Method for correcting the relative density of coral sand

Abstract

The embodiment of the application relates to the technical field of geotechnical engineering test, and particularly relates to a correction method for determining the relative density of coral sand, which comprises the following steps: determining a plurality of maximum pore ratios by using a grading-decreasing preparation energy, extrapolating to zero energy, and obtaining a real maximum pore ratio; determining a plurality of minimum pore ratios by using a grading-decreasing vibration time length, extrapolating to zero time length, and obtaining a real minimum pore ratio; determining an inner porosity and converting the inner pore ratio, and obtaining an effective pore ratio by deducting the total pore ratio; taking the difference between the real maximum pore ratio and the minimum pore ratio as a benchmark, taking the difference between the effective pore ratio and the minimum pore ratio as a deviation, calculating a ratio, and determining an effective relative density. The application realizes accurate determination of the real effective relative density of the coral sand by eliminating the interference of the preparation energy, the vibration time length and the inner pore of the particles on the determination result.

Description

Technical Field

[0001] This application relates to the field of geotechnical engineering testing technology, and in particular to a corrected method for determining the relative density of coral sand. Background Technology

[0002] relative density Relative density is a core indicator for evaluating the compaction of cohesionless soils and is widely used in the engineering classification and mechanical property evaluation of coarse-grained soils such as sand and gravel. The definition of relative density is... ,in For maximum void ratio, Minimum void ratio, This refers to the natural void ratio. The current national standard "Standard for Geotechnical Testing Methods" GB / T50123-2019 specifies the standard methods for determining the maximum and minimum void ratios: the maximum void ratio is determined by the funnel method or the graduated cylinder loose sand method, and the minimum void ratio is determined by the vibration hammer method or the dry vibration method.

[0003] However, coral sand is a calcium carbonate sand formed from the broken, transported, and deposited skeletons of marine organisms, and its particles exhibit significant engineering geological characteristics such as porosity, high brittleness, and low strength. Directly applying the GB / T50123-2019 standard method to determine the relative density of coral sand has the following four technical shortcomings:

[0004] First, the standard method does not consider the systematic impact of particle breakage during the determination process on the determination of the limiting void ratio. In the funnel method determination... When sand grains fall freely from a certain height and impact the bottom of the sample container or the surface of accumulated sand, the impact causes the grains to break, and the measured... It is actually the larger void ratio after "crushing," not the true maximum void ratio of the original graded sand sample; this is determined by the dry vibration method or the hammer impact method. At that time, the vibration or hammering energy further breaks down the particles, rounds their edges, and fills the pores, as measured. This also deviates from the true minimum void ratio of the original graded sand sample. Because The measured value is too small. The measured value was too high (relative to the original gradation), causing the calculation according to the standard method to be incorrect. The systemic error is too high and cannot accurately reflect the density of the coral sand.

[0005] Second, the standard method fails to distinguish between skeletal porosity and intraparticle porosity, causing relative density to not reflect the true particle compaction. Coral sand particles contain numerous closed or semi-closed pores (internal pores) left over from biological skeletal structures. These internal pores do not participate in interparticle mechanical transfer or pore water flow. However, in conventional volume-mass porosity determination, the volume of internal pores is included in the total volume, leading to an inaccurate calculation based on the total porosity. The actual density of the coral sand's skeletal structure was underestimated. In engineering practice, this can lead to misjudgments of the bearing capacity and deformation characteristics of coral sand foundations.

[0006] Third, the standard method does not consider the impact of gradation variations on the comparability of relative density evaluation results. Coral sand with different initial gradations will have different relative densities even if measured. Similarly, due to different evolution paths after crushing, their mechanical properties (such as internal friction angle, compressibility, and permeability coefficient) may also differ significantly. Using a single... The index cannot distinguish the differences in mechanical behavior caused by gradation differences, which reduces the reliability of relative density as an engineering evaluation index.

[0007] Fourth, standard methods lack evaluation tools for the long-term mechanical stability of coral sand. Coral sand undergoes continuous particle breakage and gradation adjustment under load, and its mechanical properties evolve over time or the load history. Standard methods only provide information on the instantaneous state. The test results cannot evaluate the breakage stability trend of coral sand under long-term load or vibration and its impact on the long-term safety of the project.

[0008] In summary, the existing GB / T50123-2019 standard method, when applied to the determination of relative density of coral sand, suffers from technical problems such as measurement distortion due to particle breakage, underestimation of density due to failure to deduct internal porosity, incomparability of evaluation results due to changes in gradation, and lack of long-term stability evaluation methods. There is an urgent need for a relative density correction method specifically designed for the engineering characteristics of coral sand. Summary of the Invention

[0009] Therefore, the present invention provides a corrected method for determining the relative density of coral sand, which overcomes the problem of inaccurate relative density determination results of coral sand caused by the influence of preparation energy, vibration time and internal porosity of particles in the prior art.

[0010] To achieve the above objectives, this invention provides a corrected method for determining the relative density of coral sand. It includes:

[0011] Step S1: The maximum porosity of coral sand under different preparation energies is determined using the funnel method with controlled drop height. A linear relationship between the maximum porosity and the preparation energy is established, and this linear relationship is extrapolated to a state where the preparation energy is zero to obtain the true maximum porosity. ;

[0012] Step S2: The minimum porosity of coral sand under different vibration durations is determined using the dry vibration method with controllable vibration time. An exponential decay relationship between the minimum porosity and the vibration duration is established. This relationship is then extrapolated to a state where the vibration duration is zero to obtain the true minimum porosity. ;

[0013] Step S3: Determine the internal porosity of the coral sand particles. Calculate the internal porosity ratio And based on the total porosity Calculate the effective void ratio ;

[0014] Step S4, based on the true maximum porosity The true minimum porosity and the effective porosity ratio Calculate the effective relative density .

[0015] Furthermore, in step S1, a funnel method with controllable drop height is used to control the preparation energy by adjusting the drop height. The maximum porosity of the coral sand at different preparation energies is measured, and a linear relationship between the maximum porosity and the preparation energy is established.

[0016] ;

[0017] in, For maximum void ratio, To generate energy, This represents the true maximum void ratio. The attenuation coefficient is the maximum porosity.

[0018] The linear relationship is then extrapolated to a preparation energy of zero to obtain the true maximum porosity.

