Method and system for determining horizontal bearing capacity of group piles in coral sand foundation based on transparent soil

Abstract

The application discloses a transparent soil-based method and system for determining horizontal bearing capacity of group piles in coral sand foundation, and belongs to the technical field of geotechnical engineering model test.The application tests basic parameters of target coral sand particles, constructs a pore light scattering correction model based on effective medium theory, and calculates the target equivalent refractive index of the coral sand particles; solid-liquid two-phase refractive index matching is completed, and a coral sand transparent soil sample with an embedded group pile model is prepared; a graded horizontal load is applied to the group pile model, and laser slice images are synchronously collected; the images are sequentially corrected in terms of perspective trapezoidal distortion and scattering blur distortion; the soil displacement field and strain field around the pile are calculated based on the corrected images, and the horizontal bearing capacity characteristics of the group pile are determined in combination with the load data.The application solves the problems that the traditional test cannot accurately observe the microscopic deformation of the soil around the pile, the transparent soil imaging matching fails, and the measurement error is large, and greatly improves the test precision, thereby providing reliable support for the engineering design of the group pile in the coral sand foundation.

Description

Technical Field

[0001] This application belongs to the field of transparent soil, and in particular relates to a method and system for determining the horizontal bearing capacity of a pile group on a coral sand foundation based on transparent soil. Background Technology

[0002] Coral sand, as the most important natural rock and soil material in island and reef areas, serves as the carrier for the foundations of various structures. Among them, pile foundations are the preferred foundation type for island and reef wharves, revetments, and high-rise buildings due to their excellent bearing capacity and strong resistance to horizontal loads. The horizontal loads generated by wind, waves, currents, and ship collisions in the marine environment are the controlling factors in the design of pile foundations. Current research on the horizontal bearing capacity characteristics of pile groups in coral sand foundations suffers from drawbacks such as high cost, long cycle, and inability to observe the internal deformation of the soil around the piles. Conventional indoor model tests can only obtain macroscopic load-displacement data at the pile top, making it difficult to capture the microscopic deformation law of the soil around the piles and reveal the interaction mechanism between the pile group and the soil without damage. Although transparent soil visualization technology provides an effective path for observing the internal deformation of the soil, existing technologies are designed for dense, non-porous fused silica sand. When applied to porous coral sand, there are problems such as systematic deviation in solid-liquid refractive index matching, severe soil diffuse scattering, and blurred and distorted imaging. There is a lack of distortion correction methods for the characteristics of coral sand and a standardized scheme for the entire process of pile group horizontal bearing capacity testing. Ultimately, this leads to large measurement errors in the displacement field of the soil around the piles and insufficient reliability of the pile group bearing capacity test results, failing to provide accurate experimental support for the engineering design of pile groups in coral sand foundations. Summary of the Invention

[0003] This application mainly addresses the shortcomings of traditional transparent soil technology, which ignores the light scattering effect of the internal pores of porous coral sand particles, resulting in failure of solid-liquid refractive index matching, low soil transmittance, and blurred imaging. It also addresses the problem of large displacement field measurement errors caused by the coupling and superposition of perspective trapezoidal distortion and scattering blur distortion in transparent coral sand imaging, which cannot be effectively eliminated by existing correction methods.

[0004] This application provides a method for determining the horizontal bearing capacity of a pile group on a coral sand foundation based on transparent soil, including the following steps: S1: Test the basic parameters of the target coral sand particles, construct a pore light scattering correction model for the coral sand particles based on the effective medium theory, and calculate the target equivalent refractive index of the coral sand particles; S2: Based on the target equivalent refractive index, complete the refractive index matching of the solid and liquid phases, and prepare a transparent coral sand sample with an embedded pile model. S3: Apply graded horizontal loads to the pile group model, and simultaneously acquire laser slice images of the coral sand transparent soil sample through a laser-camera visualization testing system during the loading process; S4: Perform perspective trapezoidal distortion correction and scattering blur distortion correction on the acquired laser slice image in sequence to obtain the corrected test image; S5: Based on the corrected test images, calculate the displacement and strain fields of the soil around the piles under graded horizontal loads, and determine the horizontal bearing characteristics of the coral sand foundation pile group by combining the graded load data.

[0005] Optionally, S1 specifically includes the following steps: S11: Test three basic parameters of the target coral sand particles: the refractive index of the solid matrix, the porosity of a single particle, and the refractive index of the internal porous medium. S12: Based on the Maxwell-Garnett effective medium theory, the dielectric constant equation is transformed into the refractive index form to construct a pore light scattering correction model for coral sand particles; S13: Substitute the three basic parameters into the pore light scattering correction model to calculate the target equivalent refractive index of the coral sand particles at the experimental laser wavelength.

[0006] Optionally, step S1 further includes full-spectrum dispersion correction and temperature correction for the target equivalent refractive index, specifically the following steps: The refractive index of the target coral sand particle solid matrix and porous medium at different wavelengths was tested, and the Cauchy dispersion coefficient was fitted to obtain the target equivalent refractive index at different wavelengths. Based on the experimental environment temperature and temperature fluctuation range, a temperature refractive index coefficient is introduced to correct the target refractive index of the porous liquid phase at temperature, thereby determining the target refractive index of the liquid phase at the standard temperature.

[0007] Optionally, S2 specifically includes the following steps: S21: Using fused silica sand as a matrix, modified silica sand is prepared to match the optical properties, mechanical properties, and particle size distribution of the target coral sand. S22: Calculate the volume ratio of n-dodecane to white oil based on the target equivalent refractive index, prepare the pore liquid phase and adjust it to the target refractive index; S23: Pre-set and fix the pile group model in the model box, fill the model box with modified quartz sand in layers, inject pore liquid phase and complete vacuum saturation to prepare a transparent coral sand sample with an internal pile group model.

[0008] Optionally, the preparation of modified quartz sand in step S21, which is adapted to the optical properties, mechanical properties, and particle size distribution of the target coral sand, specifically includes the following steps: The refractive index of the solid matrix of fused silica sand is controlled by doping with TiO2 or ZrO2 nanoparticles to match the refractive index of the solid matrix of the target coral sand. A solid-phase sintering pore-forming process is adopted, using polymer microspheres as pore-forming agents to construct micron-level pores inside quartz sand particles, so that the porosity of a single particle matches that of the target coral sand. Adjust the sintering temperature, holding time, and pore-forming agent ratio to match the particle strength, internal friction angle, cohesion, and compressive modulus mechanical parameters of the modified quartz sand with those of the target coral sand. The modified quartz sand is crushed and screened, and particles of different particle size ranges are mixed in proportion to make its particle size distribution curve coincide with the target coral sand.

[0009] Optionally, in step S22, the volume ratio of n-dodecane to white oil is calculated, and the porous liquid phase is prepared and adjusted to the target refractive index. This specifically includes the following steps: The measured refractive indices of n-dodecane and white oil were tested at standard temperature and experimental laser wavelength. Based on the principle of linear superposition of refractive indices in a binary miscible system, the initial volume ratio of the two components was calculated. The porous liquid phase was prepared according to the initial ratio, and its actual refractive index at the experimental laser wavelength was tested. The addition amounts of the two components were adjusted using a gradient adjustment method until the refractive index of the porous liquid phase was the same as the target equivalent refractive index. The full-spectrum refractive index of the porous liquid phase within a preset visible light range was tested to verify the full-spectrum matching effect.

[0010] Optionally, S3 specifically includes the following steps: S31: Build a laser-camera visualization testing system, adjust the line laser so that the laser plane coincides with the plane containing the pile axis of the pile group model to form a laser slice; adjust the shooting parameters and position of the high-speed industrial camera so that the laser slice area is completely within the camera's field of view; S32: Apply graded horizontal loads to the pile group model using a loading device. After each load is applied, use a high-speed industrial camera to simultaneously acquire laser slice images under that load and simultaneously record the load value and pile top horizontal displacement value corresponding to each load until the pile group model reaches the horizontal ultimate bearing state.

[0011] Optionally, S4 specifically includes the following steps: S41: Select calibration feature points, solve the homography matrix, and perform perspective trapezoidal distortion correction on the laser slice image to obtain an orthophoto image without geometric distortion; S42: Based on the point spread function of the pile boundary identification image, perform regional scattering blur distortion correction on the orthophoto image; S43: Perform contrast optimization and noise removal on the corrected image to obtain the final corrected test image.

[0012] Optionally, S41 specifically includes the following steps: Capture images of the checkerboard calibration plate and the boundary of the pile group within the laser slice plane, extract multiple sets of non-collinear calibration feature points, and record the world physical coordinates and image pixel coordinates corresponding to each feature point; The initial homography matrix is ​​solved by the direct linear transformation algorithm, and the homography matrix is ​​iteratively optimized by the random sampling consensus algorithm to eliminate mismatched feature points; Based on the optimized homography matrix, inverse projection transformation is performed on each frame of laser slice image to complete perspective trapezoidal distortion correction; S42 specifically includes the following steps: A point spread function model for scattering ambiguity was constructed using a two-dimensional Gaussian function. Based on the gray-scale gradient distribution of the vertical boundary of the pile after geometric correction, the Gaussian kernel standard deviation of the point spread function was obtained by fitting. The image is divided into three regions: the pile perimeter deformation region, the pile boundary region, and the model edge region. Different filtering parameters are set according to the scattering degree of different regions and the focus of the experiment. The Wiener inverse filtering algorithm is used to perform frequency domain filtering on the images of each region to complete the correction of scattering blur distortion.

[0013] This application also discloses a system for determining the horizontal bearing capacity of a pile group on a coral sand foundation based on transparent soil, including: The equivalent refractive index calculation module is used to test the basic parameters of the target coral sand particles. Based on the effective medium theory, a pore light scattering correction model of the coral sand particles is constructed to calculate the target equivalent refractive index of the coral sand particles. The horizontal loading and image acquisition module is used to apply graded horizontal loads to the coral sand transparent soil sample after the solid-liquid two-phase refractive index matching is completed according to the target equivalent refractive index and the built-in pile model is prepared. During the loading process, the laser slice images of the coral sand transparent soil sample are acquired synchronously through the laser-camera visualization test system. The imaging distortion correction module is used to perform perspective trapezoidal distortion correction and scattering blur distortion correction on the acquired laser slice image in sequence to obtain the corrected test image; The bearing characteristics analysis module is used to calculate the displacement and strain fields of the soil around the piles under graded horizontal loads based on the corrected test images, and to determine the horizontal bearing characteristics of the pile group in the coral sand foundation by combining the graded load data.

