Fast prediction method for particle size distribution curves of calcareous sand under different loading paths

Abstract

The present invention relates to a rapid prediction method for the particle size distribution curve of calcareous sand under different loading paths, comprising the steps of: obtaining the particle size distribution curves of calcareous sand with the same initial gradation and initial void ratio under different confining pressures under the condition of isotropic compression test; calculating the relative breakage rate under the isotropic compression test; determining the stress-strain relationship of the calcareous sand specimen in the compression test under different loading paths; calculating the total input energy; obtaining the particle size distribution curve; calculating the relative breakage rate under different loading paths; determining the size of the characteristic particle size; plotting the data scatter relationship diagram; obtaining the fitting parameters; and obtaining the rapid prediction equation. The present invention solves the influence of the stress path on the gradation evolution law, so that the particle size distribution model is not affected by the matching degree between the actual particle size distribution and the functional relationship of the assumed particle size distribution curve; and enables the influence of the stress path on the particle size distribution not to be restricted by the initial gradation condition, broadening the application conditions and application scenarios.

Description

Technical Field

[0001] The present invention relates to the technical field of reef construction engineering, and particularly to a method for quickly predicting the particle size distribution curve of calcareous sand under different loading paths. Background Art

[0002] As the main filling material and foundation material for ocean reef engineering, calcareous sand is a special geotechnical material with low particle strength, complex shape and rich internal pores, and significant particle breakage effect will occur under low stress. The particle breakage effect will change the gradation of calcareous sand, and the gradation has an important impact on the void ratio, permeability coefficient, maximum dry density, shear strength, settlement deformation and critical characteristics of calcareous sand, etc. On the one hand, this change in gradation changes with the change of external load or deformation, making the mechanical properties of calcareous sand more complex. On the other hand, in different actual projects, calcareous sand is often under different loading paths, and the loading path is also an important factor affecting the particle breakage effect, which also leads to great differences in the particle gradation of calcareous sand under different loading paths. This change in gradation may cause changes in the shear strength, permeability or settlement deformation of calcareous sand, leading to engineering structure problems. Therefore, considering the stability and structural safety of ocean reef engineering, obtaining the particle size distribution curve of calcareous sand under different loading paths is of great significance for evaluating the mechanical behavior and deformation characteristics of calcareous sand.

[0003] There are mainly two methods for obtaining the particle size distribution curve of granular soil in the prior art: (1) By assuming the functional relationship of the particle size distribution curve (such as the fractal model), and then through the particle breakage index (such as the relative breakage rate proposed by Hardin), establishing the relationship between the particle breakage index and the parameters in the functional relationship of the particle size distribution curve, and finally based on the test results, establishing the relationship between the stress-strain relationship and the particle breakage index. In this way, the conversion relationship of stress-strain relationship - particle breakage index - particle size distribution curve is formed; (2) Starting from the single-particle breakage test, assuming the relationship between the single-particle breakage probability and the particle size (such as the concept that the "survival probability" of particles proposed by McDowell and the load conform to the Weibull distribution), and then superimposing the single-particle breakage law based on the gradation evolution Markov model proposed by Ozkan to obtain the particle size distribution curve of multi-particle size groups with particle breakage.

[0004] Furthermore, by combining the above two methods, based on the functional relationship between the single-particle breakage probability and the particle size and the assumed functional relationship of the particle size distribution curve, establishing the connection between the parameters of the two types of functional relationships, and finally obtaining the particle size distribution curve of multi-particle size groups with particle breakage.

[0005] The defects of the prior art are as follows:

[0006] 1. The prediction method of the particle gradation evolution based on the functional relationship of the particle size distribution curve depends to a great extent on the matching degree between the particle size distribution of calcareous sand after particle breakage under stress and the functional relationship of the assumed particle size distribution curve. Based on the above logical basis, if the matching effect between the two is poor, it will inevitably lead to a large discreteness of the prediction results, and further lead to a very poor prediction accuracy.

[0007] 2. When using the Markov model to superimpose the single-particle breakage law, the implementation basis of the Markov model is to assume that the probability of a large particle breaking into smaller particles of different sizes is the same, which is obviously inconsistent with the actual situation. Therefore, it is actually not practical.

[0008] 3. When using computer particle flow software to simulate the influence of particle breakage effect on the mechanical properties of granular soil, the existing technology often selects particles of a single grain group for simulation in order to eliminate the influence of the particle shape of multi-sized particles on the test simulation. Then, if you want to verify the accuracy of the simulation results, you need to compare and verify the particle size distribution curves of the simulation calculation and the test results. However, the initial gradation of the previous particle size distribution evolution models is mostly continuous gradation, so it cannot reflect the particle size distribution law of a single gradation under different stress conditions.

[0009] 4. Since most of the existing particle size distribution evolution models are proposed under the conventional triaxial compression test path, they cannot reflect the influence of the loading path on particle breakage, and further cannot reflect the influence of the loading path on the gradation evolution law. Summary of the Invention

[0010] The present invention aims at the above problems and provides a rapid prediction method for the particle gradation curve of calcareous sand under different loading paths, aiming to solve the influence of the stress path on the gradation evolution law, and further making the particle size distribution model not affected by the matching degree between the actual gradation and the functional relationship of the assumed particle size distribution curve; making the influence of the stress path on the particle size distribution not restricted by the initial gradation conditions, broadening the application conditions and application scenarios, and also more in line with the requirements of engineering design and construction, and solving the problems existing in the prior art.