[0019] Furthermore, in step S2, a dry vibration method with controllable vibration time is used to determine the minimum porosity of coral sand under different vibration durations, and an exponential decay relationship between the minimum porosity and the vibration duration is established:

[0020] ;

[0021] in, Minimum void ratio, For the duration of vibration, To represent the true minimum void ratio, The minimum porosity in steady state is given by τ, which is the characteristic time constant.

[0022] The exponential decay relationship is then extrapolated to a vibration duration of zero to obtain the true minimum porosity. .

[0023] Furthermore, in step S3, the method for determining the internal porosity of the coral sand includes mercury infiltration or gas adsorption.

[0024] The internal porosity ratio Calculate using the following formula:

[0025] ;

[0026] in, Internal porosity Gs represents the internal porosity of the coral sand and the specific gravity of the coral sand particles.

[0027] The effective porosity Calculate using the following formula:

[0028] ;

[0029] in, For the effective porosity, The total porosity of the coral sand is denoted as .

[0030] Further, in step S4, the effective relative density Calculate using the following formula:

[0031] ;

[0032] in, For effective relative density, This is the true maximum porosity. This is the true minimum porosity. The effective porosity is denoted as .

[0033] Furthermore, it also includes:

[0034] Coral sand was subjected to standard vibration until the particles broke and stabilized. The maximum and minimum porosity in the steady state were measured, and the relative density in the steady state was calculated.

[0035] ;

[0036] in, For the steady-state relative density, The maximum porosity in the steady state is [value missing]. The minimum porosity in the steady state is given. Natural porosity;

[0037] The long-term mechanical stability of coral sand is evaluated based on the steady-state relative density.

[0038] Furthermore, it also includes:

[0039] Calculate the porosity index:

[0040] ;

[0041] in, Porosity index Natural porosity This is the true minimum porosity. This is the true maximum porosity;

[0042] The density of coral sand is evaluated based on the porosity index.

[0043] Furthermore, it also includes:

[0044] Calculate the breakage impact index:

[0045] ;

[0046] Wherein, BI stands for Fragmentation Impact Index. To measure the breakage rate, Maximum breakage rate;

[0047] The density of coral sand is evaluated based on the aforementioned fragmentation impact index.

[0048] Furthermore, it also includes conducting at least three parallel measurements on the same coral sand sample and taking the average of the results as the final measurement value.

[0049] Furthermore, both the true maximum porosity and the true minimum porosity are output in dimensionless form, and the effective relative density is output as a percentage.

[0050] Compared with the prior art, the beneficial effects of the present invention are as follows: This embodiment establishes an exponential decay model between the minimum porosity and the vibration duration, and extrapolates the fitted curve to a state where the vibration duration is zero. This effectively eliminates the additional interference of input energy on the compaction of particle arrangement during vibration, avoiding the problem of the measurement results being too small due to the fixed vibration duration in conventional methods. At the same time, by combining multi-duration measurement with nonlinear fitting, the gradual compaction behavior of coral sand particles under vibration is fully considered. It can simultaneously obtain the true minimum porosity, the steady-state minimum porosity, and the characteristic time constant. This not only improves the accuracy and physical meaning of the minimum porosity measurement results, but also provides a reliable benchmark parameter for the subsequent calculation of effective relative density. Moreover, this method does not depend on the empirically selected vibration duration and has good repeatability and operational standardization.

[0051] Furthermore, in this embodiment, the internal porosity of coral sand particles is accurately determined by mercury infiltration or gas adsorption, and converted into internal porosity ratio. This internal porosity ratio is then subtracted from the overall total porosity ratio to obtain the effective porosity ratio, which characterizes the effective interconnected pores between particles. This effectively eliminates the influence of ineffective pores such as biological remains cavities inside coral sand particles on the relative density calculation, making the subsequent calculation of effective relative density more accurate and reliable, and its physical meaning clearer.

[0052] Furthermore, this embodiment eliminates the combined interference of preparation energy, vibration duration, and internal pores on the measurement results by substituting the true maximum and true minimum void ratios obtained through extrapolation correction with the effective void ratio after deducting internal pores into the effective relative density formula, and by combining consistency verification and correction mechanisms. This ensures that the calculated value of the effective relative density is strictly limited to a physically reasonable range of 0 to 1. Compared with conventional methods, this significantly improves the accuracy and physical rationality of the measurement, providing a more reliable parameter basis for the design and evaluation of coral sand foundation engineering.

[0053] Furthermore, this embodiment provides a quantitative indicator for evaluating the long-term mechanical stability of coral sand foundations by measuring the maximum and minimum porosity of the stable state of coral sand under particle breakage and stabilization, and calculating the stable relative density. This makes up for the deficiency of conventional relative density tests, which can only reflect the current state and cannot evaluate long-term stability, and provides important experimental basis for the long-term safe operation of coral sand island and reef projects. Attached Figure Description

[0054] Figure 1 This is a flowchart of the corrected method for determining the relative density of coral sand according to an embodiment of this application. Detailed Implementation

[0055] To make the objectives and advantages of the present invention clearer, the present invention will be further described below with reference to embodiments; it should be understood that the specific embodiments described herein are merely for explaining the present invention and are not intended to limit the present invention.

[0056] Preferred embodiments of the present invention will now be described with reference to the accompanying drawings. Those skilled in the art should understand that these embodiments are merely illustrative of the technical principles of the present invention and are not intended to limit the scope of protection of the present invention.

[0057] like Figure 1 As shown, Figure 1 This is a flowchart of the corrected method for determining the relative density of coral sand according to an embodiment of this application.

[0058] The technical solution provided in this application includes the following steps:

[0059] Step S1: The maximum porosity of coral sand under different preparation energies is determined using the funnel method with controlled drop height. A linear relationship between the maximum porosity and the preparation energy is established, and this linear relationship is extrapolated to a state where the preparation energy is zero to obtain the true maximum porosity. ;

[0060] Step S2: The minimum porosity of coral sand under different vibration durations is determined using the dry vibration method with controllable vibration time. An exponential decay relationship between the minimum porosity and the vibration duration is established. This relationship is then extrapolated to a state where the vibration duration is zero to obtain the true minimum porosity. ;

[0061] Step S3: Determine the internal porosity of the coral sand particles. Calculate the internal porosity ratio And based on the total porosity Calculate the effective void ratio ;

[0062] Step S4, based on the true maximum porosity The true minimum porosity and the effective porosity ratio Calculate the effective relative density .

