A method for converting soil dynamic parameters based on bending element and resonant column tests

Abstract

This application relates to the field of geotechnical engineering testing technology and discloses a method for converting soil dynamic parameters based on bending element and resonant column tests. This method determines the plasticity index of the sample and performs bending element and resonant column tests under the same effective consolidation pressure to obtain the high-frequency small-strain shear modulus and the resonant column modulus as a function of strain. The method determines the frequency dispersion characteristics of the soil based on the plasticity index and calculates the frequency correction coefficient using a conversion model to correct the high-frequency bending element modulus to a low-frequency reference small-strain modulus; for cohesive soils, a logarithmic decay function is used to calculate the correction coefficient. This reference modulus is used to normalize the resonant column data and perform nonlinear regression analysis to construct a dynamic shear modulus decay function across the entire strain range. This invention uses the plasticity index to correct the modulus error caused by frequency dispersion, achieving effective fusion of bending element and resonant column test data and improving the accuracy of obtaining soil dynamic parameters.

Description

Technical Field

[0001] This invention relates to the field of geotechnical engineering testing technology, specifically to a method for converting soil dynamic parameters based on bending element and resonant column tests. Background Technology

[0002] The dynamic shear modulus of soil is a calculation parameter used for site seismic safety assessment, foundation dynamic response analysis, and seismic design of engineering projects. To describe the mechanical behavior of soil under dynamic loads, it is necessary to obtain the dynamic shear modulus decay curves over a range from small strain to medium and large strain.

[0003] Resonant column tests and bending element tests are commonly used laboratory testing methods for determining soil dynamic parameters. Resonant column tests are suitable for determining the dynamic shear modulus and damping ratio of soil in the medium and small strain ranges. However, when determining the maximum dynamic shear modulus under extremely low strain conditions, they are easily affected by background noise from the electromagnetic drive system and equipment coupling effects, resulting in relatively low stability of the measurement data. Bending element tests utilize piezoelectric ceramic sensors to excite and receive shear waves. The operation process does not damage the sample and is often used to determine the maximum dynamic shear modulus of soil in the extremely low strain stage.

[0004] The excitation frequency of bending element tests is typically between several kilohertz and tens of thousands of hertz, while engineering dynamics such as seismic waves and wave loads fall into the low-frequency range. Soil, as a viscoelastic medium, exhibits frequency dispersion characteristics, and its dynamic shear modulus increases with increasing loading frequency. Directly applying the maximum dynamic shear modulus obtained from high-frequency bending element tests to low-frequency engineering analysis would result in an overestimation of the modulus value, failing to reflect the stiffness characteristics of the soil under actual engineering conditions.

[0005] Existing technologies, when comprehensively utilizing bending element and resonant column data, typically fail to consider frequency dispersion effects or merely apply fixed coefficients to reduce the bending element test results. Such methods do not establish a quantitative relationship between soil plasticity index and frequency sensitivity, and cannot classify and correct for differences between cohesive and non-cohesive soils. Because the influence of soil physical properties on frequency response is not considered, the initial modulus benchmark is inaccurate, thus affecting the quality of constructing dynamic parameter curves across the entire strain range. Summary of the Invention

[0006] To address the shortcomings of existing technologies, this invention provides a method for converting soil dynamic parameters based on bending element and resonant column tests. This method solves the technical problem that the high-frequency characteristics of bending element tests differ from the low-frequency conditions in actual engineering projects, and that existing conversion methods do not consider the influence of soil plasticity index on frequency dispersion effects, leading to inaccurate values ​​for the soil reference small strain variable shear modulus.

[0007] To achieve the above objectives, the present invention provides the following technical solution: This invention provides a method for converting soil dynamic parameters based on bending element and resonant column tests. This method obtains the soil's baseline small strain shear modulus by combining bending element and resonant column tests under the same effective consolidation pressure and incorporating the soil plasticity index to correct for frequency dispersion effects.

[0008] This method includes sample preparation, dynamic testing, parameter conversion, and curve construction. In the sample preparation and property determination stage, undisturbed soil samples are selected to prepare cylindrical specimens, and their natural density, natural moisture content, and plasticity index are measured. Multiple specimens prepared in the same batch are divided into two groups, used for bending element testing and resonance column testing respectively. The differences in natural density and natural moisture content between the two groups are controlled within a preset allowable range to ensure consistency in physical state.

[0009] In the dynamic testing phase, a bending element testing system was used to excite and receive shear waves in the specimen. After subtracting the system's inherent delay time, the net propagation time of the shear wave in the specimen was obtained. Combined with the natural density, the dynamic shear modulus of the bending element under high-frequency, low-strain conditions was calculated. Simultaneously, under the same effective consolidation pressure, a resonant column testing system was used to excite the specimen under cyclic torsional loading. The resonant frequency was measured, and the dimensionless frequency factor and shear wave velocity were analytically obtained. Thus, the dynamic shear modulus of the resonant column under medium-to-low strain conditions, which varies with shear strain, was obtained.

[0010] In the parameter conversion stage, the frequency dispersion characteristics of the soil are determined based on the plasticity index, and the frequency correction coefficient is calculated using a preset conversion model. Based on the value of the plasticity index, the conversion path is divided into a constant coefficient mode for cohesive soil and a variable coefficient decay mode for cohesive soil. When the plasticity index is less than or equal to zero, a frequency correction factor of 1.0 is used, that is, the frequency dispersion effect is ignored; When the plasticity index is greater than zero, the frequency correction factor is calculated using a logarithmic decay function. The calculation method for this logarithmic decay function is as follows: The minuend is the reference constant characterizing the properties of low-plasticity clay, and the product of the coefficient characterizing the decay rate and the logarithmic term is subtracted. The logarithmic term is the natural logarithm of the sum of the plasticity index and a preset mathematical correction value. The bending dynamic shear modulus is reduced using the frequency correction coefficient and converted into a reference small strain dynamic shear modulus under low-frequency conditions.

[0011] To improve the applicability of the conversion model, this method includes a parameter calibration process based on site-specific data. By obtaining the measured values ​​of the dynamic shear modulus of the bending element and the dynamic shear modulus of the resonant column from the calibration samples, the measured frequency correction coefficient is calculated. Then, the least squares method is used to perform regression analysis on the dataset of the measured frequency correction coefficient and the plasticity index. When the coefficient of determination in the regression analysis reaches a preset threshold, the baseline constant and attenuation rate coefficient applicable to the site are obtained through inversion, and the conversion model is updated accordingly.

[0012] After obtaining the baseline small-strain dynamic shear modulus, the method also includes data consistency verification and the construction of dynamic parameter curves across the entire strain range. The relative error between the converted baseline small-strain dynamic shear modulus and the small-strain modulus measured by the resonant column test is calculated. If the error is within an acceptable threshold, the baseline small-strain dynamic shear modulus is set as the maximum dynamic shear modulus. This maximum dynamic shear modulus is used to normalize the modulus data obtained from the resonant column test that varies with shear strain. A modified hyperbolic model is then used to perform nonlinear regression analysis on the normalized data to determine the reference shear strain parameter and curvature coefficient parameter, constructing a continuous dynamic shear modulus decay function covering the range from small strain to medium-large strain.

[0013] This invention provides a method for converting soil dynamic parameters based on bending element and resonant column tests. It has the following beneficial effects: 1. This invention utilizes the plasticity index to quantify the frequency dispersion effect of soil, correcting the dispersion bias that exists when high-frequency bending element test results are directly applied to low-frequency engineering analysis. By distinguishing between the constant coefficient mode of cohesive soil and the variable coefficient decay mode of cohesive soil, and using the logarithmic decay function to describe the frequency variation law of cohesive soil modulus with plasticity index, the dynamic shear modulus of bending elements measured under high-frequency laboratory conditions is converted into the benchmark small-strain dynamic shear modulus under low-frequency engineering conditions, reducing the modulus value error caused by the difference in test frequency.

[0014] 2. This invention combines the data characteristics of bending element testing and resonant column testing to construct dynamic parameter curves covering the entire strain range from small to medium-large strains. Using the frequency-corrected baseline small-strain dynamic shear modulus as the maximum dynamic shear modulus, the data obtained from the resonant column test that varies with shear strain are normalized, and regression analysis is performed using a modified hyperbolic model. This method combines the maximum modulus measured by the bending element test with the nonlinear attenuation data measured by the resonant column test, thereby obtaining a continuous dynamic shear modulus attenuation function for soil.