[0011] To solve the above problems, the technical solution provided by the present invention is as follows:

[0012] A rapid prediction method for the particle gradation curve of calcareous sand under different loading paths, comprising the following steps:

[0013] S100. Obtain the particle size distribution curves of calcareous sand with the same initial gradation and initial void ratio under different confining pressures under the isotropic compression test conditions; and then calculate the relative breakage rate under the isotropic compression test.

[0014] S200. Prepare calcareous sand specimens with the same initial gradation as that in S100 and the same initial porosity ratio; then, determine the stress-strain relationship of the calcareous sand specimens in the compression test under different loading paths; then calculate the total input energy in the shear stage of the specimen under each of the loading paths; then, after the compression test in S200 is completed, obtain the particle size distribution curve of the compression test in S200; then calculate the relative breakage rate of the calcareous sand specimens in the shear stage under different loading paths;

[0015] S300. For each of the particle size distribution curves under the loading paths obtained in S200, determine the size of the characteristic particle size on the particle size distribution curve;

[0016] S400. According to the characteristic particle size obtained in S300 and the relative breakage rate of the calcareous sand specimens in the shear stage under each of the loading paths obtained in S200, plot a data scatter relationship diagram of the characteristic particle size and the relative breakage rate of the calcareous sand specimens in the shear stage under different loading paths in a rectangular coordinate system;

[0017] Or, according to the characteristic particle size obtained in S300 and the total input energy in the shear stage under each of the loading paths obtained in S200, plot a data scatter relationship diagram of the characteristic particle size and the total input energy in the shear stage under each of the loading paths in a rectangular coordinate system;

[0018] Then obtain the fitting parameters; obtain the rapid prediction equation according to the fitting parameters; the rapid prediction equation is the final result of the rapid prediction method of the present invention.

[0019] Preferably, in S100 and S200, the Hardin relative breakage rate concept calculation method is used to calculate the relative breakage rate; specifically expressed by the following formula:

[0020]

[0021] Where: B r is the relative breakage rate; B t is the particle breakage potential, which is calculated by obtaining the area enclosed by the initial particle size distribution curve of the compression test, the particle size distribution curve after the compression test loading is completed, and the particle size, where the value of the particle size is set manually; B p represents the total breakage potential, which is calculated by obtaining the area enclosed by the initial particle size distribution curve of the particle breakage, the breakage probability, and the particle size, where the value of the breakage probability is set manually.

[0022] Preferably, S100 specifically includes the following steps:

[0023] S110. Take no less than three portions of the calcareous sand with the same initial gradation, and calculate the mass of each calcareous sand specimen one by one according to the artificially set initial porosity ratio; specifically, it is expressed by the following formula:

[0024]

[0025] where m is the mass of the calcareous sand specimen; G s is the specific gravity of calcareous sand particles; w0 is the initial water content of calcareous sand; ρ w is the density of pure water; V is the volume of the calcareous sand specimen; e0 is the initial porosity ratio.

[0026] S120. According to the mass of the calcareous sand specimen calculated in S110, weigh the required mass of calcareous sand one by one in sequence, and use the sand rain method to directly prepare the calcareous sand specimen on the instrument base of the stress path triaxial apparatus, and saturate the calcareous sand specimen by the combined method of back pressure and carbon dioxide saturation;

[0027] S130. For each calcareous sand specimen obtained in S120, conduct the isotropic compression test under different confining pressures preset manually; after each isotropic compression test is completed, take out the specimen and place it in a ceramic basin, dry it in an oven and then cool it to room temperature;

[0028] S140. For the dried and cooled calcareous sand specimens obtained in S130, conduct the sieving test one by one by the vibrating sieve method to obtain the particle size distribution curves under different confining pressure conditions;

[0029] S150. According to the particle size distribution curves under different confining pressure conditions obtained in S140, calculate and obtain the relative breakage rates under isotropic compression tests under different confining pressure conditions.

[0030] Preferably, S200 specifically includes the following steps:

[0031] S210. Prepare multiple calcareous sand specimens for compression tests under different loading paths; each calcareous sand specimen has the same initial gradation as that in S100, the same initial porosity ratio, the same sample preparation method, and the same saturation method;

[0032] S220. After the calcareous sand specimens in S210 are saturated, first conduct the isotropic compression tests under different confining pressures through the stress path triaxial apparatus;

[0033] S230. After the calcareous sand specimens in S220 complete the isotropic compression tests under the corresponding confining pressures, conduct the conventional triaxial compression path test, the triaxial compression test with a constant mean principal stress, and the triaxial compression test of decompression under the corresponding confining pressures respectively;

[0034] S240. For each of the conventional triaxial compression path tests, the triaxial compression test with a constant mean principal stress, and the triaxial compression test with decompression in S230, not less than 3 different artificially preset confining pressures are taken for each loading path compression test; the values of the mean effective principal stress, deviator stress, volumetric strain, and axial strain of each calcareous sand specimen are obtained respectively under different confining pressure conditions in the conventional triaxial compression path test, the triaxial compression test with a constant mean principal stress, and the triaxial compression test with decompression;