[0014] As can be seen from the above technical solutions, the method and system for determining the horizontal bearing capacity of coral sand foundation piles based on transparent soil provided in this application, based on the Maxwell-Garnett effective medium theory, first constructs a pore light scattering correction model for porous coral sand particles, derives an explicit calculation formula for the equivalent refractive index, solves the problem of refractive index matching failure caused by neglecting the influence of internal pores in traditional methods, improves the solid-liquid refractive index matching degree, and lays the foundation for visual observation of soil deformation around piles; at the same time, through the correction process of perspective trapezoidal distortion correction and scattering fuzzy distortion correction, combined with homography matrix and regional Wiener inverse filtering algorithm, geometric distortion and scattering fuzziness are eliminated, the relative error of soil displacement field measurement around piles is reduced, and the measurement accuracy of deformation data is improved. This application establishes a standardized method for the entire process, from coral sand parameter testing, equivalent refractive index calculation, solid-liquid matching, sample preparation, graded loading to quantitative determination of the horizontal bearing capacity of pile groups. It can accurately determine the horizontal ultimate bearing capacity of pile groups in coral sand foundations, and can also capture the microscopic deformation law of the soil around the piles and the interaction mechanism between the pile groups and the soil, which greatly improves the reliability and repeatability of the test results. It provides high-precision visualization test methods and data support for the design, construction and safety assessment of pile groups in marine coral sand engineering. Attached Figure Description

[0015] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0016] Figure 1 This paper illustrates a flowchart of a method for determining the horizontal bearing capacity of a coral sand foundation pile group based on transparent soil, according to an embodiment of this application. Figure 2 This paper illustrates a method for determining the horizontal bearing capacity of a coral sand foundation pile group based on transparent soil according to a specific process flow diagram of step S1 in an embodiment of this application. Figure 3 This paper illustrates a method for determining the horizontal bearing capacity of a coral sand foundation pile group based on transparent soil according to a specific process flow diagram of step S2 in an embodiment of this application. Figure 4 This illustration shows a front view of a transparent soil test model in a specific embodiment of a method for determining the horizontal bearing capacity of a coral sand foundation pile group based on transparent soil, as described in this application. Figure 5 This paper illustrates a method for determining the horizontal bearing capacity of a coral sand foundation pile group based on transparent soil according to a specific process flow diagram of step S3 in an embodiment of this application. Figure 6This paper shows a side view of a transparent soil test model in a specific embodiment of a method for determining the horizontal bearing capacity of a coral sand foundation pile group based on transparent soil, according to an embodiment of this application. Figure 7 The illustration shows a schematic diagram of the specific process of determining the horizontal bearing capacity of a coral sand foundation pile group based on transparent soil according to S4 in an embodiment of this application. Detailed Implementation

[0017] This application relates to the field of geotechnical engineering model testing technology, and in particular to a method and system for determining the horizontal bearing capacity of a group of piles in coral sand foundations based on transparent soil. It is applicable to the visualization model test of the horizontal bearing capacity characteristics of a group of piles in marine coral sand foundations, and can support related research on the bearing capacity of coral sand foundation piles and the interaction mechanism between piles and soil. It solves the problems that traditional coral sand pile horizontal bearing capacity tests cannot accurately capture the internal micro-deformation of the soil around the piles, the severe imaging blurring and distortion of traditional transparent soil technology in coral sand tests, the large measurement error of the horizontal bearing capacity characteristics of piles, and the insufficient reliability of the results. It can provide high-precision, visualized, full-process test data support for the engineering design and safety assessment of coral sand foundation pile groups.

[0018] In this embodiment, the technical terms involved in the method are first defined in a unified and clear manner to ensure that those skilled in the art can understand the technical solution of this application without ambiguity: Transparent soil refers to soil that appears transparent by matching the refractive indices of solid particles and pore liquid phases. It is used in conjunction with laser slicing technology to visualize the internal deformation of the soil and serves as a carrier for studying the microscopic deformation of the soil around the piles in coral sand foundation groups.

[0019] The equivalent refractive index refers to the overall refractive index of the composite system of porous coral sand particles as a solid matrix and internal porous media, calculated by the pore light scattering correction model in this application. It is the target value for matching the refractive indices of the solid and liquid phases.

[0020] Solid-liquid refractive index matching refers to adjusting the refractive index of the pore liquid phase to make it completely consistent with the equivalent refractive index of the solid particles. At this time, light is not reflected, refracted, or scattered at the solid-liquid interface, and the soil appears completely transparent. This is a prerequisite for the successful transparent soil test and the accurate collection of pile group deformation data.

[0021] Perspective trapezoidal distortion refers to the phenomenon that the acquired image exhibits trapezoidal geometric deformation and coordinate scale distortion due to the camera not being perpendicular to the laser slicing plane and the refraction of the model box glass wall. It is the cause of systematic errors in the measurement of soil displacement field around piles.

[0022] Scattering blur distortion refers to the phenomenon that the acquired image appears blurred at the edges, with overlapping speckles and reduced contrast due to the residual diffuse scattering of coral sand particles. It is the cause of errors in tracer particle identification and random errors in the measurement of soil displacement field around piles.

[0023] Homography matrix is ​​a transformation matrix that describes the projection mapping relationship between the world physical coordinate system and the image pixel coordinate system, and is used for perspective trapezoidal distortion correction.

[0024] The point spread function is a function that describes the scattering characteristics of an optical system. It characterizes the distribution features of the image formed by an ideal point light source after passing through the optical system and is a model for correcting scattering blur and distortion.

[0025] The Maxwell-Garnett effective medium theory, a classical theory describing the equivalent dielectric properties of composite media containing dispersed spherical encapsulated phases in a matrix phase, is the theoretical basis for constructing the coral sand pore light scattering correction model in this application.

[0026] The ultimate horizontal bearing capacity of a pile group refers to the maximum horizontal load that a pile group foundation on a coral sand foundation can withstand under horizontal loads when the foundation soil becomes unstable or the horizontal displacement of the pile top reaches the allowable critical value specified in the code.

[0027] The displacement field of the soil around the pile refers to the distribution characteristics of the displacement vector of each point inside the soil around the pile during the horizontal loading of the pile group. It is the basic data for analyzing the interaction mechanism between the pile group and the soil and determining the horizontal bearing capacity of the pile group.

[0028] Graded horizontal loading refers to a loading method in which horizontal loads are applied to a pile group model in stages according to a preset load difference, and the model is kept stable after each load is applied, while test data is collected simultaneously. It is the standard loading system for testing the horizontal bearing capacity characteristics of pile groups.

[0029] The PIV / PTV algorithm, or particle image velocimetry / particle tracking velocimetry, is an algorithm that calculates the soil displacement and strain fields by identifying the positional changes of tracer particles in a laser slice image. It is used in the pile perimeter soil deformation analysis in this application.

[0030] In the embodiments of this application, such as Figure 1 As shown, the method for determining the horizontal bearing capacity of a coral sand foundation pile group based on transparent soil includes: S1: testing the basic parameters of the target coral sand particles, constructing a pore light scattering correction model of the coral sand particles based on the effective medium theory, and calculating the target equivalent refractive index of the coral sand particles; S2: Based on the target equivalent refractive index, complete the refractive index matching of the solid and liquid phases, and prepare a transparent coral sand sample with an embedded pile model. S3: Apply graded horizontal loads to the pile group model, and simultaneously acquire laser slice images of the coral sand transparent soil sample through a laser-camera visualization testing system during the loading process; S4: Perform perspective trapezoidal distortion correction and scattering blur distortion correction on the acquired laser slice image in sequence to obtain the corrected test image; S5: Based on the corrected test images, calculate the displacement and strain fields of the soil around the piles under graded horizontal loads, and determine the horizontal bearing characteristics of the coral sand foundation pile group by combining the graded load data.

[0031] As can be seen from the above technical solutions, the method and system for determining the horizontal bearing capacity of coral sand foundation piles based on transparent soil provided in this application, based on the Maxwell-Garnett effective medium theory, first constructs a pore light scattering correction model for porous coral sand particles, derives an explicit calculation formula for the equivalent refractive index, solves the problem of refractive index matching failure caused by neglecting the influence of internal pores in traditional methods, improves the solid-liquid refractive index matching degree, and lays the foundation for visual observation of soil deformation around piles; at the same time, through the correction process of perspective trapezoidal distortion correction and scattering fuzzy distortion correction, combined with homography matrix and regional Wiener inverse filtering algorithm, geometric distortion and scattering fuzziness are eliminated, the relative error of soil displacement field measurement around piles is reduced, and the measurement accuracy of deformation data is improved. This application establishes a standardized method for the entire process, from coral sand parameter testing, equivalent refractive index calculation, solid-liquid matching, sample preparation, graded loading to quantitative determination of the horizontal bearing capacity of pile groups. It can accurately determine the horizontal ultimate bearing capacity of pile groups in coral sand foundations, and can also capture the microscopic deformation law of the soil around the piles and the interaction mechanism between the pile groups and the soil, which greatly improves the reliability and repeatability of the test results. It provides high-precision visualization test methods and data support for the design, construction and safety assessment of pile groups in marine coral sand engineering.

[0032] In alternative implementations, such as Figure 2 As shown, S1 includes: S11: Test the three basic parameters of the target coral sand particles: the refractive index of the solid matrix, the porosity of a single particle, and the refractive index of the internal porous medium. S12: Based on the Maxwell-Garnett effective medium theory, the dielectric constant equation is transformed into the refractive index form to construct a pore light scattering correction model for coral sand particles; S13: Substitute the three basic parameters into the pore light scattering correction model to calculate the target equivalent refractive index of the coral sand particles at the experimental laser wavelength.

[0033] It should be noted that traditional transparent soil testing methods are designed for dense, non-porous fused silica sand, requiring only the testing of a single refractive index parameter of the solid matrix. However, coral sand, as a porous medium of marine biogenic origin, contains numerous micron-sized interconnected and closed pores within each particle, forming a two-phase composite system of solid matrix and internal porous medium. Testing only the refractive index of the solid matrix cannot fully reflect the overall optical properties of coral sand particles. This is the root cause of the complete failure of traditional methods in transparent soil testing of coral sand and their inability to accurately test the bearing capacity of pile groups. Those skilled in the art understand that the mineral composition of coral sand is mainly aragonite and calcite. Coral sand from different sea areas and depths exhibits significant differences in mineral composition, particle porosity, and internal pore structure. Therefore, it is essential to conduct batch-by-batch basic parameter testing on the target coral sand used in the experiment; otherwise, it will directly lead to systematic deviations in subsequent refractive index matching, ultimately causing the failure of pile group soil deformation observation.

[0034] In this embodiment of the application, the basic parameters of the target coral sand particles tested include three basic parameters: the refractive index of the solid matrix of the coral sand particles, the porosity of a single particle, and the refractive index of the internal porous medium. The following provides a detailed explanation of the testing principles, testing methods, and accuracy requirements for these three parameters.

[0035] The first step involves testing the refractive index of the solid matrix of the coral sand particles. In this embodiment, the solid matrix refractive index refers to the true refractive index of the mineral matrix constituting the coral sand particles, excluding the influence of internal pores, and is the fundamental parameter for calculating the equivalent refractive index. It should be noted that the typical range of solid matrix refractive index for aragonite coral sand is 1.530 to 1.686, and for calcite coral sand it is 1.486 to 1.658. Coral sand of different origins exhibits significant dispersion in its solid matrix refractive index; therefore, it must be obtained through actual measurement and cannot be directly based on empirical values.

[0036] In this embodiment, the refractive index of the solid matrix is ​​tested using an Abbe refractometer. The test light source uses the same laser wavelength as the subsequent model test, preferably a 532nm green light source or a 635nm red light source, to eliminate the influence of dispersion effect on the test results. The specific test steps are as follows: First, target coral sand particles are taken and ground into micron-sized powder using an agate mortar, ensuring that the particle size of the powder particles is smaller than the incident light wavelength, thereby eliminating the scattering effect of internal pores in the particles and only testing the refractive index of the mineral body; then, the ground coral sand powder is evenly coated on the test prism surface of the Abbe refractometer, and a contact liquid with a refractive index similar to that of the coral sand matrix is ​​dropped in to eliminate the air gap between the powder and the prism, ensuring test accuracy; then, the refractive index value of the coral sand solid matrix under the test laser wavelength is read through the reading system of the Abbe refractometer. No less than 5 parallel samples are tested for each batch of samples, and the average value is taken as the final solid matrix refractive index test result. The test deviation of the parallel samples must be controlled within ±0.0005 to ensure test accuracy.

[0037] Next, the porosity of individual coral sand particles is tested. In this embodiment, the porosity of a single particle refers to the proportion of pore volume to the total volume of a single coral sand particle. It is dimensionless and typically ranges from 0.1 to 0.4. It is a parameter that affects the equivalent refractive index of the coral sand particles. It should be noted that traditional methods completely ignore the influence of this parameter. However, in the modified model of this application, the porosity of a single particle directly determines the volume ratio of the porous medium in the composite system and is a variable for correcting the equivalent refractive index. It must be obtained through testing.