[0063] Specifically, in step S1, a funnel method with controllable drop height is used. The preparation energy is controlled by adjusting the drop height, and the maximum porosity of the coral sand at different preparation energies is measured to establish a linear relationship between the maximum porosity and the preparation energy.

[0064] ;

[0065] in, For maximum void ratio, To generate energy, This represents the true maximum void ratio. The attenuation coefficient is the maximum porosity.

[0066] The linear relationship is then extrapolated to a preparation energy of zero to obtain the true maximum porosity.

[0067] In this embodiment, a coral sand sample taken from an island reef was selected, dried, and its particle specific gravity Gs was determined. The maximum porosity of the coral sand was determined using a funnel method with controlled drop height. The experimental setup included a height-adjustable funnel support, a standard funnel, and a sample container. The specific operating steps were as follows: the sample container was placed directly below the funnel outlet, and a certain mass of coral sand sample (e.g., 500g) was weighed. By adjusting the height of the funnel support, four different drop heights were set: 10mm, 20mm, 50mm, and 100mm. Under each drop height condition, the sample was slowly dropped into the sample container through the funnel. After dropping, the container opening was leveled with a scraper, the mass of the sample in the container was weighed, and the sample volume was measured. The maximum porosity corresponding to that drop height was calculated. Three parallel measurements were performed for each drop height condition, and the average value was taken as the maximum porosity at that drop height.

[0068] To fall high Characterization of preparation energy ( (Proportional to drop height), establishing the maximum porosity With energy production The linear relationship between them:

[0069] Linear fitting was performed on the measurement data under four drop height conditions using the least squares method to obtain the fitting parameters. and Extrapolating the preparation energy to (i.e., the drop height is zero) to obtain the true maximum void ratio. .

[0070] In this embodiment, the measured data are as follows: when the drop height is 10mm When the drop height is 20mm When the drop height is 50mm When the drop height is 100mm The linear fit yielded the following results. , The results show that the maximum porosity decreases linearly with increasing preparation energy. Extrapolating to a zero-energy state can effectively eliminate the interference of energy input on the porosity of particle arrangement during sample preparation and obtain the true porosity of the porosity state.

[0071] Specifically, in step S2, a dry vibration method with controllable vibration time is used to determine the minimum porosity of coral sand under different vibration durations, and an exponential decay relationship between the minimum porosity and the vibration duration is established:

[0072] ;

[0073] in, Minimum void ratio, For the duration of vibration, To represent the true minimum void ratio, The minimum porosity in steady state is given by τ, which is the characteristic time constant.

[0074] The exponential decay relationship is then extrapolated to a vibration duration of zero to obtain the true minimum porosity. .

[0075] In this embodiment, the minimum porosity of coral sand is determined using a dry vibration method with controllable vibration time. The same batch of coral sand samples is used as in step S1 to ensure consistency in basic physical properties such as particle size distribution, water content, and particle specific gravity. The experimental setup mainly includes an electromagnetic vibration table, a vibration container, a timing controller, and an amplitude adjustment module. The vibration table applies sinusoidal vibration in the vertical direction, with a fixed vibration frequency of 50Hz and an amplitude set to 2mm via the amplitude adjustment module. The timing controller precisely controls the vibration duration, with a settable range of 0.1min to 60min and an accuracy of ±0.1min. The vibration container is a rigid cylinder with a smooth inner wall, its bottom fixed to the vibration table surface. The container has an inner diameter of 100mm and a height of 150mm.

[0076] The specific operating steps are as follows: Weigh a certain mass (approximately 1000g) of coral sand sample and evenly fill it into the vibration container. Avoid tamping the sample during filling; allow it to accumulate naturally by gravity. Fix the vibration container on the vibration table, turn on the vibration table and simultaneously start the timing controller. Set six different vibration durations: 0.5min, 1min, 2min, 5min, 10min, and 20min, covering the complete process from short-term to long-term vibration to ensure the reliability of the fitting extrapolation.

[0077] Under each vibration duration, the vibration table was immediately shut off after vibration ended. Once the sample had stabilized, the height of the sample inside the vibration container was measured, and the total volume of the sample was calculated based on the container's cross-sectional area. Simultaneously, the mass of the sample inside the container was weighed. The minimum porosity ratio corresponding to that vibration duration was calculated from the sample mass and the total volume. After each vibration cycle, a new sample is used for the next vibration duration test to avoid the cumulative effect of repeated vibration of the same sample. Three parallel measurements are performed under each vibration duration condition, and the average value is taken as the minimum porosity under that vibration duration.

[0078] Based on vibration duration The x-axis represents the minimum void ratio. A scatter plot was drawn with the vertical axis as the ordinate. Observations revealed that in the initial stage of vibration (0.5 min to 2 min), the void ratio decreased rapidly with increasing vibration duration, indicating that the particles quickly rearranged and compacted under vibration. In the middle stage of vibration (2 min to 10 min), the rate of decrease in void ratio gradually slowed down. In the later stage of vibration (10 min to 20 min), the void ratio tended to stabilize, and further extending the vibration duration had very limited effect on the void ratio, which is consistent with the exponential decay law.

[0079] Based on the above principles, a minimum void ratio is established. With vibration duration The exponential decay fitting relationship between them:

[0080] ;

[0081] in, Vibration duration The corresponding minimum porosity; The duration of vibration; The true minimum void ratio is the void ratio extrapolated to the point where the vibration duration is zero, representing the initial compact state before being disturbed by vibration energy. The minimum porosity in the steady state is the porosity when the vibration duration approaches infinity, representing the final stable and dense state reached by the particles under full vibration; τ is the characteristic time constant, reflecting the rate at which the porosity decreases with the vibration duration. The smaller the value of τ, the easier it is for the particles to reach a dense state in a short time.

[0082] The Levenberg-Marquardt nonlinear least squares algorithm was used to fit the measured data under six vibration duration conditions. The goal was to minimize the sum of squared residuals, and the fitting parameters were obtained by iterative solution. , And the best estimate of τ. Extrapolate the vibration duration to To obtain the true minimum porosity, we need to determine the state of the void ratio. This extrapolated value eliminates the interference of energy input during vibration on the density of particle arrangement and reflects the intrinsic minimum porosity of particles under the action of vibrational energy.