[0015] 3. This invention includes a parameter calibration process based on specific site data, improving the engineering applicability of the parameter conversion method. By selecting calibration samples and performing regression analysis on measured data, the baseline constants and attenuation rate coefficients characterizing the soil features of a specific site are obtained through inversion, and the conversion model is updated accordingly. This model update method based on measured data can adjust model parameters according to the geological characteristics of a specific engineering site, improving the problem of poor regional adaptability caused by fixed parameters in traditional empirical formulas, and enhancing the accuracy of the conversion results for specific engineering sites. Attached Figure Description

[0016] Figure 1 This is a schematic diagram of the method flow of the present invention; Figure 2 This is a diagram verifying the consistency of modulus conversion in this invention. Figure 3 This is a fusion diagram of the full strain range curves of the present invention; Figure 4 This is a comparison chart of errors in different modes of the present invention. Detailed Implementation

[0017] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0018] Please see the appendix Figure 1-4 This invention provides a method for converting soil dynamic parameters based on bending element and resonance column tests. The method mainly includes sample preparation and property measurement, bending element test, resonance column test, and parameter conversion and analysis.

[0019] In this embodiment, the method is applicable to fine-grained soil, specifically including clay, silty clay and silt.

[0020] The sample preparation and property determination process is used to obtain the basic physical state parameters of the soil sample to be tested. This process first involves selecting a representative undisturbed soil sample and determining its basic physical properties. These basic physical properties include at least natural density and plasticity index, which are key variables for establishing subsequent conversion relationships. Furthermore, the sample preparation and property determination process also includes preparing the soil sample into a cylindrical specimen that meets standard geometric dimensions. During preparation, strict control of the operation is required to minimize disturbance to the undisturbed soil structure, thereby ensuring that the subsequent dynamic test results accurately reflect the mechanical properties of the in-situ soil.

[0021] The bending element test aims to obtain the stiffness characteristics of soil under minimal strain conditions. This process is applied to cylindrical specimens prepared through sample preparation and property determination. Under a preset effective consolidation pressure, the specimen is subjected to non-destructive testing using a shear wave excitation signal from the bending element test system. During the test, the propagation time of the shear wave in the soil is determined by capturing the initial arrival characteristics of the signal at the receiving end, and then the shear wave velocity is calculated. Subsequently, based on the product of the shear wave velocity and the natural density of the soil, the dynamic shear modulus of the bending element under minimal strain conditions is calculated.

[0022] The resonant column test is used to obtain the baseline stiffness characteristics of soil under small to medium strain conditions. This process is conducted under the same effective consolidation pressure conditions as the bending element test to ensure consistency in the soil stress state. The resonant column test involves applying a cyclic torsional load to the specimen and adjusting the excitation frequency to induce a resonant response. Based on the resonant frequency measured by the system, specimen dimensions, and boundary constraints, the dynamic shear modulus of the resonant column under small to medium strain conditions is calculated. This dynamic shear modulus serves as a verification benchmark or calibration basis for parameter conversion within the system.

[0023] The parameter conversion and analysis process is used to establish and perform a quantitative conversion between the dynamic shear modulus of the bending element and the dynamic shear modulus of the resonant column. This process receives physical property indices from the specimen preparation and property measurement processes, as well as the dynamic shear modulus of the bending element from the bending element testing process. The parameter conversion and analysis process is internally configured with a preset conversion model that characterizes the influence of soil plasticity on stiffness differences at different frequencies and strain levels. Based on the input physical property indices, the process selects the appropriate calculation path or correction coefficient to convert the dynamic shear modulus of the bending element at high frequency and low strain into the target dynamic shear modulus of the resonant column at low frequency and medium strain.

[0024] In practice, the above processes are executed in a predetermined logical order. First, soil samples are classified and prepared to establish physical benchmarks. Then, high-frequency small-strain parameters are determined using bending element testing. For soil types with established conversion relationships, the parameter conversion and analysis process can directly output the converted dynamic parameters. For specific soil types requiring new conversion relationships, a resonance column test is performed, using measured data to calibrate the coefficients in the parameter conversion model. Through the synergistic effect of each process, this method leverages the convenience and non-destructive nature of bending element testing, combined with the correction effect of soil physical properties, to achieve accurate prediction of resonance column test results, thereby constructing a continuous and unified soil dynamic parameter system.

[0025] In the process of sample preparation and property determination, the applicability of the test object must first be strictly defined and classified. This process clarifies the effective boundary of the dynamic parameter conversion system based on the contact characteristics between soil particles, the dynamic response mechanism, and specific physical property indicators.

[0026] This embodiment applies to fine-grained soils, specifically clay, silty clay, and silt. These soils have fine particles, large specific surface areas, and exhibit cohesion and bound water films between particles. Under the low-frequency, low-strain conditions of resonant column tests, these physical characteristics maintain the stability of the soil skeleton. The electrostatic attraction between fine-grained soil particles and the bound water film provide shear resistance, preventing particle dispersion before the sample reaches resonance, thus generating a stable resonant response and allowing for the acquisition of an accurate reference dynamic shear modulus. The fine-grained soils mentioned in this specification and claims refer to the aforementioned clay, silty clay, and silt with cohesive properties.

[0027] This method explicitly excludes sandy soils as applicable materials. This exclusion is based on the incompatibility between the resonant column test mechanism and the mechanical properties of sandy soil. Sandy soil particles lack cohesion or have extremely weak cohesion, exhibiting an overall loose state. During the resonant column test, the specimen needs to reach a resonant state under low-frequency cyclic torsional loading. For loose sandy soil, vibrational shearing easily induces relative slippage, rolling, and rearrangement between particles, causing the input vibrational energy to be rapidly dissipated mainly through interparticle friction and inelastic deformation, rather than being converted into an elastic resonant response. This rapid energy dissipation makes it difficult for the test system to capture a stable resonant frequency, thus making it impossible to accurately invert the dynamic shear modulus and damping ratio based on elastic wave propagation theory. Due to the lack of reliable resonant column test data as a verification benchmark, the conversion logic based on the joint testing of bending elements and resonant columns cannot be established in sandy soils.

[0028] To accurately distinguish the aforementioned fine-grained soil subclasses and provide a quantitative basis for selecting subsequent parameter conversion coefficients, this embodiment uses the plasticity index as a quantitative indicator for classification. The plasticity index comprehensively reflects the mineral composition of soil particles, clay content, and the strength of soil-water interaction, and is a sensitive parameter characterizing the nonlinear dynamic properties of soil.

[0029] Plasticity Index The calculation is based on the following formula: ; In the formula: This is the plasticity index of the soil, a dimensionless value (in engineering calculations, the percentage sign is usually omitted and the value is taken directly). The liquid limit of soil refers to the water content at which soil transitions from a fluid state to a plastic state, and is expressed as a percentage. The plastic limit of soil refers to the water content at which soil changes from a plastic state to a semi-solid state, and is expressed as a percentage.

[0030] Based on the calculated plasticity index This method divides the applicable soil into the following three intervals, which will serve as the basis for subsequent conversion model path selection: Clay: Plasticity index meets the requirements Soil; silty clay: plasticity index meets Soil; silt: plasticity index meets The soil.

[0031] The quantitative definition based on physical thresholds ensures the consistency of the dynamic characteristics of the soil samples involved in the conversion, making the subsequent conversion relationship have clear physical meaning and engineering applicability.

[0032] The sample preparation and property determination process includes a standard sample preparation step. This step involves processing the selected undisturbed soil into a physical model that conforms to the dimensions of the dynamic testing instrument's base and the mechanical boundary conditions. The geometric accuracy of the sample preparation directly determines the uniformity of the stress field and the signal-to-noise ratio of the fluctuation signal during testing, which is fundamental to ensuring that the test data truly reflects the intrinsic properties of the soil.

[0033] The standard specimens were prepared using undisturbed soil as the substrate. The undisturbed soil retains the skeletal structure, cementation, and pore distribution characteristics formed during the natural deposition process; these microstructural factors significantly influence the shear modulus under small strain. The preparation process followed the principle of minimal disturbance, using specialized soil-cutting equipment to process the soil samples into standard cylindrical specimens. In this embodiment, the geometric dimensions of the standard cylindrical specimens were strictly set as diameter D = 50 mm and height H = 100 mm.

[0034] The aforementioned geometric dimensions and the 2:1 height-to-diameter ratio are supported by a clear physical mechanism: First, to satisfy the one-dimensional wave propagation condition: in bending element testing, the propagation of shear waves in the soil requires a sufficient path length to distinguish it from near-field effects. This is because the wave propagation distance (i.e., the specimen height H) is related to the wavelength... ratio When the height is small, the excited longitudinal wave component can interfere with the initial arrival signal of the shear wave. Setting the height to 100 mm can effectively increase the wave propagation path, reduce near-field interference, and improve the accuracy of initial arrival wave interpretation. Secondly, in order to optimize the stress boundary: in the resonant column torsional shear mode, a larger height-to-diameter ratio can reduce the stiffness hardening effect of the end-fixed constraint on the shear deformation region in the middle of the specimen, ensuring the uniformity of stress distribution along the axial direction.