[0038] In this embodiment, the micro-CT scanning method is preferred for testing the internal porosity of a single particle. This method can non-destructively obtain the internal three-dimensional pore structure of a single coral sand particle, accurately calculate the internal porosity, and also obtain the morphology and size distribution characteristics of the pores, providing a basis for the subsequent preparation of modified quartz sand. The specific testing steps are as follows: First, select a representative single particle of the target coral sand with the same particle size as that used in the model test. Fix it on the sample stage of the micro-CT and set a scanning resolution that matches the particle size, preferably using micron-level resolution to ensure that the micron-level pores inside the particle can be identified. Then, perform a three-dimensional CT scan on the single coral sand particle to obtain continuous tomographic images of the particle's interior. Next, use an image segmentation algorithm to binarize the scanned images, distinguish between the solid matrix and the pore space, and reconstruct the three-dimensional digital model of the particle. Finally, calculate the total volume of the pores inside the particle and the total volume of the particle through the volume calculation of the three-dimensional digital model. Divide the total volume of the pores inside the particle by the total volume of the particle to calculate the porosity of a single particle. Test no less than 10 representative particles in each batch of samples, and take the average value as the final porosity test result. The test error must be controlled within ±0.02. If the test site does not have the conditions for micro-CT testing, the mercury intrusion porosimetry method can also be used in this embodiment to test the porosity of a single coral sand particle. The mercury intrusion porosimetry method uses high pressure to inject mercury into the pores inside the particle, and calculates the pore volume and porosity based on the relationship between the amount of mercury injected and the pressure.

[0039] In this embodiment, the refractive index of the internal porous medium refers to the refractive index of the medium filling the pores within a single coral sand particle. The value of this parameter is determined by the filling medium within the pores. It should be noted that before preparing the transparent soil sample, the pores inside the coral sand particles are typically filled with air. The refractive index of air under standard atmospheric pressure is 1.0003, a fixed value that can be directly substituted into the model calculation. After the transparent soil sample is prepared, the pores inside the particles are completely filled with a pore liquid phase. At this point, the refractive index of the internal porous medium is the same as the refractive index of the pore liquid phase. In the initial equivalent refractive index calculation stage, the pore medium is air, so the refractive index value of air can be used. Those skilled in the art will understand that if there is residual moisture in the pores inside the coral sand particles, it will cause a change in the refractive index of the pore medium, thus affecting the accuracy of the equivalent refractive index calculation. Therefore, before sample preparation, the coral sand particles or modified quartz sand must be thoroughly dried to remove residual moisture from the pores, ensuring that the pore medium is only air, and ensuring the accuracy of this parameter.

[0040] Of course, in practical applications, those skilled in the art can also use other feasible methods to test and obtain the basic parameters of the target coral sand particles according to actual needs, and this application does not limit this.

[0041] After completing the tests of the three basic parameters, in this embodiment, a pore light scattering correction model for coral sand particles is constructed based on the effective medium theory. The tested basic parameters are substituted into the model to calculate the target equivalent refractive index of the coral sand particles at the experimental laser wavelength. It should be noted that this step is the theoretical basis for achieving high-quality imaging of transparent coral sand. Only by accurately calculating the target equivalent refractive index can the complete matching of the solid and liquid phases be achieved, ensuring high light transmittance of the soil. This allows for the acquisition of clear laser slice images during the horizontal loading of the pile group, providing reliable raw data for the deformation analysis of the soil around the pile. Traditional transparent soil methods lack a corresponding pore light scattering correction model, using only the refractive index of the solid matrix as the matching target, ignoring the influence of internal pores. This leads to a systematic deviation in the matching target value, ultimately causing a mismatch between the solid and liquid refractive indices, resulting in strong diffuse scattering in the soil, blurred and ineffective imaging, and an inability to support accurate testing of the horizontal bearing capacity of the pile group.

[0042] In this embodiment, the effective medium theory used is the Maxwell-Garnett (MG) effective medium theory. This theory is a classic theory that describes the equivalent dielectric properties of composite media containing dispersed spherical encapsulated phases in the matrix phase. It is perfectly suited to the microstructural characteristics of spherical pores encapsulated in the solid phase matrix of coral sand, and can accurately calculate the equivalent dielectric constant of the composite system, which is then converted into the equivalent refractive index.

[0043] Those skilled in the art will understand that, for non-magnetic media, under optical frequency conditions, the relative permeability of the medium... ≈1, therefore the refractive index of the medium is... With relative permittivity The following formula applies between them:

[0044] This formula transforms the dielectric constant equation of the MG effective medium theory into the refractive index form. Through this formula, the calculation of the equivalent dielectric constant of composite media can be transformed into the calculation of the equivalent refractive index, which is suitable for the refractive index matching requirements of transparent soil tests.

[0045] Next, in the embodiments of this application, the dielectric constant equation of the Maxwell-Garnett effective medium theory is first given. For a two-phase composite system in which a spherical encapsulated phase is uniformly dispersed in the matrix phase, its equivalent dielectric constant satisfies the following equation:

[0046] In the formula, The equivalent relative permittivity of the two-phase composite system is dimensionless and corresponds to the overall equivalent permittivity of a single coral sand particle. It is the variable that needs to be solved in this model. The relative permittivity of the matrix phase is dimensionless and corresponds to the relative permittivity of the coral sand solid matrix. It can be obtained through the refractive index of the solid matrix. The square of the result is obtained, that is ; The relative permittivity of the dispersed encapsulated phase is dimensionless and corresponds to the relative permittivity of the porous medium within the coral sand. It can be expressed through the refractive index of the porous medium. The square of the result is obtained, that is ; : Volume fraction of dispersed encapsulated phase, dimensionless, corresponding to the internal porosity of a single coral sand particle, i.e., the proportion of pore volume to the total particle volume.

[0047] It should be noted that the Maxwell-Garnett effective medium theory is applicable under the following conditions: the dispersed phase particles are spherical, uniformly dispersed in the matrix phase, and the volume fraction of the dispersed phase does not exceed 50%. Coral sand contains mostly near-spherical micron-sized pores, and the porosity of a single particle is usually no more than 40%, which fully meets the applicable conditions of the theory. Therefore, the modified model constructed using this theory can accurately reflect the equivalent optical properties of coral sand particles, and the calculation results have sufficient theoretical basis.

[0048] Next, in this embodiment, the aforementioned correspondence between refractive index and dielectric constant is substituted into the MG dielectric constant equation to transform it into the equivalent refractive index fundamental equation in refractive index form. The specific process is as follows: First, , , Substituting into the original dielectric constant equation, we get:

[0049] This equation is the fundamental equation for the equivalent refractive index of coral sand particles, where... The target equivalent refractive index of a single coral sand particle is the variable that needs to be solved in this equation. The other parameters are known quantities obtained through testing.

[0050] However, this fundamental equation is implicit, which is inconvenient for direct calculation in practical engineering. Therefore, in this embodiment, the implicit equation is algebraically transformed to derive an explicit formula for calculating the equivalent refractive index, making it easier for those skilled in the art to directly substitute parameters for calculation. The specific derivation process is as follows: First, let the constant term on the right side of the equation be... Simplify the equation form, where The expression is:

[0051] After substitution, the original basic equation simplifies to:

[0052] The second step is to perform a cross-multiplication expansion on the simplified equation to separate the components. Item:

[0053] Will include Move the term to the left side of the equation and the remaining terms to the right side, resulting in:

[0054] The third step is to extract the common factors from both sides of the equation, resulting in:

[0055] The fourth step is to Substitute the original expression into the above formula and replace Variables, resulting in an expression containing only known parameters: Will Substitute the right side item:

[0056] Substitute the left side again item:

[0057] Substitute the above two items into The expression, the denominators on both sides They cancel each other out, resulting in:

[0058] Fifth step: Take the square root of both sides of the equation to obtain the final explicit formula for calculating the equivalent refractive index of coral sand particles:

[0059] This formula is the calculation formula for the aperture light scattering correction model of this application. The physical meaning of each parameter in the formula is the same as that described above, and is as follows: The target equivalent refractive index of the coral sand particles at the laser wavelength used in the experiment is dimensionless and represents the target value for refractive index matching between the solid and liquid phases. : Measured refractive index of the coral sand solid matrix at the experimental laser wavelength, dimensionless; : The refractive index of the porous medium inside the coral sand, dimensionless, taken as 1.0003 when the pores are filled with air; Internal porosity of a single coral sand particle, dimensionless, obtained through actual measurement.

[0060] Those skilled in the art will understand that this explicit calculation formula allows for the rapid and accurate calculation of the target equivalent refractive index of coral sand particles simply by substituting the three basic parameters obtained from the aforementioned tests. It eliminates the need for complex numerical solutions and possesses strong engineering practicality. It should be noted that the calculation result of this formula represents the target value for refractive index matching between the solid and liquid phases. In other words, only when the refractive index of the pore liquid phase is completely consistent with this target equivalent refractive index can a perfect match between the refractive indices of the solid and liquid phases be achieved. In this case, light will not be reflected, refracted, or scattered at the interface between the coral sand particles and the pore liquid phase, resulting in a completely transparent soil surface. This provides a foundation for clear imaging during subsequent pile loading.

[0061] In an optional implementation, step S1 further includes full-spectrum dispersion correction and temperature correction for the target equivalent refractive index, specifically the following steps: The refractive index of the target coral sand particle solid matrix and porous medium at different wavelengths was tested, and the Cauchy dispersion coefficient was fitted to obtain the target equivalent refractive index at different wavelengths. Based on the experimental environment temperature and temperature fluctuation range, a temperature refractive index coefficient is introduced to correct the target refractive index of the porous liquid phase at temperature, thereby determining the target refractive index of the liquid phase at the standard temperature.

[0062] Specifically, after calculating the target equivalent refractive index at the experimental laser wavelength, this embodiment also requires full-spectrum dispersion correction and temperature correction to ensure that the refractive indices of the solid and liquid phases remain matched throughout the full spectral range and temperature range of the experiment. This avoids matching failure caused by dispersion effects and temperature changes, ensuring that the soil maintains high light transmittance and stable imaging quality throughout the entire pile group horizontal loading test. It should be noted that the refractive index of the medium is not a fixed value and will change with the wavelength of the incident light; this phenomenon is called dispersion effect. It will also change with the ambient temperature. If corresponding corrections are not made, the refractive index matching accuracy will decrease during the experiment, the soil transmittance will decrease, the imaging quality will deteriorate, and ultimately the accuracy of the pile perimeter soil deformation data will be affected.

[0063] First, there is the full-spectrum dispersion correction. In this embodiment, the Cauchy dispersion formula is used to correct the refractive index at different wavelengths. The Cauchy dispersion formula is a classic empirical formula describing the variation of the refractive index of a transparent medium with wavelength, and it can fit the dispersion characteristics of a medium in the visible light range. Its specific expression is as follows:

[0064] The physical meanings of each parameter in the formula are as follows: Wavelength is The refractive index of the medium corresponding to the incident light is dimensionless; : Wavelength of the incident light; Cauchy dispersion coefficient of the medium, dimensionless, obtained by fitting the refractive index of the medium at multiple measured wavelengths.

[0065] In this embodiment, the specific implementation steps of the full-spectrum dispersion correction are as follows: First, using an Abbe refractometer, the refractive index of the coral sand solid matrix and porous medium at different wavelengths is tested. Preferably, at least three wavelengths are selected, covering the main range of the laser wavelength and visible light used in the experiment. The visible light range is typically 400nm to 800nm, and the commonly used laser wavelengths for transparent soil model experiments are 532nm green light and 635nm red light. Next, the measured wavelength and refractive index data are substituted into the Cauchy dispersion formula, and the Cauchy dispersion coefficient of the coral sand solid matrix is ​​obtained by least squares fitting. and the Cauchy dispersion coefficient of porous media. Subsequently, different wavelengths Substituting into the Cauchy dispersion formula, the refractive index of the coral sand solid matrix at that wavelength was calculated. Refractive index of coral sand porous media Ultimately, , Compared with the measured porosity Substituting into the aforementioned explicit formula for calculating the equivalent refractive index, we obtain the target equivalent refractive index at different wavelengths. This is how the full-spectrum dispersion correction is achieved.