[0083] This embodiment establishes an exponential decay model between the minimum porosity and vibration duration, and extrapolates the fitted curve to a state where the vibration duration is zero. This effectively eliminates the additional interference of input energy during vibration on the compaction of particle arrangement, avoiding the problem of conventional methods where the measured results are too small due to fixed vibration duration. At the same time, by combining multi-duration measurement with nonlinear fitting, it fully considers the gradual compaction behavior of coral sand particles under vibration, and can simultaneously obtain the true minimum porosity, steady-state minimum porosity, and characteristic time constant. This not only improves the accuracy and physical meaning of the minimum porosity measurement results, but also provides a reliable benchmark parameter for the subsequent calculation of effective relative density. Moreover, this method does not depend on the empirically selected vibration duration and has good repeatability and operational standardization.

[0084] Specifically, in step S3, the method for determining the internal porosity of the coral sand includes mercury infiltration or gas adsorption.

[0085] The internal porosity ratio Calculate using the following formula:

[0086] ;

[0087] in, Internal porosity Gs represents the internal porosity of the coral sand and the specific gravity of the coral sand particles.

[0088] The effective porosity Calculate using the following formula:

[0089] ;

[0090] in, For the effective porosity, The total porosity of the coral sand is denoted as .

[0091] In this embodiment, the internal porosity of coral sand particles is determined using the mercury infiltration method. Coral sand, as a biogenic granular material, has numerous internal pores composed of cavities, holes, and microcracks formed by biological remains within its particles. These pores are located inside the particles and do not participate in fluid transport or mechanical contact between particles, but they are included in the pore volume in conventional total porosity measurements, leading to an overestimation of the effective porosity. Therefore, it is necessary to measure the internal porosity separately and deduct it from the total porosity.

[0092] The internal porosity of coral sand particles was determined using mercury intrusion porosimetry. The specific procedures are as follows: A coral sand sample with the same gradation as in steps S1 and S2 was taken, dried to constant weight in an oven at 105℃, cooled, and then sealed for storage. An AutoPore IV 9500 fully automated mercury intrusion porosimetry instrument was used for testing. The pressure range of this instrument is 0.001 MPa to 228 MPa, corresponding to a pore size measurement range of 0.003 μm to 1000 μm. Approximately 0.5 g of the dried sample was weighed and placed in a dilatometer. A vacuum was drawn to below 50 μmHg to remove adsorbed gases, and then mercury was injected. The pressure was gradually increased, and the volume of mercury entering the particles at different pressures was recorded. Based on the Washburn equation, a correlation was established between pressure and pore size; the cumulative volume of mercury entering the particles represents the internal pore volume. During the test, the low-pressure section (<0.5MPa) mainly fills the external pores between particles, while the high-pressure section (>0.5MPa) fills the tiny pores inside the particles. The internal pore volume can be obtained by distinguishing the amount of mercury entering in the high-pressure section, and the internal porosity is obtained by dividing it by the total sample volume. .

[0093] As an alternative, gas adsorption methods (such as...) can also be used. Adsorption method or The adsorption method is used to determine the internal porosity. This method is based on the adsorption isotherm of gas molecules on the particle surface, and uses BET or BJH theory to calculate the specific surface area and pore volume of micropores and mesopores inside the particle, which are then converted into internal porosity. For materials such as coral sand, which are mainly mesoporous and macroporous, the mercury infiltration method is more suitable. To ensure the representativeness and reliability of the measurement results, the following quality control measures are adopted: each sample is measured in triplicate, and the average value is taken as the final internal porosity; blank correction and volume correction are performed before each test; for pressure data, it is ensured that the mercury infiltration rate in the high-pressure section reaches a stable plateau, that is, the mercury infiltration rate no longer changes significantly after further increasing the pressure, to ensure that all accessible internal pores have been completely filled.

[0094] With internal porosity Based on this, convert the internal void ratio using the following formula. :

[0095] ;

[0096] in, Internal porosity Gs represents the internal porosity measured, and Gs represents the specific gravity of the coral sand particles measured in step S1. The basic principle of this formula is to convert the ratio of the internal pore volume to the solid skeleton volume of a unit mass of particle into a porosity form, and then correlate the volume with the mass through specific gravity.

[0097] In obtaining the internal porosity Then, the effective void ratio was further calculated. First, the overall total porosity of the coral sand sample was determined. The specific method is as follows: Weigh a certain mass of coral sand sample, and determine its apparent volume using conventional methods (such as volumetric method or immersion method). Calculate the overall total porosity from the sample mass, particle specific gravity, and apparent volume. The overall total porosity includes both interparticle porosity and intraparticle porosity. The intraparticle porosity is then subtracted using the following formula. To obtain the effective porosity :

[0098] ;

[0099] in, The effective porosity represents the volume percentage of interconnected pores between particles. This portion of pores is a key parameter that determines the engineering mechanical properties of coral sand, such as permeability, compressibility, and strength. The overall total porosity; It represents the internal porosity ratio.

[0100] In this embodiment, the mercury infiltration method showed that the internal porosity of the coral sand particles was... The percentage is approximately 12% to 25%, with the specific value closely related to the source, grain size, and biogenicity of the coral sand. Taking coral sand from a certain island reef as an example, actual measurements... Particle specific gravity Substituting into the formula, the internal porosity ratio is calculated. Overall total porosity The effective void ratio is 1.05, as determined by the volumetric method. .

[0101] In this embodiment, the internal porosity of coral sand particles is accurately determined by mercury infiltration or gas adsorption, and converted into an internal porosity ratio. This internal porosity ratio is then subtracted from the overall total porosity ratio to obtain the effective porosity ratio, which characterizes the effective interconnected pores between particles. This effectively eliminates the influence of ineffective pores such as biological remains cavities inside the coral sand particles on the relative density calculation, making the subsequent calculation of effective relative density more accurate and reliable, and its physical meaning clearer.

[0102] Specifically, in step S4, the effective relative density Calculate using the following formula:

[0103] ;

[0104] in, For effective relative density, This is the true maximum porosity. This is the true minimum porosity. The effective porosity.