[0035] S250. Calculate the total input energy in the shear stage of the calcareous sand specimen under the conventional triaxial compression path test, the triaxial compression test with a constant mean principal stress, and the triaxial compression test with decompression respectively; specifically expressed by the following formula:

[0036] W = ∫pdε v +qdε s

[0037] where: W is the total input energy; p is the mean effective principal stress; q is the deviator stress; ε v is the volumetric strain; ε s is the shear strain, expressed by the following formula:

[0038]

[0039] where: ε1 is the axial strain;

[0040] S260. After each test in S240 is completed, carefully take out the calcareous sand specimen and place it in a ceramic basin, dry it in an oven and then cool it to room temperature;

[0041] S270. For the dried and cooled calcareous sand specimens obtained in S260, conduct sieving tests one by one using the vibrating sieve method, and respectively obtain the particle size distribution curves of the conventional triaxial compression path test, the triaxial compression test with a constant mean principal stress, and the triaxial compression test with decompression under different confining pressure conditions;

[0042] S280. For the particle size distribution curves of the conventional triaxial compression path test, the triaxial compression test with a constant mean principal stress, and the triaxial compression test with decompression under different confining pressure conditions obtained in S270, calculate and obtain the relative breakage rate under different loading paths; then deduct the relative breakage rate under the isotropic compression test under different loading path compression tests, and calculate and obtain the relative breakage rate of the calcareous sand specimen in the shear stage under different loading paths; specifically expressed by the following formula:

[0043] B rq = B rc - B rh

[0044] Wherein: B rc is the relative breakage rate under the different loading paths; B rq is the relative breakage rate of the calcareous sand specimen during the shear stage under the different loading paths; B rh is the relative breakage rate of the isotropic compression test under the different confining pressure conditions.

[0045] Preferably, in S300, the characteristic particle sizes include the restricted particle size, the intermediate particle size, the median particle size, and the effective particle size. The restricted particle size, the intermediate particle size, the median particle size, and the effective particle size under the different confining pressure conditions are respectively obtained through the particle size distribution curves under the different loading paths.

[0046] Preferably, in S400, the rapid prediction equation is obtained according to the following steps:

[0047] Sa410. Plot the data scatter diagram of the relationship between the characteristic particle size and the relative breakage rate of the calcareous sand specimen during the shear stage under the different loading paths in a rectangular coordinate system; wherein the data fitting method is expressed by the following formula:

[0048]

[0049] Wherein: d 0i , d 1i and d 2i are all fitting parameters;

[0050] Sa420. Obtain the rapid prediction equation according to the fitting parameters.

[0051] Preferably, in S400, the rapid prediction equation is obtained according to the following steps:

[0052] Sb410. Plot the data scatter diagram of the relationship between the characteristic particle size and the total input energy during the shear stage under each loading path in a rectangular coordinate system; wherein the data fitting method is expressed by the following formula:

[0053]

[0054] Sb420. Obtain the rapid prediction equation according to the fitting parameters.

[0055] Preferably, the relative breakage rate of the calcareous sand specimen during the shear stage under the different loading paths is expressed by the following formula:

[0056]

[0057] Wherein: a, b, v, m, n are all fitting parameters; q max is the maximum value of the deviator stress under each loading path. B rhThe relative breakage ratio under the isotropic compression test under the different confining pressure conditions

[0058] Compared with the prior art, the present invention has the following advantages:

[0059] 1. Since the present invention obtains the distribution law of the particle size by directly acquiring the data points of the particle size distribution curve, the prediction result no longer depends on the matching degree between the assumed functional relationship of the particle size distribution curve and the actual particle size distribution. Moreover, the test prediction result is no longer limited to the initial gradation must be a continuous gradation, and it is still applicable to the calcareous sand with a single particle size as the initial gradation, so that the calculation result has higher accuracy and a wider application range than the prior art.

[0060] 2. Since the present invention can not only predict the particle size distribution of calcareous sand under the conventional triaxial test conditions, but also determine the particle size distribution of calcareous sand under other loading path conditions, and can also determine the particle size distribution of calcareous sand under any specified shear strain condition during the shear process, it is no longer necessary to obtain the particle size distribution curve of calcareous sand under a certain loading path through a large number of screening tests, greatly reducing the test workload of engineering personnel;

[0061] 3. When this method is extended to the design, construction or stable operation and maintenance of other granular soil foundations such as rockfill materials, it can also be used for the calculation of the seepage coefficient of rockfill dams, the prediction of seepage failure forms, etc., and has broad application value. Description of the Drawings

[0062] Figure 1 Schematic diagram for calculating the relative breakage ratio;

[0063] Figure 2 Schematic diagram of the particle size distribution curve under each confining pressure condition of the isotropic compression test in the specific embodiment of the present invention;

[0064] Figure 3 Schematic diagram of the relationship curve between the confining pressure and the relative breakage ratio under each confining pressure condition of the isotropic compression in the specific embodiment of the present invention;

[0065] Figure 4a Schematic diagram of the deviator stress - volumetric strain - axial strain relationship curve in the CTC experiment in the specific embodiment of the present invention;