[0066] In this embodiment, a temperature refractive index coefficient is introduced to correct the target refractive index of the porous liquid phase based on the experimental ambient temperature to determine the target refractive index of the liquid phase at the standard temperature. It should be noted that the refractive index of organic liquid phases changes significantly with temperature; for every 1°C change in temperature, the refractive index typically changes. The magnitude of the solid-liquid refractive index is significant, while the transparent soil test requires the solid-liquid refractive index matching error to be no more than 0.002. At the same time, the horizontal loading test of pile groups usually lasts for several hours, and the ambient temperature may fluctuate. Therefore, the influence of temperature must be corrected, otherwise the fluctuation of the test ambient temperature will directly lead to the failure of matching.

[0067] In this embodiment, the correction formula for the change of the refractive index of the medium with temperature is:

[0068] The physical meanings of each parameter in the formula are as follows: Actual ambient temperature The refractive index of the medium is dimensionless. Standard temperature The refractive index of the medium is dimensionless, and the standard temperature in this application is... 20℃ is taken as the standard temperature for refractive index testing; Temperature refractive index coefficient of a medium, expressed in °C, characterizes the magnitude of change in the refractive index of a medium with temperature; a negative value indicates that the refractive index decreases as temperature increases. : The actual temperature of the test environment, in °C.

[0069] In this embodiment, the specific implementation steps for temperature correction are as follows: First, determine the actual test environment temperature at the model test site. The experiment also included the possible temperature fluctuation range during the experiment; next, the temperature refractive index coefficients of the two components in the porous liquid phase were obtained, including the temperature refractive index coefficient of n-dodecane. The temperature refractive index coefficient of food-grade white oil is -0.0004 / ℃. The initial value was -0.0003 / ℃. Subsequently, based on the experimental ambient temperature, a temperature correction was applied to the target equivalent refractive index, and the target refractive index that the porous liquid phase needed to achieve at a standard temperature of 20℃ was calculated. Finally, based on the target refractive index at the standard temperature, the pore liquid phase was prepared and adjusted to ensure that the refractive index of the pore liquid phase completely matches the target equivalent refractive index of the coral sand at the actual experimental temperature.

[0070] It should be noted that, in practical applications, those skilled in the art can use other specific implementation methods to perform full-spectrum dispersion correction and temperature correction of the target equivalent refractive index according to actual needs, and this application does not limit this.

[0071] In alternative implementations, such as Figure 3 As shown, step S2 specifically includes the following steps: S21: Using fused silica sand as a matrix, modified silica sand is prepared to match the optical properties, mechanical properties, and particle size distribution of the target coral sand. S22: Calculate the volume ratio of n-dodecane to white oil based on the target equivalent refractive index, prepare the pore liquid phase and adjust it to the target refractive index; S23: Pre-set and fix the pile group model in the model box, fill the model box with modified quartz sand in layers, inject pore liquid phase and complete vacuum saturation to prepare a transparent coral sand sample with an internal pile group model.

[0072] In this embodiment, after calculating the target equivalent refractive index of the coral sand particles and completing dispersion and temperature corrections, the next step is to match the refractive indices of the solid and liquid phases based on the target equivalent refractive index and prepare a transparent coral sand sample with an embedded pile model. It should be noted that this step transforms the aforementioned theoretical calculation results into an actual test substrate. This requires not only accurate refractive index matching between the solid and liquid phases to ensure high light transmittance of the soil, but also ensuring that the mechanical properties, particle size distribution, and permeability of the prepared transparent soil sample are completely consistent with those of natural coral sand. Simultaneously, it requires accurate pre-setting and fixing of the pile model to meet the similarity requirements of the pile horizontal bearing capacity model test, ensuring that the obtained pile horizontal bearing capacity characteristics accurately reflect the actual engineering situation.

[0073] In this embodiment, the specific implementation process of this step is divided into three stages: preparing modified quartz sand that is compatible with the optical properties, mechanical properties, and particle size distribution of the target coral sand; calculating the volume ratio of n-dodecane to white oil according to the target equivalent refractive index, preparing the pore liquid phase and adjusting it to the target refractive index; pre-setting and fixing the pile group model in the model box, filling the model box with modified quartz sand, injecting the pore liquid phase to complete saturation, and preparing a transparent coral sand sample with an internal pile group model. The specific implementation methods, technical requirements, and operational details of each stage are explained in detail below.

[0074] In this embodiment, fused silica sand is used as the matrix to prepare modified silica sand with optical properties, mechanical properties, and particle size distribution adapted to the target coral sand. It should be noted that there are three main reasons why natural coral sand is not directly used as the solid phase material for transparent soil: First, the mineral composition of natural coral sand is mainly aragonite and calcite, which are prone to dissolution when immersed in organic porous liquid phase for a long time, leading to particle structure damage and changes in mechanical properties, affecting the long-term stability of pile group model tests; Second, the refractive index of natural coral sand has large dispersion, with significant differences in mineral composition and porosity between different particles, making it difficult to achieve overall uniform refractive index matching and ensuring the stability of imaging quality; Third, natural coral sand is easily broken, and particle breakage easily occurs during the filling and loading process of the model test, leading to changes in the pore structure and optical properties of the soil, resulting in deterioration of imaging quality and affecting the accuracy of soil deformation data around the piles. Fused silica sand has the advantages of stable chemical properties, resistance to organic liquid phase corrosion, high strength, and resistance to breakage. Through modification treatment, its optical properties, pore structure, mechanical properties, and particle size distribution can be accurately controlled, perfectly simulating the various characteristics of natural coral sand. It is an ideal solid phase material for coral sand transparent soil experiments.

[0075] In this embodiment, the preparation of modified quartz sand specifically includes the following four steps: optical property adaptation, porous structure adaptation, mechanical property adaptation, and particle size distribution adaptation. These four steps are interconnected, and finally, modified quartz sand that is completely adapted to the target coral sand is obtained.

[0076] The first step involves controlling the refractive index of the solid matrix of fused silica sand by doping with nanoparticles to match that of the target coral sand. It should be noted that the refractive index of pure fused silica sand at 589 nm wavelength and 20°C is approximately 1.458, while the refractive index of the solid matrix of natural coral sand is typically between 1.486 and 1.686, higher than that of pure fused silica sand. Therefore, it is necessary to dope with high-refractive-index nanoparticles to increase the refractive index of the solid matrix of the fused silica sand, making it perfectly match the measured refractive index of the target coral sand. In this application, TiO2 (titanium dioxide) or ZrO2 (zirconia) nanoparticles are preferentially used as dopants. These two types of nanoparticles have the advantages of high refractive index, chemical stability, and good compatibility with the quartz matrix, enabling accurate control of its refractive index without damaging the quartz matrix structure. The specific implementation steps are as follows: First, based on the difference between the refractive index of the target coral sand solid matrix and the refractive index of pure fused silica sand, the doping ratio of nanoparticles is calculated. The larger the refractive index difference, the higher the doping ratio. Next, the fused silica sand powder and nano-dopant are uniformly mixed according to a preset ratio, and deionized water and dispersant are added. The nanoparticles are uniformly dispersed in the silica powder through ball milling. Subsequently, the uniformly mixed powder is spray-granulated to obtain spherical particle precursors. Finally, the particle precursors are placed in a high-temperature sintering furnace and sintered at a temperature of 1200℃ to 1500℃ to fully fuse the nanoparticles with the silica matrix, resulting in modified silica sand particles with a refractive index that perfectly matches the target coral sand solid matrix.

[0077] The second step involves using a sintering pore-forming process to construct micron-sized pores within the quartz sand particles, ensuring that the porosity of each particle matches that of the target coral sand. It should be noted that this step is to simulate the porous structure of natural coral sand, guaranteeing that the difference between the internal porosity of the modified quartz sand particles and the measured porosity of the target coral sand does not exceed ±0.02, thereby ensuring that the equivalent refractive index of the modified quartz sand is completely consistent with that of natural coral sand. In this embodiment, a solid-phase sintering pore-forming process is used, employing polymer microspheres as the pore-forming agent. The particle size of the pore-forming agent matches the particle size of the pores within the target coral sand, preferably using polystyrene microspheres of 3μm to 50μm. This pore-forming agent completely decomposes and volatilizes during the high-temperature sintering process, leaving uniform micron-sized pores within the quartz sand particles without leaving impurities that could affect optical properties. The specific implementation steps are as follows: First, calculate the addition ratio of the pore-forming agent based on the internal porosity of the target coral sand particles, ensuring that the volume fraction of the pore-forming agent matches the target porosity. Next, uniformly mix the aforementioned refractive index-adapted quartz powder, pore-forming agent, and binder according to a preset ratio, and obtain a particle precursor through ball milling and spray granulation. Subsequently, place the particle precursor into a sintering furnace and first maintain it at a low temperature range of 300℃ to 500℃ to allow the pore-forming agent to completely decompose and volatilize, forming a porous structure inside the particles. Finally, raise the temperature to a preset sintering temperature for high-temperature sintering to densify the particle matrix, resulting in porous modified quartz sand particles with an internal porosity completely consistent with the target coral sand.

[0078] The third step is to adjust the sintering parameters and the ratio of the pore-forming agent to match the mechanical parameters of the modified quartz sand with those of the target coral sand. It should be noted that the pile group horizontal bearing capacity model test simulates the interaction mechanical behavior between the pile group and the soil; therefore, it is essential to ensure that the mechanical properties of the modified quartz sand are consistent with those of natural coral sand. Otherwise, the pile group horizontal bearing capacity results obtained from the model test will not reflect the actual engineering situation. In this embodiment, the mechanical parameters that need to be matched include particle strength, crushing characteristics, internal friction angle, cohesion, and compression modulus. These parameters directly determine the bearing capacity and deformation characteristics of the coral sand foundation. The specific implementation steps are as follows: First, by adjusting the sintering temperature, holding time, and pore-forming agent ratio, the particle strength and crushing characteristics of the modified quartz sand are controlled. The higher the sintering temperature and the longer the holding time, the denser the particle matrix and the higher the particle strength; conversely, the lower the strength, the lower the strength. The particle crushing strength of the modified quartz sand is tested through single-particle crushing tests to ensure that its deviation from the particle crushing strength of the target coral sand does not exceed 5%. Next, the internal friction angle and cohesion of the modified quartz sand are tested through direct shear tests. By adjusting the particle gradation, particle morphology, and surface roughness, its shear strength parameters are ensured to deviate from those of the target coral sand by no more than 5%. Subsequently, the compression modulus of the modified quartz sand is tested through consolidation tests. The pore structure and sintering parameters of the particles are adjusted to ensure that its compression deformation characteristics are consistent with those of the target coral sand. Finally, a series of geotechnical tests are conducted to comprehensively verify the mechanical parameters of the modified quartz sand, ensuring that its mechanical properties match those of natural coral sand.

[0079] The fourth step is to crush and screen the modified quartz sand to ensure its particle size distribution matches that of the target coral sand. It's important to note that particle size distribution directly determines the void ratio, permeability, density, and mechanical properties of the soil. It's a parameter for similarity ratio design in geotechnical engineering model tests, and it's crucial to ensure that the particle size distribution curve of the modified quartz sand coincides with that of the target coral sand. The specific steps are as follows: First, the sintered modified quartz sand particles are crushed using a jaw crusher. Crushing parameters must be controlled during the crushing process to avoid over-crushing and excessive fine particle content. Next, the crushed quartz sand is sieved using a standard geotechnical sieve to obtain particles in different size ranges. Then, based on the particle size distribution sieving results of the target coral sand, modified quartz sand particles of different size ranges are mixed in a specific ratio, and the particle size distribution curve of the mixture is plotted to coincide with that of the target coral sand. Finally, the mixed modified quartz sand is washed with water to remove dust from the particle surface and then dried in a vacuum drying oven for later use.