[0105] In this embodiment, the true maximum porosity obtained by extrapolation using the controlled drop funnel method in step S1 is used. The true minimum porosity obtained by extrapolation using the controlled vibration duration method in step S2. And in step S3, the total porosity is reduced by the internal porosity. The resulting effective porosity Substitute into the effective relative density formula to calculate the effective relative density of coral sand. .

[0106] The calculation formula is:

[0107] ;

[0108] in, The effective relative density, expressed as a decimal or percentage, reflects the current effective porosity of the coral sand sample. The relative positions of the most loose and most compact states under the given conditions; The true maximum porosity represents the most porous state of coral sand when it is completely unaffected by the energy required for its preparation. The true minimum porosity represents the densest state of coral sand when it is completely free from vibrational energy disturbance; The effective porosity represents the effective interconnected porosity between particles after deducting the pores within the particles.

[0109] Effective relative density The physical meaning is: when near hour, Approaching 0 indicates that the sample is in a state close to its most porous; when near At that time, D r_eff A value close to 1 indicates that the sample is in a state close to its densest state. This value is between 0 and 1. The larger the value, the denser the coral sand, and its engineering mechanical properties (such as shear strength, compression modulus, etc.) are usually better.

[0110] In this embodiment, the parameters obtained in the preceding steps are substituted into the formula for calculation. Taking coral sand from a certain island reef as an example, the true maximum porosity is obtained by linear extrapolation in step S1. In step S2, the true minimum porosity is obtained by extrapolation through exponential decay. In step S3, the internal porosity is determined by mercury indentation method, and the effective porosity ratio is obtained after subtraction. Substituting into the formula, the effective relative density is calculated as follows:

[0111] ;

[0112] The calculated result is greater than 1, exceeding the theoretical range of 0 to 1. This indicates that the effective porosity (0.969) of the coral sand sample in its current state is lower than the extrapolated true minimum porosity (0.99), which is physically unreasonable. This may be because the extrapolated value of the true minimum porosity is affected by factors such as fitting accuracy and sample inhomogeneity, resulting in some deviation. To ensure the physical rationality of the effective relative density calculation results, this embodiment... and The measured values ​​are checked for consistency: if any... >1 or In the case of <0, then for and To improve extrapolation accuracy, the maximum value of the measured maximum void ratio and the minimum value of the measured minimum void ratio are taken as alternative boundary values, or the number of samples measured and fitted is increased.

[0113] After correction, the refitting results were obtained by adding vibration duration test points (adding three test points of 0.8 min, 3 min, and 15 min within the range of 0.5 min to 30 min). , Substitute into the formula:

[0114] ;

[0115] The effective relative density of the coral sand sample was finally obtained. That is, 90.2%, indicating that the sample is in a very dense state.

[0116] This embodiment eliminates the combined interference of preparation energy, vibration time, and internal pores on the measurement results by substituting the true maximum and true minimum void ratios obtained through extrapolation correction with the effective void ratio after deducting internal pores into the effective relative density formula, and combines consistency verification and correction mechanisms. This ensures that the calculated value of the effective relative density is strictly limited to a physically reasonable range of 0 to 1. Compared with conventional methods, this significantly improves the accuracy and physical rationality of the measurement, providing a more reliable parameter basis for the design and evaluation of coral sand foundation engineering.

[0117] Specifically, it also includes:

[0118] Coral sand was subjected to standard vibration until the particles broke and stabilized. The maximum and minimum porosity in the steady state were measured, and the relative density in the steady state was calculated.

[0119] ;

[0120] in, For the steady-state relative density, The maximum porosity in the steady state is [value missing]. The minimum porosity in the steady state is given. Natural porosity;

[0121] The long-term mechanical stability of coral sand is evaluated based on the steady-state relative density.

[0122] In this embodiment, to further evaluate the mechanical stability of coral sand during long-term service, the embodiment also includes a step of subjecting the coral sand to standard vibration until the particles are stable due to breakage. Coral sand, as a biogenic brittle granular material, is prone to particle breakage under long-term loading or cyclic dynamic action. After breakage, fine particles fill the gaps between coarse particles, leading to changes in particle size distribution and a redistribution of porosity, which in turn affects the long-term settlement and stability of the foundation. Therefore, determining the steady-state relative density of coral sand in a particle breakage-stable state is of great significance for evaluating its long-term mechanical stability.

[0123] The specific operating steps are as follows: Take a coral sand sample with the same gradation as in the previous steps, place it in a vibration container, and apply continuous standard vibration to the sample using an electromagnetic vibration table. The vibration frequency is fixed at 50Hz, and the amplitude is set at 3mm. These vibration parameters have been verified through preliminary tests to enable the coral sand particles to reach a sufficiently stable state of fragmentation in a relatively short time. The vibration duration is set at 60min. Preliminary tests show that under this duration, the fragmentation rate of the coral sand particles tends to stabilize with the increase of vibration duration. When the vibration duration is further extended (e.g., to 120min), the increase in the fragmentation rate does not exceed 2%, which indicates that the particles have reached a stable state of fragmentation.

[0124] After vibration, the vibrated sample was sieved for analysis. The particle size distribution curve after vibration was measured and compared with the initial gradation before vibration. The particle breakage rate Br was calculated. If the change in breakage rate is less than 1% in two consecutive sampling measurements taken 10 minutes apart, the particles are considered to have reached a stable breakage state.

[0125] Under the stable state of particle crushing, the maximum porosity in the steady state was determined using the controlled drop funnel method, the same as in step S1. That is, the maximum porosity was measured under different drop heights and extrapolated to the point where the preparation energy was zero to obtain the maximum porosity in the steady state. Simultaneously, the minimum porosity in the steady state was determined using the same controlled vibration duration dry vibration method as in step S2. That is, the minimum porosity is determined under multiple vibration duration conditions and extrapolated to the vibration duration of zero to obtain the minimum porosity under steady state.

[0126] Determination of the natural porosity of coral sand samples in their natural state The specific method is as follows: while taking samples in situ on site, the natural density and water content of the coral sand are determined using the ring cutter method or sand filling method, and the natural porosity is calculated in combination with the particle specific gravity. .

[0127] The above measured steady-state maximum porosity minimum porosity in steady state Compared to natural porosity Substituting into the steady-state relative density formula:

[0128] ;

[0129] in, The relative density in the steady state is expressed as a decimal or percentage, reflecting the position of the natural density of coral sand in the stable state of particle breakage relative to the loosest and densest steady state. The maximum porosity in the steady state represents the most porous state of coral sand after the particles have been broken down and stabilized. The minimum porosity in the steady state represents the densest state of coral sand after the particles have been broken down and stabilized. It is the natural porosity.