[0035] The specific preparation process includes meticulous trimming of the soil sample's end faces and sides. Using a soil cutter and wire saw, the soil is cut perpendicular to its natural bedding, ensuring that the upper and lower end faces are strictly parallel and perpendicular to the axis. The flatness error of the end faces must be controlled within 0.05 mm to ensure complete contact between the sample and the permeable stone of the instrument when axial consolidation pressure is applied, allowing stress to be evenly transmitted to the interior of the sample and preventing localized stress concentration or eccentric compression. For the sample sides, loose particles and coatings generated during the cutting process are removed to keep the sidewalls smooth, reducing lateral boundary friction effects after the rubber membrane is installed.

[0036] In the sample grouping and configuration stage, the prepared samples from the same batch were divided into two groups, one for the bending element test and the other for the resonance column test. To ensure the effectiveness of subsequent parameter conversions, the consistency of the physical state of the two groups of samples must be quantitatively controlled. The principle for selecting the two groups of samples is: the natural density of the two groups of samples. The difference should not exceed ±0.03 g / cm³. 3 And natural moisture content The difference should not exceed ±1%. This strict homogeneity control is a prerequisite for establishing the correlation between bending elements and resonance column data, eliminating parameter dispersion caused by individual differences in the samples. After preparation, the samples must be immediately sealed and moisturized or directly mounted to the test base to prevent suction changes and microcrack development caused by moisture evaporation. For the specific soil cutting tools and moisturizing methods involved in the preparation process, those skilled in the art can follow the current geotechnical testing procedures, and will not be elaborated here.

[0037] After sample preparation and grouping, precise determination of key physical properties of the soil samples is required. The physical parameters obtained in this process will serve as input variables, directly participating in the subsequent construction of the conversion model between the bending element and the dynamic shear modulus of the resonant column. Among these, natural density... With plasticity index It is a decisive physical quantity that affects the dynamic stiffness and nonlinear attenuation characteristics of soil.

[0038] First, the natural density is determined. Natural density characterizes the mass distribution per unit volume of soil and directly determines the inertial effect during wave propagation in dynamics. It is a fundamental parameter for inverting the dynamic shear modulus using shear wave velocity. For the standard cylindrical specimens with regular shapes prepared in the preceding steps, a geometric measurement method is used. The total mass of the specimen in its natural water-bearing state is weighed using a high-precision balance, and its geometric volume is accurately calculated based on the specimen's diameter and height. If the unique structure of the undisturbed soil makes it difficult to cut into a regular geometric shape, a wax-sealing method is used to determine its volume to isolate moisture exchange and obtain an accurate volume using Archimedes' principle.

[0039] Natural density The ratio of mass to volume is used to determine the value, and the calculation formula is as follows: ; In the formula: This indicates the natural density of the soil sample, expressed in g / cm³. 3 ; This indicates the mass of a soil sample while maintaining its natural water content, expressed in grams. The volume of the soil sample is expressed in cm³. 3 .

[0040] Subsequently, the plasticity characteristics of the soil were quantitatively determined. The plasticity characteristics of soil reflect the strength of the interaction between clay mineral particles and water (i.e., the double-layer characteristic). Microscopically, this determines the contact stiffness and damping characteristics between particles, while macroscopically it manifests as the difference in the rate at which the dynamic shear modulus decreases with increasing strain. Therefore, accurately determining the plasticity index is a physical prerequisite for correcting the conversion coefficients of moduli for different soil types.

[0041] This process involves testing representative remolded soil samples using a combined liquid and plastic limit tester. The test requires preparing soil pastes with different moisture contents, and determining the liquid limit of the soil at a standard penetration depth using a conic disc apparatus. With plastic limit Among them, liquid limit Physically, the water content limit represents the point at which the shear strength of soil approaches zero, i.e., the critical point at which it transitions from a fluid state to a plastic state; plastic limit. Physically, it represents the water content limit at which soil begins to crack, that is, the critical point at which it changes from a plastic state to a semi-solid state.

[0042] The obtained plasticity index This will be used to subsequently determine the soil type correction factor. The specific range of values ​​can be used, or substituted into the continuous function correction formula as the independent variable to adjust the stiffness dispersion effect.

[0043] In addition, the natural moisture content needs to be monitored and measured throughout the testing period. The wet soil sample is dried at a specified temperature (usually set at 105℃) using an oven-drying method. Dry the soil at 110℃ to constant weight and calculate the ratio of the mass of water in the soil to the mass of dry soil particles. Maintaining a constant natural moisture content is key to ensuring that the bending element test and the resonant column test are under the same matrix suction and effective stress state, thereby eliminating the modulus measurement error caused by moisture loss and ensuring the comparability of the two sets of test data.

[0044] The bending element test is performed under specific system configurations and physical conditions to ensure accurate capture of soil within its minimum strain range (typically shear strain). The elastic wave propagation characteristics.

[0045] The bending element testing system is integrated into the triaxial pressure chamber base and top loading cap. The core sensor assembly consists of pairs of piezoelectric ceramic bending elements, serving as the transmitting and receiving probes, respectively. The piezoelectric ceramic elements employ a cantilever beam mounting structure, with one end fixed within a permeable stone base and the other end extending into the soil sample end. This structure operates based on the piezoelectric effect: the transmitting end, under voltage excitation, utilizes the inverse piezoelectric effect to generate lateral bending deformation, thereby inducing shear disturbance in the soil sample; the receiving end utilizes the direct piezoelectric effect, generating an electrical signal upon sensing the shear micro-vibrations transmitted from the soil. To ensure effective signal coupling and minimize damage to the soil structure, the insertion length of the bending element into the soil sample must be strictly controlled within the range of 2mm to 4mm, and the transmitting and receiving ends should be kept in the same vertical axis plane.

[0046] Before triggering the test signal, the installed specimen must undergo isotropic consolidation. The consolidation process aims to restore the stress state of the soil at a certain depth and eliminate residual stress generated during specimen preparation. This embodiment sets a preset effective confining pressure. The pressure is 100 kPa, which serves as a standardized reference stress state to unify the comparison benchmark between different soil samples. This is achieved by controlling the surrounding pressure within the pressure chamber. With the pore water pressure inside the sample This ensures that the effective stress reaches the target value. Effective confining pressure. The calculation follows Terzaghi's effective stress principle, and the formula is as follows: ; In the formula: Indicates the effective confining pressure, in kPa; This represents the total confining pressure applied, expressed in kPa. This represents the pore water pressure, expressed in kPa.

[0047] Once the pore water pressure dissipates and the volume deformation of the sample stabilizes, the primary consolidation is considered complete. At this point, the soil skeleton structure reaches a stable state and is ready for dynamic testing.

[0048] The choice of excitation conditions for the bending element directly determines the quality of the received signal and the accuracy of subsequent wave velocity interpretation. This invention uses a shear wave (S-wave) as the detection wave source. The signal generator is configured to output a single sine wave signal. The physical mechanism of using "single" transmission instead of continuous transmission is to prevent the boundary reflected wave and the direct wave from overlapping and interfering in the time domain, ensuring the clarity of the initial arrival signal; using a sine wave is to concentrate the excitation energy near the dominant frequency, reducing the dispersion effect caused by high-frequency components. The amplitude of the excitation voltage is set to ±10V~±20V to ensure sufficient signal-to-noise ratio in fine-grained soil.

[0049] The frequency of the excitation signal is set to 1kHz. This frequency parameter was chosen as an optimal balance between "near-field effect" and "material damping attenuation." The near-field effect refers to the coupling between the longitudinal wave component and the shear wave component generated by the wave source near the wave source, which may mask the true initial arrival point of the shear wave. Although theoretically increasing the frequency can shorten the wavelength... Increase the ratio of propagation distance to wavelength. This reduces the near-field effect, but in cohesive soil, the energy of high-frequency signals decays extremely quickly. Therefore, this embodiment selects 1kHz as the optimal observation frequency, which, together with the subsequent initial arrival wave interpretation algorithm, ensures that the signal has a recognizable strength and allows for the effective monitoring of wave propagation conditions through wavelength calculation.

[0050] wavelength The monitoring calculation formula is as follows: ; In the formula: This indicates the wavelength of the shear wave, in meters (m). This represents the shear wave velocity in the soil, expressed in m / s. This indicates the frequency of the input signal, measured in Hz.

[0051] By calculation, when wavelength relative to the height of the sample When the relationship meets a certain ratio, it can help verify the credibility of the initial arrival wave in the received signal and ensure the physical authenticity of the test data.

[0052] After signal excitation, the core task is to accurately extract the propagation time of the shear wave within the soil from the received voltage-time history curve. This embodiment uses the "first arrival wave method" as the benchmark method for signal interpretation.

[0053] The physical mechanism for choosing the first-arrival wave method over the peak-to-peak method lies in the fact that soil is a typical dispersive medium, and wave components of different frequencies propagate at different speeds in soil (i.e., phase velocity and group velocity are inconsistent). The peak-to-peak method relies on the phase characteristics at a specific frequency and is easily affected by dispersion effects and boundary reflections. The first-arrival wave method, on the other hand, captures the moment when the shear wave energy wavefront first arrives at the receiver, corresponding to the wave component propagating at its fastest speed, thus minimizing wave velocity calculation errors caused by dispersion effects.