[0080] It should be noted that in this application, the matching or overlap of parameters and other features refers to the difference between two matching or overlapping values ​​or shapes being within a set precision range. Two parameters whose difference is within the set precision range are considered to be matching or overlapping. The set precision range can be set by those skilled in the art according to actual needs, and this application does not limit it.

[0081] It should be noted that after the modified quartz sand is prepared, it needs to undergo comprehensive performance verification, including solid matrix refractive index testing, single-particle internal porosity testing, mechanical parameter testing, and particle size distribution verification, to ensure that all indicators are highly compatible with the target coral sand before it can be used for subsequent transparent soil sample preparation. Simultaneously, the prepared modified quartz sand needs to be dried in a vacuum drying oven at 105℃ for at least 24 hours to completely remove moisture and air from the internal pores of the particles. This prevents residual air and moisture in the pores from causing changes in the equivalent refractive index, which would affect the subsequent solid-liquid refractive index matching effect.

[0082] In an optional embodiment, the preparation of modified quartz sand in step S21, which is adapted to the optical properties, mechanical properties, and particle size distribution of the target coral sand, specifically includes the following steps: The refractive index of the solid matrix of fused silica sand is controlled by doping with TiO2 or ZrO2 nanoparticles to match the refractive index of the solid matrix of the target coral sand. A solid-phase sintering pore-forming process is adopted, using polymer microspheres as pore-forming agents to construct micron-level pores inside quartz sand particles, so that the porosity of a single particle matches that of the target coral sand. Adjust the sintering temperature, holding time, and pore-forming agent ratio to match the particle strength, internal friction angle, cohesion, and compressive modulus mechanical parameters of the modified quartz sand with those of the target coral sand. The modified quartz sand is crushed and screened, and particles of different particle size ranges are mixed in proportion to make its particle size distribution curve coincide with the target coral sand.

[0083] In this embodiment of the application, it should be noted that the preparation accuracy of the pore liquid phase directly determines the solid-liquid refractive index matching effect, and thus determines the light transmittance and imaging quality of the soil, which is the key to whether a clear laser slice image can be acquired during the horizontal loading of pile groups.

[0084] In this embodiment, a binary miscible system composed of n-dodecane and food-grade white oil is used as the pore liquid phase. This system meets the following requirements: First, it matches the target equivalent refractive index of modified quartz sand, with an adjustable refractive index range covering 1.42 to 1.48, adapting to the equivalent refractive index range of most coral sands; Second, it is chemically stable, does not react with modified quartz sand, model boxes, or pile model materials, and does not dissolve or deteriorate during long-term immersion, ensuring the stability of the liquid phase properties during long-term pile loading tests; Third, it is non-toxic, non-corrosive, and has low volatility, ensuring the operational safety of test personnel and avoiding refractive index changes caused by liquid phase volatilization during the test; Fourth, the two components are completely miscible, and the refractive index after mixing satisfies the principle of linear superposition, facilitating accurate proportioning and adjustment.

[0085] In this specific example, in the binary porous liquid system, n-dodecane is a straight-chain alkane with a refractive index of 20℃ and 589nm wavelength. The temperature refractive index is 1.421. It has a refractive index of -0.0004 g / ℃, exhibiting low viscosity and good fluidity; food-grade white oil is mineral oil, with a refractive index of -0.0004 g / ℃ at 589 nm. The temperature refractive index coefficient is 1.470. With a temperature of -0.0003 °C, it possesses chemical stability, extremely low volatility, and is non-toxic and harmless. Both are completely miscible in any proportion, and the refractive index of the mixture satisfies the principle of linear superposition, fully meeting the refractive index matching accuracy requirements for transparent soil tests. Those skilled in the art will understand that by adjusting the volume ratio of n-dodecane to white oil, the refractive index of the porous liquid phase can be continuously adjusted within the range of 1.421 to 1.470. This range completely covers the target equivalent refractive index range of most coral sand particles, demonstrating extremely strong applicability.

[0086] Next, in this embodiment, based on the principle of linear superposition of refractive indices in a binary miscible system, the initial volume ratio of n-dodecane to white oil is calculated. The specific formula for the linear superposition principle is as follows:

[0087] The physical meanings of each parameter in the formula are as follows: The target refractive index of the porous liquid phase is dimensionless, i.e., the target equivalent refractive index of the coral sand particles calculated above. And temperature correction has been completed; : Volume fraction of n-dodecane in porous liquid phase, dimensionless, ranging from 0 to 1; The volume fraction of white oil in the porous liquid phase, dimensionless, satisfying... ; Measured refractive index of n-dodecane corresponding to the laser wavelength used in the experiment at a standard temperature of 20℃, dimensionless; : Measured refractive index of white oil corresponding to the laser wavelength used in the test at the standard temperature of 20℃, dimensionless.

[0088] It should be noted that in the formula and Values ​​measured on-site must be used because different batches of n-dodecane and white oil may have slight differences in refractive index. Directly using empirical values ​​will lead to deviations in the initial mixing ratio, increasing the workload of subsequent adjustments. In the embodiments of this application, and The test uses the same high-precision Abbe refractometer as the solid matrix refractive index test, the test light source is the same wavelength as the test laser, the test temperature is the standard temperature of 20℃, and each batch of liquid phase is tested no less than 3 times, and the average value is taken as the final measured refractive index.

[0089] Next, the above linear superposition formula is transformed to derive an explicit calculation formula for the volume ratio of n-dodecane to white oil, which facilitates direct calculation of the initial ratio. Substituting into the original formula, we get:

[0090] Rearrange the terms in the formula and separate them. Item, obtained:

[0091] The final explicit formula for calculating the volume ratio is obtained:

[0092] The physical meanings of the parameters in the formula are consistent with those described above. Using this formula, we only need to substitute the target refractive index of the porous liquid phase. And the measured refractive index of n-dodecane and white oil. , This allows for the rapid calculation of the initial volume ratio of the two components.

[0093] In an optional implementation, step S22 involves calculating the volume ratio of n-dodecane to white oil, preparing a porous liquid phase, and adjusting it to the target refractive index. This specifically includes the following steps: The measured refractive indices of n-dodecane and white oil were tested at standard temperature and experimental laser wavelength. Based on the principle of linear superposition of refractive indices in a binary miscible system, the initial volume ratio of the two components was calculated. The porous liquid phase was prepared according to the initial ratio, and its actual refractive index at the experimental laser wavelength was tested. The addition amounts of the two components were adjusted using a gradient adjustment method until the refractive index of the porous liquid phase was the same as the target equivalent refractive index. The full-spectrum refractive index of the porous liquid phase within a preset visible light range was tested to verify the full-spectrum matching effect.

[0094] In this embodiment, a porous liquid phase is prepared according to an initial ratio, and its actual refractive index at the experimental laser wavelength is tested. The addition amounts of the two components are adjusted using a gradient adjustment method until the error between the refractive index of the porous liquid phase and the target equivalent refractive index does not exceed a preset threshold. The specific implementation steps are as follows: First, based on the calculated initial volume ratio, the corresponding volumes of n-dodecane and white oil are measured using a graduated cylinder with an accuracy of at least 1 mL, poured into a clean, dry brown reagent bottle, sealed, and thoroughly stirred to prepare the initial porous liquid phase. Next, using a high-precision Abbe refractometer, at a standard temperature of 20°C and the experimental laser wavelength, the actual refractive index of the initial porous liquid phase is tested. Each batch is tested at least three times, and the average value is taken as the measured refractive index. Subsequently, based on the deviation between the measured refractive index and the target refractive index, the addition amounts of the two components are adjusted using a gradient adjustment method. If the measured refractive index is higher than the target value, it indicates that the proportion of white oil is too high. Add 1 mL of n-dodecane each time, stir evenly, and then remeasure the refractive index. If the measured refractive index is lower than the target value, it indicates that the proportion of n-dodecane is too high. Add 1 mL of white oil each time, stir evenly, and then remeasure the refractive index. Finally, continue to adjust until the error between the measured refractive index of the porous liquid phase and the target equivalent refractive index does not exceed the preset accuracy range. In this embodiment, the preset accuracy range is ±0.002, and in the optimal case, it can be controlled within ±0.001, thereby ensuring the accuracy of solid-liquid refractive index matching.

[0095] It should be noted that during the preparation and adjustment of the porous liquid phase, it is essential to ensure that reagent bottles, measuring cylinders, stirring rods, and other containers are completely clean and dry to prevent moisture and impurities from contaminating the liquid phase and causing deviations in the refractive index test. Simultaneously, the prepared porous liquid phase must be sealed and stored in a brown reagent bottle to prevent light exposure and evaporation, ensuring long-term stability of its refractive index. Furthermore, in this embodiment, it is also necessary to test the full-spectrum refractive index of the porous liquid phase within a preset visible light range to verify the full-spectrum matching effect and ensure that the refractive index of the porous liquid phase maintains a good match with the equivalent refractive index of the coral sand throughout the entire visible light range. This improves the full-spectrum transmittance of the soil and enhances imaging quality.

[0096] In this embodiment, a pile group model is preset and fixed inside a model box. Modified quartz sand is filled into the model box, and pore liquid phase is injected to complete saturation, thus preparing a transparent coral sand sample with an internal pile group model. Figure 4 As shown. It should be noted that the sample preparation process directly determines the soil's density, uniformity, air bubble content, and the positioning accuracy of the pile group model, which in turn affects the soil's optical and mechanical properties, as well as the accuracy of the pile group horizontal loading test. Therefore, it is essential to strictly follow the standardized procedures.

[0097] In this embodiment, the specific steps for preparing the transparent coral sand sample with a built-in pile group model are as follows: The first step is the pretreatment and fixation of the model box and the pile group model. The model box is preferably made of high-transmittance plexiglass to ensure that the laser can penetrate the model box wall without distortion and irradiate the soil inside. Before the test, the model box is cleaned and completely dried. Then, a layer of silicone oil with a refractive index matching that of the porous liquid phase is applied to the inner wall of the model box to eliminate the interface refraction caused by the refractive index difference between the plexiglass wall and the liquid phase, and to avoid additional distortion in the imaging.

[0098] The pile group model should preferably be made of materials with high rigidity and low deformation, such as aluminum alloy and acrylic. The model size, pile spacing, number of piles, and arrangement should be determined based on the similarity ratio between the engineering prototype and the model test. The pile surface should be matte to avoid overexposure of the image caused by laser reflection. The pile group model, high-precision checkerboard calibration plate, displacement sensors, and other devices required for the test should be pre-installed in the model box. The pile group model should be fixed to the bottom of the model box or the loading system with a rigid fixing frame to ensure that the pile axis is perpendicular to the bottom surface of the model box and that the pile does not undergo any additional displacement other than the design displacement during horizontal loading. The calibration plate should be placed in the laser slice plane of the subsequent test to ensure that the plane of the calibration plate coincides with the plane of the laser slice, providing a reference for subsequent distortion correction.

[0099] The second step involves the layered filling of modified quartz sand and the incorporation of tracer particles. The dried modified quartz sand is uniformly mixed with fluorescent tracer particles. The refractive index of the tracer particles matches the pore liquid, and the particle size matches the modified quartz sand particles. Fluorescent polystyrene microspheres with a particle size of 5μm to 50μm are preferred, and their dosage is controlled at 0.1% to 0.5% of the modified quartz sand mass. These microspheres are used for subsequent PIV / PTV algorithm identification of the soil displacement field.