[0130] steady-state relative density The physical significance lies in the fact that it reflects the dense state of coral sand after it has undergone sufficient particle breakage. If... A higher value (e.g., greater than 0.7) indicates that coral sand in its natural state can maintain a relatively dense structure even after the particles are broken, resulting in good long-term mechanical stability and making it less prone to significant settlement or strength reduction under cyclic loading; conversely, if... A low value (e.g., less than 0.4) indicates that the coral sand tends to be loose after the particles are broken, resulting in poor long-term mechanical stability and a greater risk of settling or liquefaction during long-term service.

[0131] The evaluation criteria based on steady-state relative density are as follows: when When the value is ≥0.70, the long-term stability is considered good; when 0.50≤ When <0.70, the long-term stability is rated as moderate; when At that time, the evaluation indicated poor long-term stability, and it was recommended to take foundation reinforcement measures.

[0132] In this embodiment, taking coral sand from a certain island reef as an example, after standard vibration until the particles are broken and stabilized, the maximum porosity in the stable state is measured. minimum porosity in steady state Natural porosity Substituting into the formula, the steady-state relative density is calculated as follows:

[0133] ;

[0134] The results show that the stable relative density of the coral sand under the stable state of particle breakage is 82.5%, which is in the range of good long-term stability. That is, even if the particles break under long-term cyclic loading, the coral sand can still maintain a relatively dense structural state and is not prone to significant additional settlement, thus exhibiting good engineering mechanical stability.

[0135] For comparison, if the test result of a certain coral sand sample is If the result is negative, it indicates that the structure of the sample tends to be loose after the particles are crushed, and the long-term stability is poor. The risk of settlement caused by particle crushing should be fully considered in the engineering design, and it is recommended to take reinforcement measures such as vibratory compaction or replacement.

[0136] This embodiment measures the maximum and minimum porosity of coral sand under stable particle breakage conditions and calculates the relative density of the stable state. This provides a quantitative indicator for evaluating the long-term mechanical stability of coral sand foundations, making up for the deficiency of conventional relative density tests, which can only reflect the current state and cannot evaluate long-term stability. This provides important experimental basis for the long-term safe operation of coral sand island and reef projects.

[0137] Specifically, it also includes:

[0138] Calculate the porosity index:

[0139] ;

[0140] in, Porosity index Natural porosity This is the true minimum porosity. This is the true maximum porosity;

[0141] The density of coral sand is evaluated based on the porosity index.

[0142] In this embodiment, the true maximum porosity obtained by extrapolation in step S1 is used. The true minimum porosity obtained by extrapolation in step S2 And the natural porosity of the coral sand measured on-site. Substitute into the porosity index formula Calculate the porosity index of coral sand. .in, The natural density and moisture content of coral sand were determined by on-site ring sampling combined with indoor tests, and then calculated based on the particle specific gravity Gs. Expressed as a decimal, it reflects the relative density of coral sand in its natural state compared to its true most porous and true densest states. This value ranges between 0 and 1; the smaller the value, the denser the coral sand. Based on... The evaluation criteria are: It is in a dense state. It is in a medium-dense state. It is in a loose state. If it appears or For any physical inconsistencies, truncate them to 0 or 1 for evaluation.

[0143] Specifically, it also includes:

[0144] Calculate the breakage impact index:

[0145] ;

[0146] Wherein, BI stands for Fragmentation Impact Index. To measure the breakage rate, Maximum breakage rate;

[0147] The density of coral sand is evaluated based on the aforementioned fragmentation impact index.

[0148] In this embodiment, the measured breakage rate is... and maximum breakage rate Substitute into the formula for the impact index of breakage The fragmentation impact index (BI) of coral sand was calculated. Among them, The percentage of the total mass of the sample containing fine particles with a diameter less than 0.075 mm after standard vibration until the particles have broken and stabilized is represented. BI represents the maximum percentage of particles of this size after the same batch of samples has been fully crushed by manual grinding. BI is expressed as a decimal, with values ​​between 0 and 1. A larger value indicates weaker resistance to breakage and higher sensitivity to particle breakage in the coral sand. The evaluation criteria based on BI are: BI < 0.3 indicates strong resistance to breakage, 0.3 ≤ BI < 0.6 indicates moderate resistance to breakage, and BI ≥ ​​0.6 indicates weak resistance to breakage.

[0149] Among them, the relative density of the steady state The introduction of the fragmentation impact index BI aims to quantify the degree of gradation evolution caused by particle fragmentation, based on the relative density at the end of fragmentation. This method evaluates the mechanical stability of coral sand under long-term loads, thus solving the problem that standard methods cannot take into account gradation changes and long-term stability.

[0150] Specifically, this also includes conducting at least three parallel measurements on the same coral sand sample and taking the average of the results as the final value.

[0151] Specifically, the true maximum porosity and the true minimum porosity are both output in dimensionless form, and the effective relative density is output in percentage form.

[0152] In this embodiment, to ensure the reliability and repeatability of the measurement results, at least three parallel measurements are performed on the same coral sand sample under the same test conditions. The arithmetic mean of the results is taken as the final measured value of the parameter. Parallel measurements are applicable to various key parameters, including but not limited to the maximum void ratio under various drop height conditions, the minimum void ratio under various vibration duration conditions, internal porosity, natural void ratio, steady-state void ratio, and measured breakage rate. The same batch of samples is used for each measurement to ensure sample consistency. When the relative standard deviation (the ratio of standard deviation to mean) of a set of parallel measurement results exceeds 5%, it is considered that the measurement results are too volatile. The consistency of the test operation should be checked, outliers should be eliminated, and supplementary measurements should be performed until the relative standard deviation is controlled within 5%.

[0153] Regarding data output, all porosity-related parameters (including the true maximum porosity) True minimum porosity Effective porosity Maximum porosity in steady state minimum porosity in steady state Natural porosity Internal porosity Overall total porosity All (etc.) are output in dimensionless decimal form, retaining three significant figures; effective relative density and steady-state relative density Output as a percentage, rounded to one decimal place and accompanied by a "%" sign; porosity index The breakage impact index (BI) is output in decimal form, retaining two decimal places. All data are recorded uniformly in the test data table, noting the corresponding sample number, test date, and test conditions to ensure data traceability. Average values ​​from parallel measurements effectively reduce the impact of random errors and operational biases on the test results. Standardized data output format ensures consistent expression of test results, facilitating comparison and evaluation in engineering applications.

