudes. S43. According to the damage degradation coefficients corresponding to different earthquake magnitudes, the magnitude and the damage degradation coefficients are fitted to obtain the fitting formula of the accumulation damage degradation coefficients A and B and the magnitude: ; S44. Conduct indoor triaxial tests to obtain the shear strength corresponding to different stone contents under natural conditions, and perform fitting to obtain the fitting formula for the shear strength of different stone contents: ; S45. Substitute the fitting formula of the accumulation damage degradation coefficient A and B and the earthquake magnitude and the fitting formula of the shear strength of different stone contents into the shear strength degradation relationship to obtain the shear strength parameter degradation model: .

[0032] In the process of constructing the shear strength parameter degradation model, the failure criterion during triaxial testing is the strain failure criterion, that is, when the soil does not liquefy, a limiting strain is specified as the failure criterion.

[0033] Based on the PFC numerical simulation software, a dynamic triaxial numerical simulation of the pile is carried out to illustrate the accuracy of the shear strength of this scheme: PFC is a numerical calculation platform built on the discrete element method. It treats the research object as a collection of independent, contacting, and interacting particles. It is suitable for studying soil-rock mixtures. Therefore, PFC was selected for parameter verification.

[0034] (1) First, a numerical model of the accumulation body was established In order to establish a close connection between numerical simulation and indoor test, this numerical simulation established a numerical simulation specimen with the same boundary size as the indoor test. First, a model domain constrained by the force-displacement criterion is established, such as Figure 3 As shown in , because the simulation work of the numerical simulation test needs to be carried out in this domain, the space of the model domain must be larger than the space of the specimen. On this basis, the wall simulation unit is used, such as Figure 4 As shown in the figure, this numerical simulation uses the wall command to generate a 100mm*200mm standard cylindrical wall and two upper and lower loading walls to simulate the bearing sample base. After the particle sample and boundary are generated, servo control is used to ensure that the stress acting on the wall reaches the target stress.

[0035] (2) Filling of particles This numerical simulation uses custom particle size to simulate the spherical particles in the model. The basic principles are: (a) about one-fifth of the minimum stone particle size is used as the average particle size of the soil particles; (b) in the case of meeting the target porosity, the number of generated particles should not exceed 20,000 to avoid excessive particles affecting the calculation efficiency. It should be pointed out that when the numerical simulation uses the PFC3D program to generate particles, spherical particles with a particle size of less than 5mm are used as soil particles, and the rest are used as stone particles. At the same time, according to the grading curve in the indoor test, the corresponding soil particle and stone sample models are generated, such as Figure 5 shown.

[0036] (3) Contact model setting of numerical simulation specimen PFC uses particles as the basic unit and utilizes the most fundamental physical relationship—Newton's second law—and the contact constitutive model between contacting particles to describe the mechanical relationships between materials. This continuous updating of the contact relationships between particles provides real-time elements for Newton's equations of motion, which are then reflected in the contact constitutive model. Therefore, selecting an appropriate constitutive model is crucial. This numerical simulation considers linear contact between soil and stone particles, i.e., between particles of different gradations.

[0037] (4) Preload and confining pressure servo control During the sampling stage, some particles and particles and particles-boundaries are not in full contact and the initial porosity is not reached. In order to make the particles fully contact each other and reach the preset state, a pre-loading stage is set: the stress is always kept at the initial confining pressure state through servo control, and the radial velocity of the confining pressure and the axial velocity of the upper and lower loading plate walls are limited so that the soil particles reach the desired value and the contact of the surrounding walls becomes more uniform, such as Figure 6 shown.

[0038] (5) Selection of loading method Cyclic loading is similar to the indoor test in that a sinusoidal normal force is loaded. The stress control of the cyclic dynamic triaxial numerical simulation wall is achieved by servo, so sinusoidal wave loading is used to achieve cyclic loading, that is, a sinusoidal variation speed related to the upper and lower loading plates is given to the side wall.

[0039] When generating the wall data file, two aspects of the wall control are necessary: ​​(a) wall size. The specimen size used in this simulation is consistent with the specimen size under indoor dynamic triaxial cyclic loading; and (b) the tangential and normal stiffness of the wall. The left and right walls are used to simulate the rubber mold, and its stiffness is usually about 1 / 10 of the wall stiffness.

[0040] Then, the numerical model was calibrated based on laboratory tests to obtain the model's microscopic parameters. Numerical model parameter calibration is a key step in simulation. Material parameters in laboratory model tests reflect the objective physical properties of the material under real conditions and are affected by various natural conditions. A common calibration method involves using the stress-strain curves obtained from laboratory tests to obtain a stress-strain curve that is essentially consistent with the numerical model through trial and error, thereby obtaining the model's microscopic parameters. The numerical simulation parameter calibration results are shown in Table 1.

[0041] Table 1 Calibration of numerical simulation parameters Based on the numerical simulation parameter calibration and test process described above, a dynamic triaxial numerical simulation study of the pile was conducted. Shear strength parameters under earthquake conditions were calculated. A comparison of the shear strength parameter results between the numerical simulation and the laboratory test can be found in Table 2.