[0054] The signal interpretation process first requires defining the effective propagation distance. Since the bending element probe extends into the sample, the actual physical propagation path of the shear wave is not the sample height, but rather the net distance between the tips of the transmitting and receiving probes. This distance correction is to subtract the propagation time of the wave within the extremely stiff piezoelectric ceramic sheet and metal base (this time is negligible compared to the propagation time in the soil), retaining only the path traveled in the soil medium. Effective propagation distance The calculation formula is as follows: ; In the formula: This indicates the effective propagation distance of the shear wave, expressed in meters (m). This indicates the height of the cylindrical specimen, in meters (m). This indicates the depth to which the bending element probe at the transmitting end extends into the sample, in meters (m). This indicates the depth to which the bending probe at the receiving end extends into the sample, in meters (m).

[0055] After determining the distance, the propagation time needs to be extracted from the time-domain signal. Due to the near-field effect, the received signal often contains longitudinal wave (P-wave) components that arrive before the shear wave and electromagnetic coupling noise. This is manifested in the waveform diagram as a slight reverse deflection of the signal baseline (i.e., the precursor wave) before the arrival of the main shear wave peak.

[0056] The specific interpretation logic is as follows: If the excitation signal is a positive sine wave, the received signal usually first shows a weak negative dip (P-wave component) under near-field interference. Subsequently, the signal curve rapidly recovers and crosses zero to climb positively. At this point, the inflection point after the zero-crossing point or the reverse extreme point where the negative dip ends and the positive climb begins is determined as the initial arrival time of the shear wave. This interpretation standard can effectively eliminate near-field interference signals propagating in the form of compression waves and accurately pinpoint the starting moment when energy is mainly transferred by the shear deformation of the soil skeleton.

[0057] To eliminate the influence of the electronic delay inherent in the test system on high-frequency measurement results, system delay correction must be performed. This correction process eliminates the inherent electronic response time of the signal generator, power amplifier, oscilloscope, and transmission cables. The correction method is as follows: Before installing the sample, the transmitter and receiver probe tips are directly contacted (i.e., point-to-point short circuit), a signal of the same frequency is excited, and the signal transmission time is recorded; this time is the system delay time. Net propagation time of shear waves in soil The difference between the initial arrival time of the read and the system latency is calculated using the following formula: ; In the formula: This represents the net propagation time of the shear wave in the soil, expressed in seconds. This indicates the initial arrival time of the signal as determined from the oscilloscope or acquisition system, in seconds (s). This indicates the inherent delay time caused by the transmission of electronic components and cables in the system, measured in seconds (s).

[0058] Based on the effective propagation distance and net propagation time obtained above, the shear wave velocity within the soil is calculated. The calculation formula is as follows: ; In the formula: This represents the soil shear wave velocity, expressed in m / s.

[0059] The shear wave velocity This directly reflects the elastic response capability of the soil particle skeleton under extremely small disturbances, and is the physical basis for subsequent calculations of small strain shear modulus. Through the aforementioned initial arrival wave interpretation logic based on wavefront physical characteristics, the uncertainty caused by phase lag under near-field disturbances in traditional methods can be effectively overcome, ensuring that the physical meaning of wave velocity measurement is clear and highly repeatable.

[0060] Based on the shear wave propagation velocity and soil physical state parameters obtained in the preceding steps, this method further calculates the dynamic shear modulus of the soil under small strain conditions using elastic wave propagation theory. This calculation process establishes a direct physical mapping between wave characteristic quantities (velocity) and medium mechanical properties (stiffness), which is a fundamental step in constructing a soil dynamic parameter system.

[0061] Within the minimal strain range excited by the bending element test (typically shear strain) The soil exhibits a near-ideal elastic body mechanical response. From a microscopic perspective, the stress amplitude generated by the external disturbance has not yet overcome the static friction between soil particles and the viscous resistance of the bound water film. No relative slippage or rolling occurs between soil particles, and the particle contact points remain stable. The input vibration energy is mainly converted into the elastic potential energy of the soil skeleton and can be completely recovered. According to the theory of elastic wave propagation in continuous media, the propagation speed of shear waves in isotropic elastic media depends only on the shear modulus and mass density of the medium. Therefore, the dynamic shear modulus obtained by inverting the measured shear wave velocity physically corresponds to the initial tangent modulus or the maximum dynamic shear modulus of the soil. ).

[0062] Bending dynamic shear modulus The calculations are based on the following physical equations: ; In the formula: This represents the dynamic shear modulus measured by the bending element, in Pascals (Pa). The natural mass density of a soil sample (i.e., the overall density including soil particles and pore water) is expressed in kilograms per cubic meter (kg / m³). 3 ); This represents the shear wave velocity in the soil, measured in meters per second (m / s).

[0063] It should be noted that the density in the formula The natural density (wet density) of the soil must be used, not the dry density. This is because during the propagation of high-frequency shear waves excited by bending elements, due to the high frequency, pore water cannot drain out quickly enough, and the water and soil skeleton undergo coupled motion, jointly contributing to the inertial mass.

[0064] In the specific calculation implementation, strict dimensional uniformity is required. This is because the natural density obtained during the physical property determination stage is usually expressed in g / cm³. 3 Before performing calculations using this formula, the density unit must be converted to kg / m³ in the International System of Units (SI). 3 That is, multiply by the conversion factor of 1000. Furthermore, for ease of engineering application and subsequent chart analysis, the calculated... The result is usually further divided by 10. 6 Convert to megapascals (MPa) as the final output unit.

[0065] The calculation results The value represents the maximum shear stiffness that the soil can provide under the current effective confining pressure and void ratio. This parameter acts as a benchmark anchor in the entire conversion system: it defines the dynamic shear modulus decay curve ( The initial intercept of the curve on the vertical axis (i.e.) The limiting modulus at high frequency (at low strain) will be used as a benchmark value for small strain at high frequency. It will be compared with the medium and small strain modulus measured by the resonant column test to provide a numerical basis for determining the frequency correction coefficient.

[0066] After completing the high-frequency, low-strain bending element test, a resonant column testing system was used to conduct dynamic response tests on the same batch of samples at lower frequencies (typically 20Hz~100Hz). This process aims to obtain the dynamic response within a medium strain range ( The dynamic shear modulus and damping ratio of the sample are used to construct a complete modulus decay curve.

[0067] The resonant column test employed a Stokoe-type fixed-free vibration mode. In this configuration, the bottom of the cylindrical specimen was rigidly fixed to the base, restricting its displacement and rotation in all directions, thus forming a zero-displacement boundary. The top of the specimen, equipped with a drive plate and an accelerometer, was in a free vibration state, forming a stress boundary. This mechanical boundary condition simplifies the specimen-drive system into a single-degree-of-freedom torsional vibration model, facilitating subsequent analytical inversion of soil stiffness. Furthermore, this mode allows for convenient application of axial loads without interfering with the torsional mode.

[0068] Pre-test consolidation state control is fundamental to ensuring data comparability. After specimen installation, an effective confining pressure identical to that used in the aforementioned bending element test is applied. Isotropic consolidation was performed at kPa. By maintaining a strictly consistent stress history path and final void ratio state, modulus deviations caused by differences in soil state variables can be eliminated, thereby physically establishing the initial modulus measured by the bending element. Modulus measured with resonant column Mechanical parameters belonging to the same soil state.

[0069] The loading control of the test relies on an electromagnetic drive system at the top. A permanent magnet on the drive plate is placed within a fixed excitation coil. By inputting a sinusoidal alternating current into the coil, a periodic torque is generated acting on the top of the specimen using the Lorentz force principle. The magnitude of the torque is directly proportional to the magnitude of the input current, and the frequency of the torque is strictly synchronized with the frequency of the input current.

[0070] The search and determination of the resonance state employs a frequency sweep method. While maintaining a constant input excitation voltage, the frequency of the sinusoidal signal is continuously adjusted. The physical criterion for determining the resonance state is: a 90° phase difference exists between the response acceleration signal at the top of the sample and the input excitation torque signal, and at this point, the amplitude of the torsional angular displacement at the top of the sample reaches its maximum value. The frequency recorded under this state is the resonance frequency. At the same time, the corresponding maximum torsional angular displacement amplitude is recorded.

[0071] To fully characterize the nonlinear decay of soil stiffness, the initial excitation shear strain was set at 10. -6 The excitation voltage is then increased incrementally in multiples until the shear strain reaches 10. -4 The magnitude of the load may be significantly different from the nonlinear response. Using a loading sequence from small to large is to avoid cumulative plastic deformation caused by large-amplitude vibrations that could damage the original cemented structure of the soil, ensuring that the soil remains in an "undisturbed" state when measuring small strain parameters.