[0100] Modified quartz sand, mixed with tracer particles, is slowly and layered into the model box. Each layer is no more than 2 cm thick. After each layer is filled, it is gently compacted to the designed density using a micro vibrator to ensure soil homogeneity and avoid segregation or stratification. The position of the pile model must be monitored in real time during filling to prevent pile displacement. After filling to the designed elevation, the soil surface is leveled to achieve the designed sample height. It should be noted that the thickness of each layer should not be too large, otherwise it may lead to porosity and uneven density within the soil, resulting in local refractive index mismatch and dark or blurred areas in the imaging. At the same time, the compaction force needs to be strictly controlled to avoid breakage of the modified quartz sand particles, which could alter the soil's gradation and mechanical properties.

[0101] The third step is the injection and vacuum saturation of the pore liquid phase. The prepared pore liquid phase is slowly injected along the side wall of the model box. The injection speed should not be too fast to avoid the liquid phase impacting the soil and causing damage to the filling structure or displacement of the pile model. The injection continues until the liquid surface completely covers the soil surface and is at least 2 cm above it. Then, the model box is placed in a vacuum saturation chamber, and a vacuum is drawn to a level not lower than -0.1 MPa. This vacuuming is maintained for at least 2 hours to completely remove air bubbles from the soil, including those in the pores between and within the particles, ensuring that the internal pores of the modified quartz sand particles are completely filled with the pore liquid phase. After vacuuming, the vacuum is slowly released, the model box is removed, and it is left to stand for 24 hours. Once the soil is fully saturated and all air bubbles have been removed, the preparation of the transparent soil sample is complete.

[0102] Those skilled in the art will understand that air bubbles in the soil are an important factor affecting the imaging quality of transparent soil. The refractive index of air bubbles is 1.0003, which is extremely different from the refractive index of the solid and liquid phases. This will lead to strong light scattering, causing the soil to appear turbid and opaque. Therefore, it is necessary to completely remove the air bubbles from the soil by vacuum pumping to ensure that the pores inside and between the particles are completely filled by the pore liquid phase. This is a key step in preparing high-quality transparent soil samples.

[0103] It should be noted that after the transparent soil sample is prepared, its matching effect needs to be finally verified. The verification indicators include soil transmittance, laser speckle contrast, and consistency of mechanical properties. First, the transmittance of the laser after penetrating the soil at the test laser wavelength is tested using a laser power meter, and the transmittance is required to be no less than 80%. Second, speckle images of the laser slices are captured using a high-speed industrial camera, and the speckle contrast is calculated, requiring a contrast of no less than 0.3 to meet the recognition requirements of the PIV / PTV algorithm. Finally, geotechnical tests are conducted on parallel samples to verify that the deviation of the mechanical parameters of the transparent soil sample from those of natural coral sand does not exceed 5%, ensuring the similarity of the model test. Only when all verification indicators meet the requirements can the transparent soil sample be used for subsequent pile group horizontal loading tests.

[0104] In alternative implementations, such as Figure 5 As shown, step S3 specifically includes the following steps: S31: Build a laser-camera visualization testing system, adjust the line laser so that the laser plane coincides with the plane containing the pile axis of the pile group model to form a laser slice; adjust the shooting parameters and position of the high-speed industrial camera so that the laser slice area is completely within the camera's field of view; S32: Apply graded horizontal loads to the pile group model using a loading device. After each load is applied, use a high-speed industrial camera to simultaneously acquire laser slice images under that load and simultaneously record the load value and pile top horizontal displacement value corresponding to each load until the pile group model reaches the horizontal ultimate bearing state.

[0105] In this embodiment, after preparing the transparent coral sand soil sample with the built-in pile group model, the next step is to apply graded horizontal loads to the pile group model. During the loading process, laser slice images of the transparent coral sand soil sample are simultaneously acquired using a laser-camera visualization testing system. It should be noted that this step is crucial for obtaining the horizontal load data of the pile group and the original images of the soil deformation around the piles. The rationality of the loading regime, the synchronization and clarity of image acquisition directly determine the accuracy of the subsequent determination of the horizontal bearing characteristics of the pile group.

[0106] In this embodiment, a laser-camera visualization test system is first built. The system mainly consists of a line laser, a high-speed industrial camera, a synchronization controller, an optical platform, and a loading device. All equipment is fixed on the optical platform to avoid equipment vibration affecting the imaging quality during the test.

[0107] The specific setup and debugging steps are as follows: First, fix the experimental line laser to one side of the model box, with the laser's output direction perpendicular to the acrylic sidewall of the model box. Adjust the height and angle of the laser so that the laser emission plane coincides with the plane containing the pile axis of the pile group model. Figure 6 As shown, a laser slice of uniform thickness is formed, with the thickness preferably controlled between 1mm and 2mm to ensure that the tracer particles within the slice do not undergo out-of-plane displacement, thus improving the accuracy of displacement field calculation. Next, a high-speed industrial camera is fixed in front of the model box, with the camera's optical axis perpendicular to the laser slice plane. The camera's focal length, aperture, exposure time, and other parameters are adjusted to ensure that the laser slice area is completely within the camera's field of view, guaranteeing a clear image without overexposure or vignetting. The camera's resolution is preferably no less than 2048×2048 pixels, and the sampling frame rate is no less than 10fps to meet the image acquisition requirements during the graded loading process. Subsequently, a synchronization controller is used to synchronize the line laser, high-speed industrial camera, and loading device, ensuring the synchronization of loading, laser emission, and image acquisition, and avoiding deviations in capturing soil deformation around the pile caused by asynchrony.

[0108] In this embodiment, the slow sustained load method is used to apply graded horizontal loads to the pile group model. This method is a standard method for horizontal static load tests of pile foundations in geotechnical engineering, and can accurately obtain the load-displacement curves and ultimate bearing capacity of the pile group.

[0109] The specific loading implementation steps are as follows: First, based on the similarity ratio of the model test and the design bearing capacity of the engineering prototype, calculate the estimated ultimate horizontal bearing capacity of the pile group model, determine the graded load difference, and the load value of each grade should be 1 / 10 to 1 / 15 of the estimated ultimate bearing capacity. For the first grade load, twice the graded load value can be applied. Next, apply a horizontal load to the top of the piles of the pile group model through a horizontal loading device. The loading direction is consistent with the arrangement axis of the pile group, and the load application point is consistent with the design elevation of the pile top, ensuring that the load is transmitted horizontally along the pile axis and avoiding the generation of additional bending moment. After each grade of load is applied, keep the load stable and record the horizontal displacement value of the pile top at a preset time interval. When the change in the horizontal displacement of the pile top does not exceed 0.1 mm within 1 hour, it is considered that the deformation under that grade of load has stabilized, and the next grade of load can be applied.

[0110] During loading, the pile group model is deemed to have reached its horizontal ultimate bearing capacity and loading is stopped when any of the following conditions occur: First, the horizontal displacement at the pile top increases sharply, and the load-displacement curve shows a significant steep drop; second, the horizontal displacement at the pile top reaches 10% of the pile diameter, exceeding the critical displacement value allowed by the specification; third, significant heaving and cracking of the soil around the pile occurs, indicating instability and failure. After loading is stopped, unloading is performed in stages according to graded load differentials. Each unloading stage is twice the graded load value at the time of loading. After each unloading stage, the load is kept stable, and the rebound displacement value at the pile top is recorded.

[0111] In this embodiment of the application, laser slice images are synchronously acquired by a high-speed industrial camera throughout the entire process of graded loading, providing raw data for subsequent calculation of the displacement field of the soil around the pile.

[0112] The specific data acquisition requirements are as follows: Before the experiment, acquire laser slice images in the unloaded state as initial reference images for displacement field calculation; after each load level is applied and the pile top deformation stabilizes, simultaneously acquire laser slice images under that load level, with no fewer than 10 frames acquired for each load level, and take the average value as the representative image for that load level to reduce the impact of image noise; during the acquisition process, the positions of the camera, laser, and model box must be kept fixed to avoid image deviations caused by equipment displacement; at the same time, monitor the image clarity and speckle contrast in real time. If image quality deterioration occurs, loading must be paused, the cause investigated and resolved before the experiment can continue. The acquired images must be numbered according to the load level, and the corresponding load values ​​and pile top horizontal displacement values ​​must be saved simultaneously and stored in the image processing system to provide raw data for subsequent distortion correction and bearing characteristic analysis.

[0113] In alternative implementations, such as Figure 7 As shown, step S4 specifically includes the following steps: S41: Select calibration feature points, solve the homography matrix, and perform perspective trapezoidal distortion correction on the laser slice image to obtain an orthophoto image without geometric distortion; S42: Based on the point spread function of the pile boundary identification image, perform regional scattering blur distortion correction on the orthophoto image; S43: Perform contrast optimization and noise removal on the corrected image to obtain the final corrected test image.

[0114] In this embodiment, after completing the horizontal loading test of the pile group and acquiring the laser slice images, the next step is to sequentially correct the perspective trapezoidal distortion and scattering blur distortion of the acquired laser slice images to obtain corrected test images. It should be noted that this step is crucial for eliminating image errors and ensuring the accuracy of the displacement field measurement of the soil around the piles. Images acquired from the coral sand transparent soil model test inevitably exhibit two types of distortion: the first is perspective trapezoidal distortion, caused by the camera not being perpendicular to the laser slice plane and refraction from the plexiglass wall of the model box, resulting in trapezoidal deformation and distorted coordinate scale, leading to systematic geometric errors in the displacement field calculation; the second is scattering blur distortion, caused by residual diffuse scattering from coral sand particles, resulting in blurred images, blurred edges, and overlapping speckles, leading to errors in tracer particle identification and random errors in the displacement field. Only by accurately correcting these two types of distortion can high-quality test images be obtained, providing a reliable data foundation for the accurate analysis of the horizontal bearing characteristics of the pile group.

[0115] In this embodiment of the application, the specific implementation process of this step is divided into three stages: perspective trapezoidal distortion correction, scattering blur distortion correction, and image post-processing optimization. The specific implementation methods, algorithm principles, and operation details of each stage are explained in detail below.

[0116] In this embodiment, calibration feature points are selected, the homography matrix is ​​solved, and perspective trapezoidal distortion correction is performed on the laser slice image to obtain an orthophoto image without geometric distortion. It should be noted that the essence of perspective trapezoidal distortion is a deviation in the projection transformation from the three-dimensional world coordinate system to the two-dimensional image pixel coordinate system, resulting in a disproportion between the geometric shape in the image and the actual physical coordinates. The homography matrix can accurately describe the projection mapping relationship between two planes. By solving the homography matrix and performing an inverse projection transformation, perspective trapezoidal distortion can be completely eliminated, restoring an orthophoto image without geometric distortion. Compared to traditional calibration methods, this application uses calibration feature points on a calibration plate, which not only achieves high-precision initial calibration but also allows for real-time correction of slight camera displacement during the experiment, avoiding calibration failures caused by camera vibration and displacement, and ensuring the accuracy of geometric correction throughout the experiment.

[0117] In this embodiment, the basic principle of homography matrix is ​​first explained in detail. It is a 3×3 homogeneous transformation matrix that describes the projection mapping relationship between the world physical coordinate system (two-dimensional plane) and the image pixel coordinate system. For any homogeneous coordinate point in the world physical coordinate system, its corresponding homogeneous coordinate point in the image pixel coordinate system satisfies the following mapping relationship:

[0118] Expanding this expression into matrix form, we get:

[0119] The physical meanings of each parameter in the formula are as follows: The horizontal and vertical pixel coordinates of a feature point in the image pixel coordinate system, in pixels; : The actual horizontal and vertical physical coordinates of the feature point in the world physical coordinate system, in mm; A 3×3 homography matrix containing to There are a total of 9 unknown parameters.