[0066] Figure 4b Schematic diagram of the deviator stress - volumetric strain - axial strain relationship curve in the TC experiment in the specific embodiment of the present invention;

[0067] Figure 4c Schematic diagram of the deviator stress - volumetric strain - axial strain relationship curve in the RTC experiment in the specific embodiment of the present invention;

[0068] Figure 5aSchematic diagram of the particle size distribution curve in the CTC experiment in the specific embodiment of the present invention;

[0069] Figure 5b Schematic diagram of the particle size distribution curve in the TC experiment in the specific embodiment of the present invention;

[0070] Figure 5c Schematic diagram of the particle size distribution curve in the RTC experiment in the specific embodiment of the present invention;

[0071] Figure 6 Schematic diagram of the relationship curve between confining pressure and relative breakage ratio in the shear stage under each confining pressure condition of three different loading paths in the specific embodiment of the present invention;

[0072] Figure 7 Schematic diagram of the relationship curve between characteristic particle size and relative breakage ratio in the shear stage under each confining pressure condition of three different loading paths in the specific embodiment of the present invention;

[0073] Figure 8 Schematic diagram of the relationship curve between characteristic particle size and total input energy under each confining pressure condition of three different loading paths in the specific embodiment of the present invention;

[0074] Figure 9 Schematic diagram for drawing a certain particle size distribution curve in the specific embodiment of the present invention;

[0075] Figure 10 Schematic diagram for calculating the relative breakage ratio parameter in the shear stage of calcareous sand specimens under TC test conditions in the specific embodiment of the present invention. Specific implementation manner

[0076] The following further clarifies the present invention in conjunction with specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and not to limit the scope of the present invention. After reading the present invention, various equivalent forms of modification by those skilled in the art fall within the scope defined by the appended claims of this application.

[0077] A rapid prediction method for the particle size distribution curve of calcareous sand under different loading paths, comprising the following steps:

[0078] S100. Using the relative breakage ratio B proposed by Hardin r Concept to calculate the relative breakage ratio, obtain the particle size distribution curve of calcareous sand with the same initial gradation and initial void ratio under different confining pressures under the isotropic compression test conditions; then calculate the relative breakage ratio under the isotropic compression test.

[0079] In this specific embodiment, in S100 and S200, the Hardin relative breakage ratio concept calculation method is used to calculate the relative breakage ratio; specifically, it is expressed by Equation (1):

[0080]

[0081] Wherein: B r is the relative breakage ratio; B t is the particle breakage potential, which is obtained by calculating the area enclosed by the initial particle size distribution curve of the compression test, the particle size distribution curve after the compression test is loaded, and the particle size. The value of the particle size is set manually. In this specific embodiment, the particle size is d = 0.075 mm; B p represents the total breakage potential, which is obtained by calculating the area enclosed by the initial particle size distribution curve of particle breakage, the breakage probability, and the particle size. The value of the breakage probability is set manually. In this specific embodiment, the breakage probability is P = 100%.

[0082] As Figure 1 shown, it is a simplified diagram of the above calculation method.

[0083] S100 specifically includes the following steps:

[0084] S110. Take no less than 3 portions of calcareous sand with the same initial gradation, and calculate the mass of each calcareous sand sample one by one according to the manually set initial void ratio; specifically expressed by formula (2):

[0085]

[0086] Wherein, m is the mass of the calcareous sand sample; G s is the specific gravity of calcareous sand particles; w0 is the initial moisture content of calcareous sand; ρ w is the density of pure water; V is the volume of the calcareous sand sample; e0 is the initial void ratio..

[0087] In this specific embodiment, the gradation of the calcareous sand sample is 1 mm to 0.5 mm, the initial void ratio is 0.9, the specific gravity of calcareous sand particles is 2.76, the initial moisture content of air-dried calcareous sand is 0.24%, ρ w = 1 g / cm 3 , the sample is a cylinder with a diameter of 50 mm and a height of 100 mm, and the volume is 196250 mm 3 . From formula (2), it can be calculated that m = 285.75 g.

[0088] S120. According to the mass of the calcareous sand sample calculated in S110, weigh the required mass of calcareous sand one by one in sequence, prepare the calcareous sand sample directly on the instrument base of the stress path triaxial apparatus by the sand rain method, and saturate the calcareous sand sample by the combined method of back pressure and carbon dioxide;.

[0089] S130. For each calcareous sand specimen obtained in S120, an isotropic compression test is carried out under different confining pressures preset manually; after each isotropic compression test is completed, the specimen is carefully taken out and placed in a ceramic basin, dried in an oven and then cooled to room temperature.

[0090] S140. For the dried and cooled calcareous sand specimens obtained in S130, a sieving test is carried out one by one by the vibrating sieve method to obtain the particle size distribution curves under different confining pressure conditions.

[0091] S150. According to the particle size distribution curves under different confining pressure conditions obtained in S140, the relative breakage rate under the isotropic compression test under different confining pressure conditions is calculated and obtained.