[0072] The equivalent shear strain of the specimen under each load level. It needs to be determined through geometric conversion. First, the voltage signal measured by the accelerometer mounted on the drive board is converted into tangential acceleration. Then, the tangential displacement of the top edge is obtained by quadratic integration over time. Finally, the maximum torsional angular displacement amplitude is calculated using the sample radius. .

[0073] Because the shear strain at different radial locations on the cross-section of a cylindrical specimen exhibits a linear distribution during torsion (zero at the center and maximum at the edges), the "equivalent shear strain" is used as a representative index. The equivalent calculation is based on the principle of strain energy integration equivalence, and the calculation formula is as follows: ; In the formula: This represents the equivalent shear strain of the specimen and is a dimensionless value. This represents the equivalent radius of the specimen, expressed in meters (m). For solid cylindrical specimens, this value is taken as the specimen radius based on the average integral of the strain energy across the entire cross-section. 0.80 times (i.e.) ); This represents the maximum torsional angular displacement amplitude measured at the top of the specimen under resonant conditions, in radians (rad). The height of the sample is indicated in meters (m).

[0074] Through the above control process, the system can accurately record different equivalent shear strains. The corresponding resonant frequency These two sets of data constitute the basis for subsequent inversion calculation of dynamic shear modulus. The core foundational data.

[0075] After obtaining the resonant frequency After determining the physical parameters of the sample, the dynamic shear modulus of the soil needs to be inverted by analyzing the one-dimensional torsional wave equation. This calculation process is based on the theory of continuum mechanics, which treats the "fixed at the bottom and free at the top" sample-instrument system as a continuous vibration model of an elastic rod with an additional concentrated mass at the top.

[0076] The determination of the dynamic shear modulus depends on solving the system's frequency characteristic equation. This equation physically describes the dynamic equilibrium condition between the standing wave field formed by shear wave propagation within the soil sample and the inertial torque driving the system from the top, when the external excitation frequency coincides with the system's natural frequency. Under resonance conditions, the system parameters satisfy the following dimensionless characteristic equation: ; In the formula: This represents the mass and moment of inertia of the soil sample itself, expressed in kilograms squared (kg / m²). For solid cylindrical specimens, this parameter reflects the inertial resistance of the soil mass distribution to rotational motion about an axis, and its calculation formula is as follows: ,in For soil sample quality, The radius of the sample; This represents the moment of inertia of the mass pole of the top drive system of the resonant column apparatus, expressed in kilograms squared (kJ / m²). This parameter is an inherent constant of the instrument, encompassing the total moment of inertia of the drive plate, top cap, accelerometer, and connecting screws, and is provided by the equipment manufacturer or determined through calibration using standard metal samples. It represents the dimensionless frequency factor, which is a characteristic variable relating the shear wave velocity to the geometric dimensions of the specimen. Its physical meaning is the amount of phase change of the shear wave propagating within the height of the specimen.

[0077] In the above characteristic equation, the variables The simultaneous appearance of linear terms and tangent function terms on the right-hand side of the equation constitutes a typical transcendental equation, for which an analytical solution cannot be directly obtained. This invention employs numerical iteration methods (such as the Newton-Raphson method or the bisection approximation method) to solve the equation.

[0078] It should be noted that, due to the tangent function Due to its periodicity, the equation has infinitely many positive roots in the real number domain. Given that this experiment was conducted under fundamental frequency (first-order mode) resonance conditions, a convergence constraint must be applied to the solution process: that is, within the interval... Search for the unique positive real root that satisfies the equation within the range. This constraint ensures that the calculation results correspond to the basic vibration modes of the soil sample, avoiding interference from higher-order harmonic solutions.

[0079] In obtaining the frequency factor After obtaining the numerical solution, combined with the measured resonant frequency Based on the sample geometry, the shear wave propagation velocity within the soil is calculated. This step utilizes the physical definition of the relationship between the frequency factor and phase velocity, and the calculation formula is as follows: ; In the formula: This represents the shear wave velocity under resonant column test conditions, in meters per second (m / s). This indicates the measured resonant frequency, expressed in Hertz (Hz). The height of the sample is indicated in meters (m). This represents the dimensionless frequency factor obtained by iteratively solving the characteristic equation. This represents pi, with a value of 3.14159.

[0080] Finally, the calculated shear wave velocity was used The dynamic shear modulus of the resonant column at this strain level was calculated based on elastic wave theory. At this point, assuming the soil behaves as an equivalent viscoelastic medium under a specific steady-state vibration amplitude, the calculation formula is as follows: ; In the formula: This represents the dynamic shear modulus of the resonant column, in Pascals (Pa). This indicates the natural density of the soil sample, expressed in kilograms per cubic meter (kg / m³). 3 ); This represents the shear wave velocity calculated from the resonant column test, expressed in meters per second (m / s).

[0081] By repeating the above inversion process for each loading level, a series of results corresponding to different equivalent shear strains can be obtained. dynamic shear modulus This results in discrete modulus decay data points. These data points quantify the nonlinear mechanical trajectory of soil stiffness gradually softening with increasing shear strain, providing a low-frequency (20Hz~100Hz) to medium-to-large strain range for subsequent construction of a full-frequency modulus fusion model. The benchmark data provides support.

[0082] The parameter conversion model constructed in this embodiment is based on the "frequency dispersion effect" of the soil medium and is used to solve the frequency matching problem between the high-frequency test results of the bending element and the low-frequency dynamic parameters required in actual engineering.

[0083] The physical basis for the conversion model lies in the dynamic response characteristics of soil as a multiphase porous medium. Soil consists of a soil skeleton, pore water, and gas, and its shear modulus is not a frequency-independent constant but exhibits significant viscoelastic characteristics. At the microscopic level, when the loading frequency increases from the low-frequency range (20Hz~100Hz) of the resonant column to the high-frequency range (1kHz~10kHz) of the bending element, the fluid motion state between soil particles and pores changes. High-frequency shear disturbance causes pore water to be unable to flow and dissipate within the pores in time, resulting in a fluid-skeleton coupling inertial effect; simultaneously, the viscous resistance of the water film bound to the particle contact surface increases with increasing strain rate. These two mechanisms work together to determine the measured dynamic shear modulus of the bending element. Numerically, it is generally higher than the resonant cylindrical dynamic shear modulus. In order to To convert it into a reference modulus suitable for earthquake engineering analysis (typically focusing on 0.1Hz~20Hz), a frequency correction factor needs to be introduced.

[0084] This invention employs a classification correction strategy based on soil physical properties. Physical tests show that the intensity of the dispersion effect is positively correlated with the specific surface area and surface electrochemical activity of soil particles. For non-cohesive soils (such as clean sand), the contact between particles is mainly mechanical interlocking, the bound water content is extremely low, and the modulus is not sensitive to frequency changes; while for cohesive soils, the plasticity index... The plasticity index directly reflects the content of clay minerals in the soil and the thickness of the bound water film. A higher plasticity index indicates a stronger double-layer effect and a more significant frequency sensitivity of dynamic stiffness caused by the viscous effect. Therefore, the plasticity index is selected as the optimal value. "As a key characteristic parameter to characterize the degree of dispersion, we construct differentiated conversion functions."

[0085] The conversion model employs a linear proportional correction form. This assumes a definite mapping relationship between the small strain shear moduli measured at different frequencies under the same effective confining pressure and void ratio. The calculation formula is as follows: ; In the formula: This represents the converted target minimum dynamic shear modulus, which is physically equivalent to the maximum dynamic shear modulus measured by the resonant column test, and is expressed in megapascals (MPa). This represents the dynamic shear modulus measured in the bending element test, in megapascals (MPa). This represents the frequency correction factor that depends on the plasticity index and is a dimensionless value.

[0086] For frequency correction coefficients The determination of the soil's plasticity is based on the following two calculation scenarios: For cohesionless soil (plasticity index) Since the elastic response of a coarse-grained soil skeleton is dominant, its frequency correction factor is approximately constant. This embodiment sets the frequency correction factor for cohesive-free soil. The value ranges from 0.95 to 1.05. In the absence of specific comparative experimental data, a default value of 1.0 is used, meaning the influence of frequency on the stiffness of clean sand is ignored.

[0087] For cohesive soil (plasticity index) Frequency correction factor for cohesive soil It exhibits the effect of plasticity index The trend is increasing but monotonically decreasing. This is because... The larger the size, the more severe the "apparent hardening" phenomenon under high-frequency testing, making... relatively The larger the ratio, the smaller the coefficient needed for reduction. This functional relationship is described using a logarithmic decay model: ; In the formula: This represents the frequency correction factor for cohesive soil, and is dimensionless. This represents the plasticity index of the soil. Here, we directly substitute the numerator value as a percentage (e.g., if the plasticity index is 15%, then substitute the value 15). The constant term is incremented by 1 to ensure mathematical continuity (avoiding...). ); This represents the reference constant, which physically reflects the frequency ratio characteristics of low-plasticity silty clay, and its value range is usually 0.90 to 1.10. This represents the plasticity sensitivity coefficient, which physically reflects the rate at which the correction coefficient decreases as plasticity increases. Its value range is usually 0.05 to 0.15.