[0042] Table 2 Comparison of shear strength parameters between numerical simulation and laboratory test Comparative analysis of numerical simulation and laboratory test results shows that the numerical simulation results closely follow the laboratory test results in terms of variation patterns and values, with parameter errors less than 50%. This indicates that the shear strength and deformation parameters obtained through numerical simulation are generally reasonable and effective. This means that the parameter accuracy obtained using this shear strength determination method is significantly superior to that of existing laboratory tests.

Claims

1. A method for determining shear strength parameters under earthquake action, characterized in that: Including steps: S1. Collect soil samples from the study area and sieve them to obtain the rock content of the soil in the study area; S2. Conduct indoor triaxial tests on soil samples collected from the study area to calculate the static shear strength of the soil samples. The static shear strength includes cohesion and internal friction angle. S3. Collect earthquake magnitude data in the study area and determine the earthquake magnitude in the study area; S4. Based on the rock content, static shear strength, and earthquake magnitude, the dynamic cohesion and dynamic internal friction angle of the study area are calculated using the shear strength parameter degradation model. The expression of the shear strength parameter degradation model is: in, is dynamic cohesion; is the dynamic internal friction angle; e is the natural logarithm; Q is the rock content; M is the earthquake magnitude; is the static cohesion; is the static internal friction angle.

2. The method for determining shear strength parameters under earthquake action according to claim 1, characterized in that: The step S1 further comprises: S11. Soil samples collected from the study area were air-dried and hammered into dispersed single particles; S12, stacking the coarse sieve and the fine sieve in sequence and placing them on a vibrating sieve machine, weighing a single granular soil sample of a preset weight and placing it into the vibrating sieve machine, and weighing the mass of the soil sample on the sieve after vibrating for a preset time, and recording the mass; S13, repeating step S12 until the difference between the mass of the soil sample on the sieve after multiple screenings and the total mass of the single granular soil samples weighed before multiple screenings is less than 1% of the total mass of the single granular soil samples weighed before multiple screenings; S14. Based on the mass of the soil sample on the sieve with a pore size greater than 5 mm, calculate the mass proportion of particles with a particle size greater than 5 mm as the stone content of the soil.

3. The method for determining shear strength parameters under earthquake action according to claim 2, characterized in that: The soil rock content is obtained with an accuracy of 1g at each weighing.

4. The method for determining shear strength parameters under earthquake action according to claim 2, characterized in that: The preset time is 15 minutes.

5. The method for determining shear strength parameters under earthquake action according to claim 1, characterized in that: Step S2 further comprises: S21. Test the density of soil samples collected from the study area. Weigh the mass of the soil sample and the amount of water required for the test according to the pressure chamber volume of the triaxial testing machine, and mix them evenly. S22. Place a permeable plate and filter paper on the base of the pressure chamber in sequence, fix the rubber membrane and sample preparation cylinder on the base of the pressure chamber, load the material into the rubber membrane, and compact it layer by layer to obtain a cylindrical specimen; S22. Assemble the pressure chamber onto the triaxial testing machine, inject water into the pressure chamber to apply confining pressure, and perform a shear test on the cylindrical specimen. Stop the test when the total strain reaches 15%. S24. Based on the stress-strain curves under different confining pressures obtained from the test, draw the stress-strain relationship curve according to the Mohr-Coulomb theory, and draw the Mohr stress circle of each sample under different confining pressures respectively, draw the circle envelope, and obtain the static shear strength of the sample.

6. The method for determining shear strength parameters under earthquake action according to claim 1, characterized in that: The construction method of the shear strength parameter degradation model includes: S41. Using the static shear strength without vibration as the basis for evaluating the strength degradation of the pile, a shear strength degradation equation considering earthquake action is constructed: ， Among them, A and B are the damage degradation coefficients of the accumulation body; S42. Triaxial tests were used to obtain the dynamic shear strength of the accumulation body under different earthquake magnitudes. The dynamic shear strength was then incorporated into the shear strength degradation equation to calculate the corresponding damage degradation coefficients under different earthquake magnitudes. S43. According to the damage degradation coefficients corresponding to different earthquake magnitudes, the magnitude and the damage degradation coefficients are fitted to obtain the fitting formula of the accumulation damage degradation coefficients A and B and the magnitude: ； S44. Conduct indoor triaxial tests to obtain the shear strength corresponding to different stone contents under natural conditions, and perform fitting to obtain the fitting formula for the shear strength of different stone contents: ； S45. Substitute the fitting formula of the accumulation damage degradation coefficient A and B and the earthquake magnitude and the fitting formula of the shear strength of different stone contents into the shear strength degradation relationship to obtain the shear strength parameter degradation model: 。 7. The method for determining shear strength parameters under earthquake action according to any one of claims 1 to 6, characterized in that: The failure criterion during triaxial testing is the strain failure criterion, that is, when the soil does not liquefy, a limiting strain is specified as the failure criterion.

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