[0092] In this specific embodiment, the confining pressure values of each isotropic compression test are preset to 0.3 MPa, 0.6 MPa, 1.2 MPa, and 2.4 MPa. The specific test saturation, loading scheme and sieving test are carried out in accordance with "National Standard of the People's Republic of China: Geotechnical Test Methods Standard (GB / T 50123-2019)".

[0093] In this specific embodiment, as Figure 2 shown, it is a schematic diagram of the particle size distribution curve under each confining pressure condition of the isotropic compression test obtained; as Figure 3 shown, it is the relative breakage rate B under the isotropic compression test under different confining pressure conditions rh .

[0094] S200. Prepare calcareous sand specimens with the same initial gradation and the same initial void ratio as those in S100; then, determine the stress-strain relationship of the calcareous sand specimens in the compression test under different loading paths; then calculate the total input energy in the shear stage of the specimen under each loading path; then, after the compression test in S200 is completed, obtain the particle size distribution curve of the compression test in S200; then calculate the relative breakage rate in the shear stage of the calcareous sand specimens under different loading paths.

[0095] S200 specifically includes the following steps:

[0096] S210. Prepare multiple calcareous sand specimens for the compression test under different loading paths; each calcareous sand specimen has the same initial gradation and the same initial void ratio as those in S100, and the same sample preparation method and the same saturation method.

[0097] S220. After the calcareous sand specimens in S210 are saturated, first carry out isotropic compression tests under different confining pressures by a stress path triaxial apparatus.

[0098] After the calcareous sand specimen in S220 has completed the isotropic compression test under the corresponding confining pressure, conduct the conventional triaxial compression path test, i.e., the CTC test, the triaxial compression test with a constant mean principal stress, i.e., the TC test, and the triaxial compression test with decompression, i.e., the RTC test, under the corresponding confining pressure respectively.

[0099] For each of the conventional triaxial compression path test, the triaxial compression test with a constant mean principal stress, and the triaxial compression test with decompression in S230, take no less than 3 specimens each and conduct the loading path compression test under different artificially preset confining pressures; then obtain the values of the mean effective principal stress, deviator stress, volumetric strain, and axial strain of each calcareous sand specimen under different confining pressure conditions in the conventional triaxial compression path test, the triaxial compression test with a constant mean principal stress, and the triaxial compression test with decompression respectively.

[0100] Calculate the total input energy in the shear stage of the calcareous sand specimen under the conventional triaxial compression path test, the triaxial compression test with a constant mean principal stress, and the triaxial compression test with decompression respectively; specifically expressed by Equation (3):

[0101] W = ∫pdε v +qdε s (3)

[0102] Where: W is the total input energy; p is the mean effective principal stress; q is the deviator stress; ε v is the volumetric strain; ε s is the shear strain, expressed by Equation (4):

[0103]

[0104] Where: ε1 is the axial strain;

[0105] After each test in S240, carefully take out the calcareous sand specimen and place it in a ceramic basin, dry it in an oven and then cool it to room temperature.

[0106] For the dried and cooled calcareous sand specimens obtained in S260, conduct the sieving test one by one using the vibrating sieve method, and obtain the particle size distribution curves of the conventional triaxial compression path test, the triaxial compression test with a constant mean principal stress, and the triaxial compression test with decompression under different confining pressure conditions respectively.

[0107] S280. Calculate the relative breakage rate under different loading paths from the particle size distribution curves under different confining pressure conditions in the conventional triaxial compression path test, the triaxial compression test with a constant mean principal stress, and the triaxial compression test with decompression obtained in S270; then subtract the relative breakage rate in the isotropic compression test under different loading path compression tests to calculate the relative breakage rate of the calcareous sand specimen in the shear stage under different loading paths; specifically expressed by Equation (5):

[0108] B rq = B rc - B rh (5)

[0109] Where: B rc is the relative breakage rate under different loading paths; B rq is the relative breakage rate of the calcareous sand specimen in the shear stage under different loading paths; B rh is the relative breakage rate in the isotropic compression test under different confining pressure conditions.

[0110] In this specific embodiment, the gradation of the calcareous sand specimen is 1 mm to 0.5 mm, the initial void ratio is 0.9, the specific gravity of the calcareous sand particles is 2.76, the initial moisture content of the air-dried calcareous sand is 0.24%, ρ w = 1 g / cm 3 , the specimen is a cylinder with a diameter of 50 mm and a height of 100 mm, and the volume is 196250 mm 3 . From Equation (2), it can be calculated that m = 285.75 g.

[0111] In this specific embodiment, the confining pressure values under each loading path are preset to 0.3 MPa, 0.6 MPa, 1.2 MPa, and 2.4 MPa. The specific test saturation, loading scheme, and screening test are carried out in accordance with "National Standard of the People's Republic of China: Geotechnical Test Methods Standard (GB / T 50123-2019)".

[0112] As shown in Table 1, the shear rate and test end standard for each loading path test are as follows:

[0113] Table 1. Data Sheet of Loading Path Test Scheme

[0114]

[0115] Where: σ1 is the axial stress; σ3 is the lateral pressure; Δ is the increment symbol.