[0088] parameter and The specific values ​​were determined using regression analysis: at least 5 groups with different plasticity indices were selected (it is recommended to cover...). Typical cohesive soil samples in the range of 10 to 50 were subjected to parallel bending element and resonant column tests under the same confining pressure to obtain measured modulus ratio data points. By using the least squares method to fit the above formula to a curve, empirical parameters applicable to the soil conditions of a specific region can be obtained. and .

[0089] Using the above model, the system can automatically match and correct the path according to the input soil physical indicators, convert the high-frequency modulus measured by the bending element into the low-frequency reference modulus required for engineering, and realize the physical equivalence of stiffness parameters under different test frequencies.

[0090] This embodiment performs a numerical conversion from the high-frequency modulus of the bending element to the low-frequency modulus of the resonant column through a preset physical discrimination and calculation process. This conversion mode is based on the input soil plasticity index. The calculation path is divided into "constant coefficient mode for cohesive soil" and "variable coefficient decay mode for cohesive soil" to adapt to the physical differences in frequency sensitivity of different soil media.

[0091] The conversion process is based on two core input parameters: the measured dynamic shear modulus of the bending element. Plasticity index of soil Among them, the plasticity index It needs to be obtained in advance through a geotechnical limit moisture content test (combined liquid and plastic limit determination method). The method is first based on... Numerical characteristics are used to determine soil type: when (or when the physical state exhibits non-plasticity), it is determined to be a cohesive-free soil path; when At that time, it was determined to be a cohesive soil path.

[0092] For soils classified as cohesive-free (such as sand, gravel, or pure silt), given that the stiffness of the coarse-grained soil skeleton is primarily determined by the rigid contact friction between particles, and that the viscous effect of pore fluid under small-strain vibration contributes minimally to the macroscopic stiffness, the influence of frequency dispersion is ignored. In this case, a constant scaling factor is used for direct reduction, calculated as follows: ; In the formula: This represents the converted baseline minimum strain variable shear modulus, in megapascals (MPa). This represents the dynamic shear modulus measured by the bending element test, in megapascals (MPa). This represents the frequency correction factor for cohesive soil, which is a dimensionless constant.

[0093] In the preferred embodiment of this invention, the correction coefficient The value is set to 1.0. This value is based on the physical fact that, in the small-strain elastic stage, the shear wave velocity of clean sand remains highly stable in a wide frequency range of 20Hz to 10kHz. If there is specific regional empirical data for special structural sands (such as sand containing trace amounts of cement), this coefficient can be fine-tuned within the range of 0.95 to 1.05, but it is locked at 1.0 in the general mode.

[0094] For cases classified as cohesive soil, the system employs a logarithmic decay model dependent on plasticity. Physical studies show that as the clay mineral content increases (i.e., ... As the water film thickens, the effect of frequency on stiffness is significantly enhanced. However, this enhancement does not increase linearly indefinitely, but rather exhibits a trend that varies with frequency. The trend of diminishing marginal returns means that the natural logarithm function can most accurately fit this physical law.

[0095] The comprehensive formula for the calculation process is as follows: ; In the formula: This represents the converted baseline minimum strain variable shear modulus, in megapascals (MPa). This represents the dynamic shear modulus measured by the bending element test, in megapascals (MPa). This represents the input plasticity index, where the numerator of the percentage is taken (e.g., ...). Then substitute the value 20). This represents the baseline constant, which physically represents the upper limit of correction for low-plasticity clay. This embodiment is based on statistical regression from numerous parallel bending element-resonance column tests of Quaternary sedimentary soils, and a value of 0.98 is recommended (range 0.90~1.10). This represents the attenuation rate coefficient, which physically represents the decreasing gradient of the correction coefficient as plasticity increases. In this embodiment, based on statistical regression, a value of 0.09 is recommended (range 0.05~0.15). Represents the natural logarithm operation.

[0096] The above recommended values 0.98 and 0.09 is a set of optimized empirical parameters that enable this conversion model to work across a wide range of cohesive soils. To maintain high prediction accuracy, the average relative error is controlled within 5%. Through automatic matching of the above calculation paths, the final output is based on a unified benchmark. This value eliminates the systematic overestimation bias caused by high-frequency testing, allowing a large number of data points easily obtained based on bending elements to be directly used as the starting stiffness of the resonant column reference curve (i.e., The modulus value at the location was used to achieve the physical fusion of multi-source experimental data.

[0097] Unlike the general conversion model that directly calls preset empirical parameters, this embodiment also provides a calibration model based on field measured data for parameter inversion (i.e., conversion model two). This model is mainly applicable to sites with high engineering safety levels or soil mineral composition with significant regional characteristics (such as containing special cementing materials or special clay mineral combinations). Its basic principle is to use a small amount of parallel comparative test data of "bending element resonance columns" to capture the unique dispersion attenuation law of the soil at the site, thereby correcting the reference constant and attenuation rate coefficient in the general model and eliminating systematic prediction bias caused by differences in geological formation.

[0098] The execution process of this calibration model mainly includes three stages: construction of the calibration sample set, inversion of model parameters, and validity verification.

[0099] The first step is the construction of the calibration sample set. Based on the survey samples from the same engineering site, the plasticity index is used... The distribution range was determined, and several representative soil samples were selected to form a calibration set. To ensure the validity of the regression analysis results across the entire plastic variation range, the selection criteria required a certain number of calibration samples. At least 5 ( Furthermore, the plasticity index of the sample should cover the variation range of the main soil layers of the site as evenly as possible, for example, it should also include low-plasticity silty clay. High plasticity clay Various typical samples.

[0100] For each selected calibration sample, under the same effective confining pressure and void ratio conditions as the in-situ soil, flexural element tests and resonant column tests were conducted simultaneously to obtain the corresponding measured modulus data. Subsequently, the measured frequency correction factor for each calibration sample was calculated. The calculation formula is as follows: ; In the formula: Indicates the first The measured frequency correction coefficient for each calibration sample, dimensionless; Indicates the first The dynamic shear modulus (i.e., low-frequency reference modulus) of each sample was measured by a resonant column test, and the unit is megapascal (MPa). Indicates the first The dynamic shear modulus (i.e., high-frequency modulus) of a sample obtained by bending element test, in megapascals (MPa).

[0101] In obtaining discrete data point sets Then, the system uses the least squares method to apply the preset logarithmic decay model. Perform regression analysis. The purpose of this step is to find an optimal set of model parameters. and This minimizes the deviation between the model's predicted curve and the measured data points. A residual sum of squares objective function is established. as follows: ; In the formula: This represents the sum of squared residuals, which serves as the objective function for regression analysis. This represents the total number of samples participating in the calibration, rounded to the nearest integer. Indicates the first The plasticity index of each calibrated sample is taken as the numerator value of its percentage. This represents the fitting parameters to be solved.

[0102] By analyzing the objective function Regarding respectively and By taking the partial derivatives and setting them to zero, and solving the system of linear equations, we can obtain the characteristic parameters that most accurately describe the dispersion characteristics of the soil at this site. and .

[0103] After parameter inversion, the system needs to perform a statistical validity evaluation of the fitting results to prevent model distortion due to experimental errors or excessive sample dispersion. The evaluation metric is the coefficient of determination. The calculation formula is as follows: ; In the formula: The coefficient of determination ranges from 0 to 1. The closer the value is to 1, the higher the degree to which the model interprets the measured data. Indicates the use of inversion parameters , The first result obtained by substituting into the model The prediction correction coefficient for each sample; Represents the measured correction factor for all calibration samples. The arithmetic mean.

[0104] The present invention sets the threshold for validity determination as follows: This threshold was established based on empirical statistical analysis of geotechnical engineering parameters, indicating that the regression model has significant statistical value.

[0105] If the calculation result satisfies The system will determine that this calibration is valid and automatically update the parameter library, using the newly acquired site-specific parameters. and Replace the default parameters. Subsequently, for a large number of other ordinary samples within the site that only underwent bending element testing, the updated formula was used for conversion: ; In the formula: It represents the baseline small strain variable shear modulus after conversion based on the field-defined parameters, in megapascals (MPa). This represents the site-specific reference constant determined through regression analysis; This represents the site-specific attenuation rate coefficient determined through regression analysis; This represents the plasticity index of the sample to be converted; This represents the measured bending dynamic shear modulus of the sample to be converted.

[0106] If the calculation result If the correlation between the soil dispersion characteristics and the plasticity index is weak, it indicates that there are significant outliers in the calibration test (such as those caused by sample preparation disturbance, internal cracks in the sample, or large particle inclusions). In this case, the system will refuse to update the parameters, maintain the default general empirical parameters, and output an anomaly warning, suggesting that technicians check the sample quality or increase the number of calibration samples. This verification mechanism ensures the reliability of the conversion model under complex geological conditions and avoids the introduction of erroneous parameters.