[0154] Example 1: This example uses coral sand from an island reef project in the South China Sea as the test object. The relative density is measured using the modified measurement method proposed in this invention, and the results are compared and analyzed with those of the standard method in GB / T50123-2019.

[0155] 1. Experimental materials;

[0156] The coral sand used in the experiment was taken from an island reef in the South China Sea, and its main component was aragonite-based calcium carbonate. The particle specific gravity Gs was measured to be 2.78, and the coefficient of uniformity was [not specified]. curvature coefficient It is a well-graded sandy soil. The initial state of the sample was air-dried and loose.

[0157] 2. True maximum void ratio The determination;

[0158] Using the funnel method with controllable drop height, the drop height h is set respectively. i Four levels were used: 10mm, 20mm, 50mm, and 100mm. Following the funnel method procedure specified in GB / T50123-2019, the maximum void ratio was measured at each drop height, with three parallel measurements taken at each height and the average value recorded. Energy preparation... According to the formula An approximate characterization is used, where m is the mass of sand falling per unit area and g is the acceleration due to gravity. The measurement results are as follows:

[0159]

[0160] To prepare relative energy values The x-axis represents the measurement of the maximum void ratio. A scatter plot was created with the vertical axis as the ordinate, and a linear regression was used to fit the relationship:

[0161] ;

[0162] Coefficient of determination The linear relationship is significant. Extrapolating the above equation to E=0 yields the true maximum porosity. .

[0163] In comparison, the maximum void ratio measured using the GB / T50123-2019 standard method with a fixed drop height (approximately 70 mm) was 1.162. This value is significantly lower than the true maximum void ratio due to particle breakage. The relative deviation is -11.4%.

[0164] 3. True minimum void ratio The determination;

[0165] The dry vibration method with controllable vibration time was adopted, and the vibration duration was set respectively. Four vibration levels were set for 1 min, 2 min, 5 min, and 10 min. The vibration frequency was set to 50 Hz, and the amplitude was set to 0.5 mm. Following the dry vibration method procedure specified in GB / T50123-2019, the minimum porosity was measured at each vibration duration, with three parallel measurements taken at each duration and the average value calculated. The measurement results are as follows:

[0166]

[0167] Based on vibration duration The x-axis represents the determination of the minimum void ratio. A scatter plot was created with the vertical axis as the ordinate, and the relationship was obtained by fitting the data using an exponential decay model:

[0168] ;

[0169] Coefficient of determination The model is significant. Extrapolating the above equation to t=0 yields the true minimum void ratio. The steady-state minimum porosity obtained by fitting. The characteristic time constant τ = 6.8 min.

[0170] In comparison, the minimum porosity measured using the GB / T50123-2019 standard method with a fixed vibration duration (approximately 10 minutes) was 0.998. This value is significantly higher than the true minimum porosity due to particle breakage. The relative deviation is +12.8%.

[0171] 4. Measurement of internal porosity and calculation of effective porosity ratio;

[0172] The specific surface area and pore size distribution of coral sand particles were determined using the Bioturbidimetric Evolution (BET) method, and the porosity within the particles was calculated. Internal porosity According to the formula

[0173] .

[0174] Take the total porosity of natural coral sand Then the effective porosity .

[0175] 5. Calculation and comparative analysis of effective relative density;

[0176] Calculate the effective relative density based on the true limiting void ratio and the effective void ratio:

[0177]

[0178] =(1.312-0.830) / (1.312-0.885)=0.482 / 0.427=1.129.

[0179] because A calculated value greater than 1.0 indicates that the sample was in an extremely dense state when evaluated based on the total porosity ratio. The effective porosity ratio was verified. Slightly smaller than the true minimum porosity The difference is within the experimental error range, indicating that the natural coral sand is in an extremely dense state.

[0180] For comparison, the relative density calculated according to the standard method of GB / T50123-2019 is:

[0181] D r = (1.162 - 1.050) / (1.162 - 0.998) = 0.112 / 0.164 = 0.683;

[0182] Comparative analysis shows that: D calculated by the standard method r =0.683 indicates a medium-dense state, while the method of this invention evaluates the sample to be in an extremely dense state. The main reason for this difference is that the standard method measures... Small Too large, resulting in a denominator Significantly smaller (0.164 vs. true value 0.427), while the molecule It is also relatively small (0.112 vs. the actual effective value of 0.482); among which, the stated The maximum void ratio determined according to the standard method (i.e., 1.162 in the above formula) is the... The minimum void ratio determined according to standard methods (i.e., 0.998 in the above formula); The natural porosity of the coral sand sample is 1.050 (as calculated in the above formula). Overall, the standard method has a serious bias in determining the density of coral sand, which may lead to conservative or dangerous engineering designs.

[0183] 6. Steady-state relative density and long-term stability evaluation;

[0184] The above samples were subjected to standard vibration until the particles broke down and stabilized (vibration time extended to 60 min, porosity change rate less than 0.5% / h), and the maximum porosity in the steady state was measured. minimum porosity in steady state Calculate the steady-state relative density:

[0185]

[0186] =(1.095-1.050) / (1.095-1.025)=0.045 / 0.070=0.643;

[0187] This indicates that the coral sand will evolve towards a medium-dense state under long-term vibration load, and its mechanical stability is generally poor. The strength and deformation attenuation under long-term load should be considered in the engineering design.

[0188] Example 2: This example uses multiple groups of coral sand samples with different initial densities to verify the applicability and evaluation consistency of the method of the present invention under different densities.

[0189] 1. Sample preparation;

[0190] Using the same batch of South China Sea coral sand as in Example 1, five groups of samples with different densities were prepared by controlling the number of compactions, numbered S1 to S5. The total porosity of each group of samples was... The measured values ​​were 1.250, 1.150, 1.050, 0.950, and 0.880, respectively.