[0116] In this specific embodiment, as Figures 4a - 4c shown, the deviator stress - volumetric strain - axial strain relationship curves of the compression tests under each loading path are obtained; as Figures 5a - 5cAs shown, it is the particle size distribution curve of the compression test obtained from the screening test; as Figure 6 shown, it is the relative breakage rate B of the calcareous sand specimen during the shear stage under different loading paths rq ; as Figure 8 shown, it is the total input energy W during the shear stage under each loading path calculated thereby.

[0117] S300. For the particle size distribution curve under each loading path obtained in S200, determine the size of the characteristic particle size d i on the particle size distribution curve; wherein, d i represents the particle size corresponding to the mass percentage equal to i% on the particle size distribution curve.

[0118] In S300, the characteristic particle size includes the restricted particle size d 60 , the intermediate particle size d 50 , the median particle size d 30 and the effective particle size d 10 . Through the particle size distribution curves under different loading paths, obtain the restricted particle size, intermediate particle size, median particle size and effective particle size under different confining pressure conditions respectively.

[0119] In this specific embodiment, through the particle size distribution curve of the compression test under different loading paths obtained from Figure 5, perform linear interpolation to obtain the corresponding characteristic particle size d i , and the specific results are shown in Table 2:

[0120] Table 2 Characteristic particle sizes of compression specimens under each confining pressure condition of different loading paths

[0121]

[0122] S400. According to the relationship between the characteristic particle size obtained in S300 and the relative breakage rate of the calcareous sand specimen during the shear stage under each loading path obtained in S200, draw a scatter plot of the relationship between the characteristic particle size and the relative breakage rate of the calcareous sand specimen during the shear stage under different loading paths in a rectangular coordinate system.

[0123] Or, according to the relationship between the total input energy during the shear stage under each loading path obtained in S200, draw a scatter plot of the relationship between the characteristic particle size and the total input energy during the shear stage under each loading path in a rectangular coordinate system.

[0124] Then use the regression analysis method to determine the fitting parameters d 0i , d 1i and d 2i ; obtain the rapid prediction equation according to the fitting parameters; the rapid prediction equation is the final result of the rapid prediction method of the present invention.

[0125] In S400, there are two methods to obtain the rapid prediction equation:

[0126] It should be noted in advance that either of these two methods can achieve the purpose of S400, and they are in an equal position. Either one can be selected in actual work.

[0127] The first one is obtained according to the following steps:

[0128] Sa410. Plot the scatter diagram of the relationship between the characteristic particle size and the relative breakage rate of the calcareous sand specimen in the shear stage under different loading paths in the rectangular coordinate system; the data fitting method is expressed by Equation (6):

[0129]

[0130] Where: d 0i , d 1i and d 2i are all fitting parameters.

[0131] In this specific embodiment, the relative breakage rate of the calcareous sand specimen in the shear stage under different loading paths is calculated according to Equation (7):

[0132]

[0133] Where: a, b, v, m, n are all fitting parameters; q max is the maximum value of the deviator stress under each loading path. B rh is the relative breakage rate under the isotropic compression test under the different confining pressure conditions

[0134] After substituting each fitting parameter into Equation (7), Equation (8) can be obtained:

[0135]

[0136] Sa420. Obtain the rapid prediction equation according to the fitting parameters.

[0137] It should be noted that in this way, the characteristic particle size points on the particle size distribution curve can be obtained through the relative breakage rate B rq of the calcareous sand specimen in the shear stage under different loading paths. Based on these characteristic particle size data points (d i , i%), the particle size distribution curve after breakage can be plotted.

[0138] In this specific embodiment, based on Figure 6 the relative breakage rate B rq obtained under different loading paths and the characteristic particle size d i obtained in step S300, plot the relationship between the two in the rectangular coordinate system, as shown in Figure 7 . The corresponding fitting parameter d0i , d 1i and d 2i See also Figure 7 .

[0139] The second kind is obtained by the following steps:

[0140] Sb410. Plot the scatter diagram of the relationship between the characteristic particle size and the total input energy during the shear stage under each loading path in the rectangular coordinate system; where the data fitting method is expressed by Equation (9):

[0141]

[0142] Sb420. Obtain the rapid prediction equation according to the fitting parameters.

[0143] It should be noted that in this way, the characteristic particle size points on the particle size distribution curve can be obtained through the total input energy W during the shear stage under different loading paths. Based on these characteristic particle size data points (d i , i%), the particle size distribution curve after crushing can be plotted.

[0144] In this specific embodiment, based on the total input energy W obtained in step S200 and the characteristic particle size d i , plot the relationship between the two in the rectangular coordinate system, see Figure 8 . The corresponding fitting parameters d 0i , d 1i and d 2i See also Figure 8 .

[0145] In this way, the characteristic particle size points on the particle size distribution curve can be obtained by one of the above two methods. Based on these characteristic particle size data points (d i , i%), the particle size distribution curve after crushing can be plotted, which is also the final result of the present invention.

[0146] As Figure 9 shown, it is the comparison between the test values of the CTC test with a confining pressure of 2.4 MPa and the predicted values obtained by calculation using Sa410.

[0147] Through the consistency test of the two types of methods, as Figure 7 and Figure 8 shown, their correlation coefficient R 2 is greater than 0.95, and the fitting effect meets the requirements of general engineering construction.

[0148] As Figure 10 shown, it is the schematic diagram of the calculation of the relative breakage rate parameter during the shear stage of the calcareous sand specimen under the TC test conditions.