[0107] Using a conversion model to convert a large number of high-frequency moduli of bending elements Convert to low-frequency reference modulus Afterwards, the physical accuracy and calculation precision of the conversion results must be verified. This process aims to eliminate calculation deviations caused by accidental errors in experimental operations, local heterogeneity of the soil, or mismatch of conversion parameters, ensuring that the subsequently constructed modulus fusion curve has a reliable mechanical basis.

[0108] The core verification mechanism is based on the "principle of comparing data from the same source." Data from the same source refers to two sets of independent modulus data obtained simultaneously for the same sample under the same physical conditions (same dry density, moisture content, and confining pressure). One set is the dynamic shear modulus obtained directly from the resonant column test. (take its shear strain) The first set of values ​​is the maximum value at that time, which has a clear physical meaning and serves as the "true value" for verification; the second set is the predicted modulus obtained from bending element tests and converted using the aforementioned model. In theory, if the conversion model is accurate and the frequency dispersion effect is eliminated, the two sets of data should be strictly equivalent in terms of mechanical properties.

[0109] The quantitative evaluation metric for data consistency is the "absolute value of relative error". The system calculates the degree of deviation between the predicted value and the benchmark value for each validation sample. The calculation formula is as follows: ; In the formula: The absolute value of the relative error is expressed as a percentage (%). It represents the baseline small strain variable shear modulus obtained by conversion using the frequency correction model, and the unit is megapascal (MPa). The small strain variable shear modulus (i.e., initial tangent modulus) measured in the resonant column test is used as a verification benchmark value, and the unit is megapascal (MPa). This represents the absolute value operator, ensuring that the error value is non-negative.

[0110] To determine whether the conversion result meets the engineering accuracy requirements, this embodiment sets an allowable error threshold. The threshold is set based on the statistical law of permissible deviation for parallel tests in the standards for indoor testing in geotechnical engineering. Considering the discreteness of the microstructure of natural soil and the superposition of systematic errors from different testing equipment (bending elements and resonant columns), this embodiment will... The value is set at 15%. This value conforms to the industry's general accuracy standard for testing the dynamic parameters of heterogeneous soil and rock materials.

[0111] The verification logic is based on the calculation. With threshold The comparison results are then split into multiple streams: When the calculated relative error satisfies (Right now When the system determines that the bending element conversion data of the sample has "physical consistency" with the measured data of the resonant column, it indicates that the conversion model effectively eliminates the spurious stiffness increments brought about by high-frequency testing and does not introduce significant computational distortion. In this case, the data point is marked as "valid" and allowed to enter the subsequent database fusion stage.

[0112] When the calculated relative error satisfies (Right now When the sample data shows a "significant bias," it is deemed unsuitable for direct use. Physical causes of this bias typically include: physical disturbance of the sample between tests (such as moisture migration or structural damage), incorrect acquisition of the first arrival wave of the bending element signal, or incorrect selection of conversion parameters. Not applicable to this specific soil type. For such anomalies, the system will perform a data rejection operation and prompt technicians to manually review the waveform signal of the sample, or check whether the sample has defects such as cracks or large particle inclusions.

[0113] Through the above point-by-point verification and screening, the system finally constructed a "fusion modulus dataset" that has undergone quality control. In this dataset, the modulus values ​​derived from the bending element are... Data points and measured resonance columns The data points are considered as the maximum dynamic shear modulus of equal precision, and together they constitute high-density basic data describing the stiffness characteristics of soil under extremely small strain, which solves the problem of scarcity of small strain data caused by the low efficiency of resonant column tests in traditional methods.

[0114] After obtaining the frequency-corrected reference small strain variable shear modulus After obtaining the modulus decay sequence from the resonant column test, multi-source data fusion technology was used to construct a data structure covering the range from small strain (10) -6 ) to medium and large strain (10 -2 A complete mathematical model of stiffness attenuation is developed. This process aims to use the high precision of bending element measurements to correct for potential testing errors in the minimum strain range of resonant column tests, while utilizing the wide strain range of resonant column tests to complete the nonlinear attenuation range that cannot be measured by bending elements.

[0115] The construction process first establishes the maximum dynamic shear modulus across the entire frequency domain. Based on soil dynamics principles, the shear strain amplitude excited by bending element testing is typically below 10. -6 At this point, the soil is in the linear elastic deformation stage, and slippage has not yet occurred between particles. The measured modulus represents the initial maximum stiffness of the soil skeleton. Therefore, the modulus obtained directly from the bending element test via frequency conversion is... The value is assigned to the maximum dynamic shear modulus of the soil under the current physical state. This processing method utilizes bending metadata as a stiffness attenuation curve in... The theoretical vertex at that point provides accurate initial boundary constraints.

[0116] Subsequently, using the determined For each discrete data point measured in the resonant column test Normalization is performed. The modulus ratio is calculated. Stiffness data at different strain levels are mapped to a dimensionless coordinate system to generate a normalized modulus attenuation dataset. This step eliminates the differences in the absolute value of the modulus under different confining pressures or densities, highlighting the morphological characteristic of the nonlinear decay of soil stiffness with increasing strain.

[0117] For the normalized dataset, a modified Hardin-Drnevich hyperbolic model was selected as the nonlinear function to describe the dynamic constitutive relationship of soil. This model can accurately fit the stiffness softening behavior of soil transitioning from the elastic stage to the elastoplastic yielding stage. The analytical expression of the model is as follows: ; In the formula: This represents the shear strain. The dynamic shear modulus, expressed in megapascals (MPa). This represents the maximum dynamic shear modulus determined by the bending element conversion value, in megapascals (MPa). This represents the shear strain amplitude and is dimensionless. This represents the reference shear strain, which physically means the strain when the dynamic shear modulus decays to half of its initial value (i.e., ...). The corresponding shear strain value at time 10. For common cohesive soils and sandy soils, the value range is usually in the range of 10. -4 ~10 -3 between; The curvature coefficient is a dimensionless shape parameter that primarily controls the degree of curvature of the attenuation curve. A larger value indicates a faster rate of stiffness decay with increasing strain. For Quaternary sedimentary soils, The value range is usually between 0.8 and 1.2.

[0118] Finally, a nonlinear least squares optimization algorithm is used to perform iterative regression analysis on the normalized dataset. To ensure the algorithm's convergence speed and the physical accuracy of the results, parameters are set... The initial value for the iteration is 5×10. -4 ,parameter The initial value for the iteration is 1.0. The algorithm uses the minimum sum of squared residuals between the calculated and measured values ​​as the convergence criterion to inversely solve for the optimal model parameters. and .

[0119] Once these two shape parameters are determined, combined with the known... This generates a continuous, full-strain-range dynamic shear modulus prediction function. Engineering designers can use this function to calculate the dynamic shear modulus under any specified shear strain, thereby obtaining a continuous and smooth dynamic constitutive curve, which solves the problem of interpolation difficulties when performing numerical simulations using traditional discrete test points.

[0120] To verify the effectiveness of the dynamic shear modulus conversion model and full strain curve construction method based on soil physical property indicators proposed in this invention, this embodiment selects a typical undisturbed soil sample from a nuclear power plant site for comparative testing. The strata of this site cover a variety of soil types, ranging from non-cohesive sand to highly plastic clay, and have good statistical representativeness.

[0121] Experimental conditions and sample overview: A total of 30 undisturbed specimens were selected for the experiment, based on the plasticity index (… Divided into three groups: Non-cohesive soil group (Group A): 10 groups, mainly consisting of fine sand and silt. ; Low-to-medium plastic clay group (Group B): 10 groups, mainly silty clay. ; High plasticity clay group (Group C): 10 groups, mainly clay. .

[0122] All samples were tested using the GDS resonant columnar analyzer system. First, bending element wave velocity was measured under a predetermined confining pressure at an excitation frequency of 5kHz–10kHz to obtain the high-frequency dynamic shear modulus. Subsequently, resonant column (RC) tests were conducted under the same confining pressure, with excitation frequencies ranging from 20 Hz to 80 Hz, to obtain small strain ( Dynamic shear modulus under ) And the subsequent stiffness decay curve.

[0123] Modulus conversion consistency verification: See attached document Figure 2 In the figure, the horizontal axis represents the measured reference modulus (true value) of the resonant column, and the vertical axis represents the relevant modulus measured by the bending element. The hollow circular data points (uncorrected data) in the figure represent the original measured values ​​of the bending element. It can be seen that the data points are generally located above the 1:1 diagonal, exhibiting a clear "convex" characteristic. This deviation is not randomly distributed, but is negatively correlated with the modulus value: in the low stiffness range (usually corresponding to highly plastic soft soil), due to the significant frequency effect, the deviation can reach a maximum of over 40%. The solid square data points in the figure (corrected data of this invention) represent the reference modulus calculated using the method of this invention. After model correction, the data points converged closely to the vicinity of the 1:1 contour lines, and the residual error exhibited a random normal distribution, no longer drifting with changes in soil properties. Statistical analysis showed that the corrected average relative error decreased from 28.4% to 4.2%, and the root mean square error was significantly reduced, confirming the physical effectiveness of the conversion model.