[0191] 2. Determination of ultimate void ratio correction;

[0192] Following the controlled drop funnel method and controlled vibration time dry vibration method described in Example 1, the true maximum porosity and true minimum porosity of each group of samples were determined. Since the limiting porosity is an inherent property of the material and is independent of the current compaction state of the sample, the true maximum porosity and true minimum porosity of each group of samples were determined. and The test results are consistent: , (Same as Example 1).

[0193] 3. Calculation of effective void ratio and effective relative density;

[0194] Internal porosity of each group of samples same Effective porosity Effective relative density of each group of samples The calculation results are as follows:

[0195]

[0196] Analysis of the data in the table above shows:

[0197] (1) For loose sample S1, the method of the present invention determines that it is in a medium-dense state. Standard methods classify it as an extremely loose state. The standard method significantly underestimates the density of the sample.

[0198] (2) For the medium-dense sample S2, the method of the present invention determines that it is in a dense state. Standard methods classify it as a loose state. The evaluation results show significant bias.

[0199] (3) For relatively dense samples S3~S5, both methods determine them to be in a dense to extremely dense state, but the standard method calculates... Outliers greater than 1.0 (S4, S5) appeared, while the method of this invention... Although it is also greater than 1.0, its calculation logic based on the true limiting void ratio and the effective void ratio is more rigorous, and the outlier amplitude is smaller.

[0200] (4) When the calculated value using the standard method is abnormally greater than 1, the root cause lies in the measurement performed by the standard method. The effective porosity (0.998) is higher than the actual porosity of samples S4 and S5, which is physically unreasonable; however, the method of this invention is based on the true limiting porosity, and the effective porosity is calculated accordingly. Always not lower than the true minimum porosity This ensures the physical rationality of the evaluation results.

[0201] 4. Calculation of porosity index and crushing effect index;

[0202] Taking sample S3 as an example, calculate the porosity index. And the fragmentation impact index BI:

[0203] Porosity index:

[0204] ;

[0205] This value is related to the effective relative density. There is a conversion relationship: when When <0.5, the corresponding A value >0.5 indicates a dense state.

[0206] Fragmentation Impact Index ,in The breakage rate of the sample under standard vibration conditions. This represents the maximum breakage rate when the sample is completely crushed. The breakage rate of sample S3 after 10 minutes of standard vibration was determined by particle analysis. =12.5%, =28.0%, then . This indicates that the sample exhibits relatively low breakage under standard vibration conditions and good gradation stability.

[0207] The above embodiments are merely illustrative examples and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations. However, obvious variations or modifications derived therefrom are still within the scope of protection of this application.

Claims

1. A corrected method for determining the relative density of coral sand, characterized in that, include: Step S1: The maximum porosity of coral sand under different preparation energies is determined using the funnel method with controlled drop height. A linear relationship between the maximum porosity and the preparation energy is established, and this linear relationship is extrapolated to a state where the preparation energy is zero to obtain the true maximum porosity. ; Step S2: The minimum porosity of coral sand under different vibration durations is determined using the dry vibration method with controllable vibration time. An exponential decay relationship between the minimum porosity and the vibration duration is established. This relationship is then extrapolated to a state where the vibration duration is zero to obtain the true minimum porosity. ; Step S3: Determine the internal porosity of the coral sand particles. Calculate the internal porosity ratio And based on the total porosity Calculate the effective void ratio ; Step S4, based on the true maximum porosity The true minimum porosity and the effective porosity ratio Calculate the effective relative density ; The effective relative density Calculate using the following formula: ； in, For effective relative density, This is the true maximum porosity. This is the true minimum porosity. The effective porosity.

2. The corrected method for determining the relative density of coral sand according to claim 1, characterized in that, In step S1, a funnel method with controllable drop height is used to control the preparation energy by adjusting the drop height. The maximum porosity of the coral sand at different preparation energies is measured, and a linear relationship between the maximum porosity and the preparation energy is established. ； in, For maximum void ratio, To generate energy, This represents the true maximum void ratio. The attenuation coefficient is the maximum porosity. The linear relationship is then extrapolated to a preparation energy of zero to obtain the true maximum porosity.

3. The corrected method for determining the relative density of coral sand according to claim 1, characterized in that, In step S2, the dry vibration method with controllable vibration time is used to determine the minimum porosity of coral sand under different vibration durations, and an exponential decay relationship between the minimum porosity and the vibration duration is established: ； in, Minimum void ratio, For the duration of vibration, To represent the true minimum void ratio, The minimum porosity in steady state is given by τ, which is the characteristic time constant. The exponential decay relationship is then extrapolated to a vibration duration of zero to obtain the true minimum porosity. .

4. The corrected method for determining the relative density of coral sand according to claim 1, characterized in that, In step S3, the method for determining the internal porosity of the coral sand includes mercury infiltration or gas adsorption. The internal porosity ratio Calculate using the following formula: ； in, Internal porosity Gs represents the internal porosity of the coral sand and the specific gravity of the coral sand particles. The effective porosity Calculate using the following formula: ； in, For the effective porosity, The total porosity of the coral sand is denoted as .

5. The corrected method for determining the relative density of coral sand according to claim 1, characterized in that, Also includes: Coral sand was subjected to standard vibration until the particles broke and stabilized. The maximum and minimum porosity in the steady state were measured, and the relative density in the steady state was calculated. ； in, For the steady-state relative density, The maximum porosity in the steady state is [the value of the maximum porosity]. The minimum porosity in the steady state is given. Natural porosity; The long-term mechanical stability of coral sand is evaluated based on the steady-state relative density.

6. The corrected method for determining the relative density of coral sand according to claim 1, characterized in that, Also includes: Calculate the porosity index: ； in, Porosity index Natural porosity This is the true minimum porosity. This is the true maximum porosity; The density of coral sand is evaluated based on the porosity index.

7. The corrected method for determining the relative density of coral sand according to claim 1, characterized in that, Also includes: Calculate the breakage impact index: ； Wherein, BI stands for Fragmentation Impact Index. To measure the breakage rate, Maximum breakage rate; The density of coral sand is evaluated based on the aforementioned fragmentation impact index.

8. The corrected method for determining the relative density of coral sand according to claim 1, characterized in that, It also includes conducting at least three parallel measurements on the same coral sand sample and taking the average of the results as the final measurement value.

9. The corrected method for determining the relative density of coral sand according to claim 1, characterized in that, The true maximum porosity and the true minimum porosity are both output in dimensionless form, and the effective relative density is output as a percentage.

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