[0149] It should be noted that when transforming Equation (7) to Equation (8), the fitting parameters are derived from 2 attached drawings, specifically: a and b are obtained from the isotropic compression test Figure 3 and v, m, and n are obtained from the TC test Figure 10 .

[0150] In the above detailed description, various features are combined together in a single embodiment to simplify the present disclosure. This method of disclosure should not be construed as reflecting an intention that the embodiments of the claimed subject matter require more features than those clearly stated in each claim. On the contrary, as reflected in the appended claims, the present invention lies in a state with fewer features than all the features of the disclosed single embodiment. Therefore, the appended claims are hereby clearly incorporated into the detailed description, where each claim stands alone as a separate preferred embodiment of the present invention.

[0151] The above-described disclosed embodiments are described to enable any person skilled in the art to implement or use the present invention. For those skilled in the art, various modification methods of these embodiments are obvious, and the general principles defined herein can also be applied to other embodiments without departing from the spirit and protection scope of the present disclosure. Therefore, the present disclosure is not limited to the embodiments given herein, but is consistent with the broadest scope of the principles and novel features disclosed in this application.

[0152] The above description includes examples of one or more embodiments. Of course, it is impossible to describe all possible combinations of components or methods for describing the above embodiments, but those of ordinary skill in the art should recognize that each embodiment can be further combined and arranged. Therefore, the embodiments described herein are intended to cover all such changes, modifications, and variations that fall within the protection scope of the appended claims. In addition, with respect to the term "comprising" used in the specification or claims, the coverage of this term is similar to the term "including", as explained when "including" is used as a transitional term in the claims. In addition, any term "or" used in the claims or the specification is to mean "non-exclusive or".

[0153] The above-described specific embodiments further elaborate on the purpose, technical solutions, and beneficial effects of the present invention. It should be understood that the above description is only the specific embodiments of the present invention and is not used to limit the protection scope of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.

Claims

1. A rapid prediction method for the particle size distribution curve of calcareous sand under different loading paths, characterized in that: It includes the following steps: S100. Obtain the particle size distribution curves of calcareous sand with the same initial gradation and initial void ratio under different confining pressures under the conditions of isotropic compression tests; then calculate the relative breakage ratio under the isotropic compression test; S200. Prepare calcareous sand specimens with the same initial gradation and the same initial void ratio as those in S100; then determine the stress-strain relationship of the calcareous sand specimens in the compression tests under different loading paths; then calculate the total input energy in the shear stage of the specimens under each of the loading paths; then, after the compression test in S200 is completed, obtain the particle size distribution curve of the compression test in S200; then calculate the relative breakage ratio of the calcareous sand specimens in the shear stage under different loading paths; S300. For each of the particle size distribution curves under each of the loading paths obtained in S200, determine the size of the characteristic particle size on the particle size distribution curve; S400. According to the characteristic particle size obtained in S300 and the relative breakage ratio of the calcareous sand specimens in the shear stage under each of the loading paths obtained in S200, plot the data scatter relationship diagram of the characteristic particle size and the relative breakage ratio of the calcareous sand specimens in the shear stage under different loading paths in a rectangular coordinate system; Or, according to the characteristic particle size obtained in S300 and the total input energy in the shear stage under each of the loading paths obtained in S200, plot the data scatter relationship diagram of the characteristic particle size and the total input energy in the shear stage under each of the loading paths in a rectangular coordinate system; Then obtain the fitting parameters; obtain the rapid prediction equation according to the fitting parameters; the rapid prediction equation is the final result of the rapid prediction method of the present invention.

2. The rapid prediction method for the particle size distribution curve of calcareous sand under different loading paths according to claim 1, characterized in that: In S100 and S200, the Hardin relative breakage ratio concept calculation method is adopted to calculate the relative breakage ratio; specifically, it is expressed by the following formula: Where: B r is the relative breakage rate; B t is the particle breakage potential, which is calculated by the area enclosed by the initial particle size distribution curve of the compression test, the particle size distribution curve after the loading of the compression test is completed, and the particle size curve. The value of the particle size is set manually; B p represents the total breakage potential, which is calculated by the area enclosed by the initial particle size distribution curve of the particle breakage, the breakage probability, and the particle size curve. The value of the breakage probability is set manually.

3. The rapid prediction method for the particle size distribution curve of calcareous sand under different loading paths according to claim 1, wherein: S100 specifically includes the following steps: S110. Take no less than 3 portions of the calcareous sand with the same initial gradation, and calculate the mass of each calcareous sand specimen one by one according to the artificially set initial void ratio; specifically, it is expressed by the following formula: where m is the mass of the calcareous sand sample; G s is the specific gravity of calcareous sand particles; w0 is the initial water content of calcareous sand; ρ w is the density of pure water; V is the volume of the calcareous sand sample; e0 is the initial void ratio; S120. According to the mass of the calcareous sand specimens calculated in S110, weigh the required mass of calcareous sand one by one in sequence, prepare the calcareous sand specimens directly on the instrument base of the stress path triaxial apparatus by the sand rain method, and saturate the calcareous sand specimens by the combined method of back pressure and carbon dioxide; S130. Conduct the isotropic compression test on each of the calcareous sand specimens obtained in S120 at different confining pressures preset artificially; after each isotropic compression test is completed, take out the specimen and place it in a ceramic basin, dry it in an oven and cool it to room temperature; S140. Conduct a screening test on each of the dried and cooled calcareous sand specimens obtained in S130 by the vibrating sieve method to obtain the particle size distribution curves under different confining pressure conditions; S150. Calculate the relative breakage rate under the isotropic compression test under different confining pressure conditions based on the particle size distribution curves under different confining pressure conditions obtained in S140.