[0124] Full strain range curve construction effect: See attached document Figure 3The figure shows a typical silty clay sample ( The data fusion process. The pentagram points (bending element conversion points) in the figure are located in the minimum strain region ( This point was obtained by reducing the high-frequency modulus using the method of this invention, providing accurate initial stiffness constraints. The hollow circular scattered points (measured points of the resonant column) in the figure are distributed in the medium strain range (…). Due to the background noise of the electromagnetic drive system, the data for the resonant column at minimal strain exhibits significant dispersion or is incomplete. The solid line in the figure (the fusion curve of this invention) shows the result after anchoring and fitting the resonant column data using the bending element conversion points. This curve smoothly transitions in the minimal strain segment, solving the problems of low maximum modulus estimation and distorted curve slope in the initial segment caused by the lack of micro-strain control points in traditional methods (shown by the dotted line in the figure).

[0125] Comparison of error distributions among different conversion methods: See attached document Figure 4 The figure shows the errors of three groups of soil samples under three different conditions, using columns filled with different shades of gray. Black bars represent the uncorrected state (original bending modulus). The dark gray bars represent the state after modification using the "general mode" of this invention; The white columns represent the state after correction using the field calibration mode of this invention.

[0126] The results show that for cohesionless soil, since its physical properties are almost unaffected by frequency dispersion effects, the error before correction was already at a low level (approximately 2.1%), and further converged after correction. For low-plasticity clay, the average relative error before correction was 18.5%, which was reduced to 5.2% after correction using the universal model of this invention. However, for the high-plasticity clay group, which is severely affected by dispersion, the average error before correction was as high as 36.8%, which was reduced to 7.8% after using the universal model. If the site-specific calibration model (using a small number of samples to retrieve parameters) is used, the error can be further compressed to about 2.5%. This proves that the hierarchical conversion strategy of this invention can adapt to engineering requirements of different precision levels.

Claims

1. A method for converting soil dynamic parameters based on bending element and resonant column tests, characterized in that, Includes the following steps: Uncirculated soil samples of fine-grained soil were selected and prepared into cylindrical specimens. The natural density, natural moisture content and plasticity index of the cylindrical specimens were measured. Under a preset effective consolidation pressure, the cylindrical sample or the same batch of samples with the same physical state are subjected to shear wave excitation and reception using a bending element test system to obtain the received signal. The shear wave velocity is calculated based on the initial arrival wave characteristics of the received signal, and the bending element dynamic shear modulus under high frequency and small strain conditions is calculated in combination with the natural density. Under the same effective consolidation pressure as the shear wave excitation and reception, the cylindrical specimen or the same batch of specimens with the same physical state is subjected to cyclic torsional load excitation using a resonant column test system. The resonant frequency is measured, and the dynamic shear modulus of the resonant column under small and medium strain conditions that vary with shear strain is calculated as a verification benchmark for parameter conversion. Based on the plasticity index, the frequency dispersion characteristics of the soil are determined, and the frequency correction coefficient is calculated using a preset conversion model to convert the bending dynamic shear modulus into the reference small strain dynamic shear modulus under low frequency conditions.

2. The method for converting soil dynamic parameters based on bending element and resonance column tests according to claim 1, characterized in that, The fine-grained soil specifically includes clay, silty clay, and silt; The preparation of cylindrical specimens from undisturbed fine-grained soil samples specifically includes: Multiple cylindrical samples prepared in the same batch are divided into two groups of samples, one for shear wave excitation and reception and the other for cyclic torsional load excitation. The differences in natural density and natural moisture content between the two groups of samples are controlled within a preset allowable range to ensure the consistency of physical state.

3. The method for converting soil dynamic parameters based on bending element and resonance column tests according to claim 1, characterized in that, When performing the shear wave excitation and reception, a single sine wave is used as the excitation signal, and the propagation time of the shear wave in the cylindrical sample is determined according to the initial arrival wave method. The method for calculating the bending dynamic shear modulus is as follows: First, the inherent delay time pre-calibrated by the bending element testing system is subtracted from the total measurement time to obtain the net propagation time of the shear wave in the cylindrical sample. Then, the shear wave velocity is calculated, and finally, the product of the natural density and the square of the shear wave velocity is taken as the dynamic shear modulus of the bending element.

4. The method for converting soil dynamic parameters based on bending element and resonance column tests according to claim 1, characterized in that, During the cyclic torsional load excitation, the cylindrical specimen is under boundary conditions where the bottom end is fixed and the top end is free. The method for obtaining the dynamic shear modulus of the resonant column is as follows: By adjusting the excitation frequency to bring the cylindrical sample to a resonant state, the frequency characteristic equation containing the system mass pole rotational inertia and the sample mass pole rotational inertia is solved using an iterative method. The dimensionless frequency factor is obtained analytically, and then the shear wave velocity under the resonant column test conditions is calculated based on the dimensionless frequency factor, and the dynamic shear modulus of the resonant column under the corresponding shear strain is obtained.

5. The method for converting soil dynamic parameters based on bending element and resonance column tests according to claim 1, characterized in that, The process of converting the bending dynamic shear modulus into a reference small strain dynamic shear modulus under low-frequency conditions specifically includes: Based on the value of the plasticity index, the conversion path is divided into a constant coefficient mode for cohesive soils and a variable coefficient decay mode for cohesive soils: When the plasticity index is less than or equal to zero, the non-cohesive soil constant coefficient mode is entered, and the bending element dynamic shear modulus is reduced by the constant frequency correction coefficient. When the plasticity index is greater than zero, the cohesive soil coefficient decay mode is entered, and the frequency correction coefficient is calculated using a logarithmic decay function whose value decreases as the plasticity index increases.

6. The method for converting soil dynamic parameters based on bending element and resonance column tests according to claim 5, characterized in that, In the constant coefficient mode for cohesive soil, the value of the frequency correction coefficient is set to 1.

0.

7. The method for converting soil dynamic parameters based on bending element and resonance column tests according to claim 5, characterized in that, In the cohesive soil coefficient decay mode, the calculation logic for the frequency correction coefficient is as follows: The minuend is a reference constant characterizing the properties of low-plasticity clay, and the product of a coefficient characterizing the decay rate and a logarithmic term is subtracted. The logarithmic term is the natural logarithm of the sum of the plasticity index and a preset mathematical correction value.

8. The method for converting soil dynamic parameters based on bending element and resonance column tests according to claim 7, characterized in that, The method also includes a parameter calibration process based on specific site data: Select no less than a preset number of calibration samples, and obtain the measured bending element dynamic shear modulus and resonant column dynamic shear modulus of each calibration sample respectively, and calculate the measured frequency correction coefficient of each calibration sample. The least squares method is used to perform regression analysis on the dataset of the measured frequency correction coefficient and the plasticity index to obtain the reference constants and coefficients representing the attenuation rate applicable to the site, and the determination coefficients of the regression analysis are calculated. When the determination coefficient is greater than or equal to 0.85, the calibration is deemed valid. The reference constants representing the characteristics of low plastic clay obtained by inversion and the coefficients representing the attenuation rate are used to replace the default parameters to update the conversion model. Subsequently, for the samples to be converted in the site, the updated conversion model is used to calculate the reference small strain variable shear modulus.

9. The method for converting soil dynamic parameters based on bending element and resonance column tests according to claim 1, characterized in that, The method also includes a data consistency verification step: The dynamic shear modulus of the resonant column at the small strain stage, measured using the resonant column testing system, was selected as the verification value. Calculate the absolute value of the relative error between the benchmark small-strain dynamic shear modulus obtained by the conversion and the verification value; If the absolute value of the relative error is less than or equal to the preset allowable error threshold, the conversion result is determined to be valid, and the data is included in the fusion modulus dataset. If the absolute value of the relative error exceeds the allowable error threshold, the data is determined to have a significant deviation and is discarded.

10. The method for converting soil dynamic parameters based on bending element and resonance column tests according to claim 1, characterized in that, The method also includes a step for constructing dynamic parameter curves across the entire strain range: The benchmark small-strain dynamic shear modulus obtained by conversion is set as the maximum dynamic shear modulus of the soil. The obtained dynamic shear modulus data of the resonant column, which varies with shear strain, is normalized using the maximum dynamic shear modulus. A modified hyperbolic model was used to perform nonlinear regression analysis on the normalized data points to determine the reference shear strain parameter and curvature coefficient parameter of the model, thereby constructing a continuous dynamic shear modulus decay function covering the range of small strain to medium and large strain.

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