[0120] It should be noted that the homography matrix is ​​a homogeneous matrix. After normalization to 1, the matrix contains 8 independent unknown parameters. According to linear algebra theory, at least 4 pairs of non-collinear feature points are needed to establish a system of equations to solve for the homography matrix. All parameters are available. Those skilled in the art will understand that solving for the homography matrix is ​​for perspective distortion correction; only by solving for an accurate homography matrix can an accurate inverse projection transformation be achieved, eliminating perspective trapezoidal distortion.

[0121] In this embodiment, the specific implementation steps for perspective trapezoidal distortion correction are as follows: The first step is the selection and coordinate recording of calibration feature points. Based on the calibration board image obtained from the checkerboard pattern within the laser slice plane before the experiment, the corner points of the checkerboard pattern are extracted using a corner detection algorithm and used as calibration feature points. The spacing between the corner points of the checkerboard pattern on the calibration board is a known standard physical dimension. Therefore, the actual physical coordinates (world coordinate system) and the corresponding image pixel coordinates (image coordinate system) of each calibration feature point can be directly obtained. The number of feature points is no less than 10 pairs, and not all of them are collinear, thereby improving the accuracy of solving the homography matrix.

[0122] The second step is to solve and optimize the homography matrix. Based on the selected calibration feature points, the initial homography matrix is ​​first solved using the Direct Linear Transform (DLT) algorithm. Specifically, for each pair of feature points, two linear equations can be established regarding the parameters of the homography matrix. Four pairs of non-collinear feature points can establish eight linear equations, from which eight normalized unknown parameters are solved to obtain the initial homography matrix. However, the direct linear transformation algorithm is sensitive to mismatches and noise in feature points, and the resulting initial matrix may contain significant errors. Therefore, in this embodiment, the Random Sample Consensus (RANSAC) algorithm is used to iteratively optimize the initial homography matrix, eliminating mismatched feature points and reducing the impact of image noise on the solution. The principle of the RANSAC algorithm is to iteratively randomly sample multiple feature points on the image, distinguishing between inliers (correct feature points conforming to the model) and outliers (abnormal feature points with mismatches). Based on the inliers, the homography matrix is ​​re-solved, ultimately obtaining the globally optimal homography matrix.

[0123] The third step is frame-by-frame geometric correction. For each frame of laser slice image acquired during the experiment, the validity of the homography matrix can be verified by calibrating feature points. If the camera experiences slight vibration or displacement during the experiment, the calibrated pixel coordinates will deviate. In this case, the system will automatically optimize and update the homography matrix based on the calibrated feature points to ensure the matrix's validity. Subsequently, for each pixel in the image, its true physical coordinates in the world coordinate system are calculated through the inverse transformation of the homography matrix. The entire image is then subjected to inverse projection transformation to complete perspective trapezoidal distortion correction, resulting in an orthophoto image without geometric distortion. It should be noted that during the inverse projection transformation, a bilinear interpolation algorithm can be used to resample the image pixels to avoid problems such as jagged edges and holes in the corrected image, ensuring the smoothness and clarity of the image.

[0124] After completing the perspective trapezoidal distortion correction and obtaining an orthorectified image without geometric distortion, this embodiment of the application performs regional scattering blur distortion correction on the orthorectified image based on the point spread function of the pile boundary identification image. It should be noted that scattering blur distortion is a unique type of distortion in coral sand transparent soil imaging, caused by residual diffuse scattering from porous coral sand particles. Even if the solid-liquid refractive index matching accuracy meets the requirements, slight residual scattering will still exist, leading to problems such as image blurring, edge blurring, and speckle overlap, severely affecting the recognition accuracy of tracer particles. Traditional image deblurring methods do not consider the scattering characteristics of coral sand, resulting in poor deblurring effects and amplification of image noise. This application, based on the physical mechanism of scattering blur, employs point spread function modeling and Wiener inverse filtering algorithm, combined with a regional differentiated correction strategy, to effectively eliminate scattering blur while suppressing noise amplification, ensuring the speckle characteristics of the image, and meeting the recognition requirements of the PIV / PTV algorithm.

[0125] In this embodiment, the mathematical model of scattering blur distortion is first described in detail. The essence of scattering blur is that an ideal, clear image undergoes convolution degradation after being scattered by an optical system. This process can be described by the following convolution model of a linear space-invariant system:

[0126] The physical meanings of each parameter in the formula are as follows: The blurred and distorted image obtained from the photograph, i.e. the orthophoto image after geometric correction, is a known quantity; An ideal, distortion-free, and clear image is an unknown quantity that needs to be restored through algorithms; The point spread function (PSF) of an optical system describes the image blurring characteristics caused by coral sand scattering and is a parameter that the algorithm needs to identify. Additive Gaussian noise in the image is caused by camera photoelectric noise and ambient light interference. : Two-dimensional convolution operator.

[0127] Those skilled in the art will understand that scattering blur distortion correction involves identifying the accurate point spread function. Then, through an inverse filtering algorithm, the blurred image is... Restore a clear image If the point spread function (PSF) is not accurately identified, it will lead to poor deblurring results and even secondary distortion. Therefore, accurate PSF identification is the key to scattering distortion correction.

[0128] In this embodiment, the scattering blur of transparent coral sand conforms to a two-dimensional Gaussian distribution. Therefore, a two-dimensional Gaussian function is used to construct a point spread function model for scattering blur. This model can accurately describe the image blurring features caused by scattering, and it has few parameters, making it easy to identify and calculate. The specific expression of the two-dimensional Gaussian point spread function is as follows:

[0129] The physical meanings of each parameter in the formula are as follows: : Two-dimensional Gaussian point spread function; The standard deviation of the Gaussian kernel is dimensionless and characterizes the degree of blur in an image. The higher the value, the more severe the image blurring; : The horizontal and vertical coordinates of a pixel, in pixels.

[0130] It should be noted that the only parameter that needs to be identified in this model is the standard deviation of the Gaussian kernel. As long as it is accurately determined By obtaining the numerical value of the point spread function, an accurate point spread function can be obtained, thus completing the modeling of scattering fuzziness. In this embodiment, the Gaussian kernel standard deviation of the point spread function is obtained based on the geometrically corrected pile boundary fitting. The specific principle is as follows: Ideally, the vertical boundary of the model pile is a step function, where the pixel grayscale value changes abruptly at the boundary. After scattering blurring, the grayscale value of the pile boundary exhibits a Gaussian distribution gradient. This gradient distribution characteristic is completely consistent with the Gaussian kernel of the point spread function. Therefore, by fitting the grayscale gradient distribution of the pile boundary, the grayscale value can be accurately obtained. The value.

[0131] In this embodiment, the specific implementation steps for scattering blur distortion correction are as follows: The first step is parameter identification of the point spread function. First, the vertical boundary region of the pile body after geometric correction is selected. Ideally, this region is a vertical step boundary, unaffected by soil deformation, and can accurately reflect the characteristics of scattering blur. Next, along the direction perpendicular to the pile boundary, the grayscale value sequence of pixels is extracted, and a grayscale distribution curve is plotted. Then, a nonlinear least squares fitting algorithm is used to fit the grayscale distribution curve with a Gaussian function to obtain the standard deviation of the Gaussian kernel. The point spread function (PSF) model for scattering ambiguity was determined. It should be noted that during the experiment, the scattering characteristics may slightly change with soil deformation and density; therefore, the PSF parameters were re-identified for each frame of the image. It adapts to changes in scattering characteristics during the loading process to ensure the stability of the correction effect.

[0132] The second step involves using the Wiener inverse filtering algorithm to perform frequency domain filtering on the images of each region, thus completing the correction of scattering blur distortion. It should be noted that traditional direct inverse filtering algorithms, when processing blurred images, severely amplify noise in the image, leading to significant noise interference in the corrected image. In contrast, the Wiener inverse filtering algorithm introduces a signal-to-noise ratio constraint during inverse filtering, effectively suppressing noise amplification while eliminating blur, making it one of the optimal algorithms for processing scattering blurred images. In this embodiment, the frequency domain expression of the Wiener inverse filtering algorithm is:

[0133] The physical meanings of each parameter in the formula are as follows: The frequency domain Fourier transform result of the restored clear image; : Frequency domain Fourier transform results of blurred and distorted images; Point spread function The frequency domain Fourier transform result, i.e., the optical transfer function; : The complex conjugate function; : The square of the modulus; The signal-to-noise ratio of an image, which is the ratio of the power spectrum of noise to the power spectrum of the clear image, is estimated from the background region of the image. : The horizontal and vertical frequency coordinates in the frequency domain.

[0134] The specific implementation process is as follows: First, perform a two-dimensional Fast Fourier Transform (FFT) on the blurred image of each region to transform the image from the spatial domain to the frequency domain, obtaining... Next, after zero-filling the identified point spread function, a two-dimensional fast Fourier transform is performed to obtain the optical transfer function in the frequency domain. Subsequently, the signal-to-noise ratio of the image is estimated based on the grayscale values ​​of the background region. Substituting into the Wiener inverse filtering formula, the frequency domain result of the clear image is calculated. Ultimately, for Perform a two-dimensional inverse fast Fourier transform (IFFT) to convert the image from the frequency domain back to the spatial domain, obtaining a clear image of each region after correction. After stitching, the scattering blur distortion correction of the entire image is completed.

[0135] After correcting for perspective trapezoidal distortion and scattering blur distortion, this embodiment of the application performs contrast optimization and noise removal on the corrected image to obtain the final experimental image. Specifically, a contrast-limited adaptive histogram equalization (CLAHE) algorithm is used to optimize the image contrast, improve the contrast of the laser speckle field, suppress local overexposed and underexposed areas, and ensure uniform grayscale distribution of the speckle. Subsequently, a nonlocal mean filtering algorithm is used to remove residual noise in the image while preserving the edge features and texture information of the speckle, avoiding damage to the characteristics of the tracer particles, and ensuring the particle recognition accuracy of the PIV / PTV algorithm. The final corrected image has no geometric distortion, no scattering blur, high speckle contrast, and low noise, and can be directly used for subsequent pile perimeter soil displacement field calculation and pile group horizontal bearing characteristics analysis.

[0136] In this embodiment, after obtaining the corrected high-quality test images, the final step is to calculate the displacement and strain fields of the soil around the piles under graded horizontal loads based on the corrected test images, and to determine the horizontal bearing characteristics of the pile group on the coral sand foundation by combining the graded load data. This step is the ultimate goal of the method in this application. Through quantitative analysis of the microscopic deformation of the soil around the piles, combined with macroscopic load-displacement data, the horizontal bearing characteristics of the pile group are comprehensively and accurately determined, revealing the interaction mechanism between the pile group and the coral sand soil.

[0137] In this embodiment, the displacement and strain fields of the soil around the pile are calculated using the PIV / PTV algorithm based on the corrected test images under various load levels. The specific implementation steps are as follows: First, using the corrected image under no-load conditions as a reference image, and the corrected image under each load level as the image to be analyzed, the image is divided into several query windows for cross-correlation analysis. The query window size is preferably set to 32×32 pixels or 64×64 pixels, with a 50% overlap between adjacent windows to improve the spatial resolution of the displacement field. Next, the displacement vector of the tracer particles within each query window is calculated using the cross-correlation algorithm to obtain the full-field displacement vector distribution of the soil around the pile under that load level, i.e., the displacement field. Subsequently, based on the spatial gradient distribution of the displacement field, the strain field of the soil around the pile is calculated using the least squares method, including horizontal strain, vertical strain, and shear strain, quantitatively characterizing the degree and range of deformation of the soil around the pile.

[0138] It should be noted that after the displacement field calculation is completed, the calculation results need to be validated and outliers removed. The median filtering algorithm is used to remove outliers in the displacement vector to ensure the continuity and rationality of the displacement field. The outliers after removal are supplemented by displacement vector interpolation of adjacent windows to finally obtain accurate displacement field and strain field data of the soil around the pile.

[0139] Of course, it should be noted that those skilled in the art may also use other parameters or calculation methods to perform displacement field analysis and obtain the final displacement field and strain field data of the soil around the pile, and this application does not limit this.