4. The rapid prediction method for the particle size distribution curve of calcareous sand under different loading paths according to claim 1, characterized in that: S200 specifically includes the following steps: S210. Prepare multiple samples of the calcareous sand for the compression test under different loading paths; each sample of the calcareous sand has the same initial gradation as that in S100, the same initial void ratio, the same sample preparation method, and the same saturation method; S220. After the samples of the calcareous sand in S210 are saturated, first conduct the isotropic compression test under different confining pressures through a stress path triaxial apparatus; S230. After the samples of the calcareous sand in S220 complete the isotropic compression test under the corresponding confining pressure, conduct the conventional triaxial compression path test, the triaxial compression test with a constant mean principal stress, and the decompression triaxial compression test under the corresponding confining pressure respectively; S240. For each of the conventional triaxial compression path test, the triaxial compression test with a constant mean principal stress, and the decompression triaxial compression test in S230, take no less than 3 samples for each loading path compression test and conduct the loading path compression test under different artificially preset confining pressures; then respectively obtain the values of the mean effective principal stress, deviator stress, volumetric change, and axial strain of each sample of the calcareous sand under different confining pressure conditions in the conventional triaxial compression path test, the triaxial compression test with a constant mean principal stress, and the decompression triaxial compression test; S250. Calculate the total input energy in the shear stage of the calcareous sand samples under the conventional triaxial compression path test, the triaxial compression test with a constant mean principal stress, and the decompression triaxial compression test respectively; specifically expressed by the following formula: W = ∫pdε v +qdε s Where: W is the total input energy; p is the average effective principal stress; q is the deviator stress; ε v is the volumetric strain; ε s is the shear strain, expressed by the following formula: Where: ε1 is the axial strain; S260. After each test in S240 is completed, carefully take out the calcareous sand samples and place them in a ceramic basin, dry them in an oven and then cool them to room temperature; S270. For the dried and cooled calcareous sand samples obtained in S260, conduct the screening test one by one using the vibrating sieve method, and respectively obtain the particle size distribution curves under different confining pressure conditions in the conventional triaxial compression path test, the triaxial compression test with a constant mean principal stress, and the decompression triaxial compression test; S280. Calculate the relative breakage rate under different loading paths based on the particle size distribution curves under different confining pressure conditions in the conventional triaxial compression path test, the triaxial compression test with a constant mean principal stress, and the decompression triaxial compression test obtained in S270; then deduct the relative breakage rate under the isotropic compression test under different loading path compression tests, and calculate the relative breakage rate in the shear stage of the calcareous sand samples under different loading paths; specifically expressed by the following formula: B rq = B rc -B rh Where: B rc is the relative breakage ratio under the different loading paths; B rq is the relative breakage ratio during the shear stage of the calcareous sand specimen under the different loading paths; B rh is the relative breakage ratio under the isotropic compression test under the different confining pressure conditions.

5. The rapid prediction method for the particle size distribution curve of calcareous sand under different loading paths according to claim 1, characterized in that: In S300, the characteristic particle sizes include the limiting particle size, intermediate particle size, median particle size, and effective particle size. Through the particle size distribution curves under different loading paths, obtain the limiting particle size, intermediate particle size, median particle size, and effective particle size under different confining pressure conditions respectively.

6. The rapid prediction method for the particle size distribution curve of calcareous sand under different loading paths according to claim 1, characterized in that: In S400, the rapid prediction equation is obtained according to the following steps: Sa410. Plot the scatter diagram of the data on the characteristic particle size and the relative breakage rate at the shear stage of the calcareous sand specimen under different loading paths in a rectangular coordinate system; the data fitting method is expressed by the following formula: where: d 0i , d 1i and d 2i are all fitting parameters; Sa420. Obtain the rapid prediction equation according to the fitting parameters.

7. The rapid prediction method for the particle size distribution curve of calcareous sand under different loading paths according to claim 1, characterized in that: In S400, the rapid prediction equation is obtained according to the following steps: Sb410. Plot the scatter diagram of the data on the characteristic particle size and the total input energy at the shear stage under each loading path in a rectangular coordinate system; the data fitting method is expressed by the following formula: Sb420. Obtain the rapid prediction equation according to the fitting parameters.

8. The rapid prediction method for the particle size distribution curve of calcareous sand under different loading paths according to claim 6, characterized in that: The relative breakage rate at the shear stage of the calcareous sand specimen under different loading paths is expressed by the following formula: where: a, b, v, m, and n are all fitting parameters; q max is the maximum value of the deviatoric stress under each loading path; B rh is the relative breakage rate under the isotropic compression test under the different confining pressure conditions.

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