[0140] In this embodiment, by combining the load data recorded during the graded loading process, the horizontal displacement data at the pile top, and the microscopic analysis results of the displacement and strain fields of the soil around the pile, the horizontal bearing characteristics of the coral sand foundation pile group are comprehensively determined from both macroscopic and microscopic dimensions, specifically including the following: First, plot the horizontal load-pile top displacement curve (H-Δ curve) of the pile group to determine the ultimate horizontal bearing capacity of the pile group. Plot the horizontal load H as the ordinate and the horizontal displacement Δ at the pile top as the abscissa. Based on the curve characteristics and the termination loading condition, determine the ultimate horizontal bearing capacity of the pile group: for H-Δ curves with a significant steep drop, take the load value corresponding to the starting point of the steep drop as the ultimate horizontal bearing capacity; for H-Δ curves without a significant steep drop, take the load value corresponding to when the horizontal displacement at the pile top reaches 10% of the pile diameter as the ultimate horizontal bearing capacity. Simultaneously, based on the rebound displacement data at the pile top during the staged unloading process, calculate the ratio of residual deformation to elastic deformation of the pile group to evaluate the deformation recovery capacity of the pile group foundation.

[0141] Second, the inter-pile soil effect and load sharing characteristics of pile groups are analyzed. Based on the displacement field data of the soil around the piles, the differences in soil deformation at different pile locations are analyzed to determine the range of inter-pile soil interaction and the pile group effect coefficient, clarify the load sharing ratio between the front and rear rows of piles, and reveal the load transfer law of the pile group system. At the same time, combined with the strain field data of the soil around the piles, the development range and process of the plastic zone of the soil around the piles are determined, and the yielding failure sequence and failure mode of the coral sand foundation soil during the horizontal loading of the pile group are clarified, providing a theoretical basis for the design of pile group foundations.

[0142] Third, determine the influencing factors and design parameters of the horizontal bearing capacity of pile groups. Through parallel tests with different pile spacings, pile numbers, and layouts, analyze the influence of parameters such as pile spacing, pile number, and soil compaction on the ultimate horizontal bearing capacity of pile groups, determine the key parameters and optimal layout for the horizontal bearing capacity design of pile groups in coral sand foundations, and provide experimental support for the design of pile group foundations in marine coral sand engineering.

[0143] Based on the same principle, this application also discloses a system for determining the horizontal bearing capacity of a group of piles in a coral sand foundation based on transparent soil, including an equivalent refractive index calculation module, a horizontal loading and image acquisition module, an imaging distortion correction module, and a bearing characteristic analysis module.

[0144] The equivalent refractive index calculation module is used to test the basic parameters of the target coral sand particles. Based on the effective medium theory, a pore light scattering correction model of the coral sand particles is constructed to calculate the target equivalent refractive index of the coral sand particles. The horizontal loading and image acquisition module is used to apply graded horizontal loads to the coral sand transparent soil sample after the solid-liquid two-phase refractive index matching is completed according to the target equivalent refractive index and the built-in pile model is prepared. During the loading process, the laser slice images of the coral sand transparent soil sample are acquired synchronously through the laser-camera visualization test system. The imaging distortion correction module is used to perform perspective trapezoidal distortion correction and scattering blur distortion correction on the acquired laser slice image in sequence to obtain the corrected test image; The bearing characteristics analysis module is used to calculate the displacement and strain fields of the soil around the piles under graded horizontal loads based on the corrected test images, and to determine the horizontal bearing characteristics of the pile group in the coral sand foundation by combining the graded load data.

[0145] The principle of the system for determining the horizontal bearing capacity of a group of piles in a coral sand foundation based on transparent soil in this application is similar to the method described above, and will not be repeated here.

[0146] It should be noted that although the application scenario of the horizontal bearing capacity model test of coral sand pile group is described in detail in the embodiments of this application, the technical solution of this application is not limited to this. It can also be applied to various geotechnical engineering model tests such as coral sand slope instability, seepage evolution, and piping development. It can also be extended to the visualization test of transparent soil of other porous media such as volcanic ash and porous rock. Any adaptive modifications based on the technical principles of this application for application scenarios, material types, and test objects shall fall within the protection scope of this application.

Claims

1. A method for determining the horizontal bearing capacity of a pile group on a coral sand foundation based on transparent soil, characterized in that, Includes the following steps: S1: Test the basic parameters of the target coral sand particles, construct a pore light scattering correction model for the coral sand particles based on the effective medium theory, and calculate the target equivalent refractive index of the coral sand particles; S2: Based on the target equivalent refractive index, complete the refractive index matching of the solid and liquid phases, and prepare a transparent coral sand sample with an embedded pile model. S2 includes: S21: Using fused silica sand as the matrix, prepare modified silica sand that is compatible with the optical properties, mechanical properties, and particle size distribution of the target coral sand. S3: Apply graded horizontal loads to the pile group model, and simultaneously acquire laser slice images of the coral sand transparent soil sample through a laser-camera visualization testing system during the loading process; S4: Perform perspective trapezoidal distortion correction and scattering blur distortion correction on the acquired laser slice image in sequence to obtain the corrected test image; S5: Based on the corrected test images, calculate the displacement and strain fields of the soil around the piles under graded horizontal loads, and determine the horizontal bearing characteristics of the coral sand foundation pile group by combining the graded load data. S1 specifically includes the following steps: S11: Test the three basic parameters of the target coral sand particles: the refractive index of the solid matrix, the porosity of a single particle, and the refractive index of the internal porous medium. S12: Based on the Maxwell-Garnett effective medium theory, the dielectric constant equation is transformed into the refractive index form to construct a pore light scattering correction model for coral sand particles; The aperture light scattering correction model is as follows: The target equivalent refractive index of the coral sand particles at the laser wavelength used in the experiment is dimensionless. : Measured refractive index of the coral sand solid matrix at the experimental laser wavelength, dimensionless; : The refractive index of the porous medium inside coral sand, dimensionless; Internal porosity of a single coral sand particle, dimensionless; S13: Substitute the three basic parameters into the pore light scattering correction model to calculate the target equivalent refractive index of the coral sand particles at the experimental laser wavelength.

2. The method according to claim 1, characterized in that, S1 also includes full-spectrum dispersion correction and temperature correction for the target equivalent refractive index, the specific steps of which are as follows: The refractive index of the target coral sand particle solid matrix and porous medium at different wavelengths was tested, and the Cauchy dispersion coefficient was fitted to obtain the target equivalent refractive index at different wavelengths. Based on the experimental environment temperature and temperature fluctuation range, a temperature refractive index coefficient is introduced to correct the target refractive index of the porous liquid phase at temperature, thereby determining the target refractive index of the liquid phase at the standard temperature.

3. The method according to claim 1, characterized in that, S2 further includes the following steps: S22: Calculate the volume ratio of n-dodecane to white oil based on the target equivalent refractive index, prepare the pore liquid phase and adjust it to the target refractive index; S23: Pre-set and fix the pile group model in the model box, fill the model box with modified quartz sand in layers, inject pore liquid phase and complete vacuum saturation to prepare a transparent coral sand sample with an internal pile group model.

4. The method according to claim 3, characterized in that, The preparation of modified quartz sand in step S21, which is compatible with the optical properties, mechanical properties, and particle size distribution of the target coral sand, specifically includes the following steps: The refractive index of the solid matrix of fused silica sand is controlled by doping with TiO2 or ZrO2 nanoparticles to match the refractive index of the solid matrix of the target coral sand. A solid-phase sintering pore-forming process is adopted, using polymer microspheres as pore-forming agents to construct micron-level pores inside quartz sand particles, so that the porosity of a single particle matches that of the target coral sand. Adjust the sintering temperature, holding time, and pore-forming agent ratio to match the particle strength, internal friction angle, cohesion, and compressive modulus mechanical parameters of the modified quartz sand with those of the target coral sand. The modified quartz sand is crushed and screened, and particles of different particle size ranges are mixed in proportion to make its particle size distribution curve coincide with the target coral sand.

5. The method according to claim 3, characterized in that, The calculation of the volume ratio of n-dodecane to white oil in step S22, the preparation of the porous liquid phase and adjustment to the target refractive index, specifically includes the following steps: The measured refractive indices of n-dodecane and white oil were tested at standard temperature and experimental laser wavelength. Based on the principle of linear superposition of refractive indices in a binary miscible system, the initial volume ratio of the two components was calculated. The porous liquid phase was prepared according to the initial ratio, and its actual refractive index at the experimental laser wavelength was tested. The addition amounts of the two components were adjusted using a gradient adjustment method until the refractive index of the porous liquid phase was the same as the target equivalent refractive index. The full-spectrum refractive index of the porous liquid phase within a preset visible light range was tested to verify the full-spectrum matching effect.

6. The method according to claim 1, characterized in that, S3 specifically includes the following steps: S31: Build a laser-camera visualization testing system, adjust the line laser so that the laser plane coincides with the plane containing the pile axis of the pile group model to form a laser slice; adjust the shooting parameters and position of the high-speed industrial camera so that the laser slice area is completely within the camera's field of view; S32: Apply graded horizontal loads to the pile group model using a loading device. After each load is applied, use a high-speed industrial camera to simultaneously acquire laser slice images under that load and simultaneously record the load value and pile top horizontal displacement value corresponding to each load until the pile group model reaches the horizontal ultimate bearing state.

7. The method according to claim 1, characterized in that, S4 specifically includes the following steps: S41: Select calibration feature points, solve the homography matrix, and perform perspective trapezoidal distortion correction on the laser slice image to obtain an orthophoto image without geometric distortion; S42: Based on the point spread function of the pile boundary identification image, perform regional scattering blur distortion correction on the orthophoto image; S43: Perform contrast optimization and noise removal on the corrected image to obtain the final corrected test image.

8. The method according to claim 7, characterized in that, S41 specifically includes the following steps: Capture images of the checkerboard calibration plate and the boundary of the pile group within the laser slice plane, extract multiple sets of non-collinear calibration feature points, and record the world physical coordinates and image pixel coordinates corresponding to each feature point; The initial homography matrix is ​​solved by the direct linear transformation algorithm, and the homography matrix is ​​iteratively optimized by the random sampling consensus algorithm to eliminate mismatched feature points; Based on the optimized homography matrix, inverse projection transformation is performed on each frame of laser slice image to complete perspective trapezoidal distortion correction; S42 specifically includes the following steps: A point spread function model for scattering ambiguity was constructed using a two-dimensional Gaussian function. Based on the gray-scale gradient distribution of the vertical boundary of the pile after geometric correction, the Gaussian kernel standard deviation of the point spread function was obtained by fitting. The Wiener inverse filtering algorithm is used to perform frequency domain filtering on the image to complete the correction of scattering blur distortion.

9. A system for determining the horizontal bearing capacity of a group of piles on a coral sand foundation based on transparent soil, using the method described in any one of claims 1-8, characterized in that, include: The equivalent refractive index calculation module is used to test the basic parameters of the target coral sand particles. Based on the effective medium theory, a pore light scattering correction model of the coral sand particles is constructed to calculate the target equivalent refractive index of the coral sand particles. The horizontal loading and image acquisition module is used to apply graded horizontal loads to the coral sand transparent soil sample after the solid-liquid two-phase refractive index matching is completed according to the target equivalent refractive index and the built-in pile model is prepared. During the loading process, the laser slice images of the coral sand transparent soil sample are acquired synchronously through the laser-camera visualization test system. The imaging distortion correction module is used to perform perspective trapezoidal distortion correction and scattering blur distortion correction on the acquired laser slice image in sequence to obtain the corrected test image; The bearing characteristics analysis module is used to calculate the displacement and strain fields of the soil around the piles under graded horizontal loads based on the corrected test images, and to determine the horizontal bearing characteristics of the pile group in the coral sand foundation by combining the graded load data.

Images