Method for determining parameters related to density of rockfill of earth-rockfill dam by additional mass method

Abstract

The embodiment of the present application provides a method for determining the density related parameters of earth and rockfill dam rockfill by using the additional mass method. The method calibrates the established rockfill density detection simulation model by using the results of indoor small-scale physical model test; carries out simulation test on the rockfill to be detected by using the calibrated simulation model, substitutes the obtained vibration main frequency of the rockfill to be detected under different additional masses into the relationship between the fitted vibration mass and the vibration main frequency respectively, obtains the vibration mass of the rockfill to be detected under different additional masses, and then combines the vibration mass and the vibration volume of the rockfill to be detected under different additional masses to calculate the density of the rockfill to be detected under different additional masses. Since the vibration mass and the vibration main frequency used for fitting the relationship change with the change of the additional mass, the present application can detect the rockfill density with high precision under the conditions that the rockfill is impacted by different additional masses, the vibration stiffness and the vibration mass of the rockfill at the detection position change.

Description

Technical Field

[0001] The embodiments of the present invention relate to the field of density detection technology for rockfill materials in earth-rock dams, and more specifically, the embodiments of the present invention relate to a method for determining relevant parameters of density detection of rockfill materials in earth-rock dams using the added mass method. Background Technology

[0002] This section is intended to provide background or context for embodiments of the invention set forth in the claims. The description herein may include concepts that may be explored, but not necessarily concepts that have been previously conceived or explored. Therefore, unless otherwise stated, what is described in this section is not prior art for the purposes of this application's specification and claims, and is not acknowledged as prior art simply by virtue of its inclusion in this section.

[0003] With the continuous development of earth-rock dam construction technology, the efficiency of filling construction has been improving. As construction progresses faster, the requirements for the efficiency of dam material quality testing are also increasing. For earth-rock filling projects, the dry density of the compacted fill material has a good correlation with construction quality and can reflect the quality to a certain extent. For a long time, the commonly used method for testing the compacted density of rockfill materials in projects such as rockfill dams, rockfill roadbeds, and rockfill foundations has been the pit testing method. Because the pit testing method requires multiple steps, including excavation, sampling, weighing, water filling, measuring the pit volume, and backfilling and compaction, and because these steps are mainly done manually to avoid disturbing the original structure of the rockfill soil along the pit's edge, the on-site work time at each testing point can range from several hours to more than ten hours. Adding the data processing and analysis work further increases the time, seriously affecting the project progress.

[0004] The added mass method is an in-situ, non-destructive dynamic measurement method for the density of rockfill. This method uses a single-degree-of-freedom linear elastic system as its theoretical model and, based on the superposition principle, adds multiple levels of rigid masses to the vibrating rockfill system. It measures the system's natural frequency, solves for the dynamic stiffness and participating masses, and then converts these into the density of the rockfill. After 30 years of development, the added mass method has been widely applied to the density measurement of rockfill in several major earth-rock dam projects. However, the theoretical model of the added mass method is still a highly idealized mass-elastic resistance model, solved by assuming the rockfill is a one-dimensional, single-degree-of-freedom moving system. In the density calculation, it is assumed that the participating stiffness and mass of the rockfill at the test location remain unchanged under different added mass impacts. As is well known, these assumptions do not conform to reality. However, the theoretical foundation of the added mass method has not been thoroughly studied, and the extent to which the difference between assumptions and reality affects the accuracy of the test results is unclear. This undoubtedly affects the further improvement and widespread application of the added mass method. Therefore, it is essential to conduct basic research related to the added mass method.

[0005] Due to the inherent complexity of rockfill materials, theoretical derivation using purely mathematical formulas to study the added mass method is clearly impractical. In recent decades, numerical simulation analysis has gradually become the mainstream method for studying rockfill materials and geotechnical engineering. Therefore, establishing a numerical model for the added mass method is crucial. Theoretically, using the discrete element method (DEM) to simulate the actual distribution of rockfill particles can yield accurate results. However, because rockfill particle sizes vary considerably, the DEM is often limited by computational capabilities, making it difficult to simulate true full-scale gradation, and the description of the mechanical properties of rockfill is often unsatisfactory. Furthermore, the DEM also struggles to reasonably simulate the propagation characteristics of shock waves.

[0006] In summary, the current common method for detecting the density of rockfill in earth-rock dams is the added mass method. However, the density test results obtained using this method are based on the assumption that the vibration stiffness and mass of the rockfill at the test location remain constant under different added mass impacts. Since these assumptions do not conform to reality, the discrepancy between the assumptions and reality will inevitably affect the accuracy of the test results. Currently, there is no effective solution to this problem.

[0007] Therefore, there is an urgent need for a detection method that can accurately calculate the density of the rockfill under impact when it is subjected to different masses, based on the changes in the vibration stiffness and mass of the rockfill at the test location. Summary of the Invention

[0008] Existing technologies for detecting the density of rockfill in earth-rock dams suffer from numerous drawbacks. Therefore, there is a strong need for a method to determine relevant parameters for detecting the density of rockfill in earth-rock dams using the added mass method. This method would address the challenge of accurately calculating the density of the rockfill under impact when different masses are added, thus altering the vibration stiffness and mass of the rockfill at the test location.

[0009] In this embodiment of the invention, a method for determining relevant parameters of the density of rockfill material in earth-rock dams using the added mass method is provided. The method includes: establishing a simulation model for rockfill material density detection using the added mass method, combining the determined dimensions of the rockfill material model, the dimensions of the added mass block, the load magnitude, as well as mesh generation and viscoelastic wave boundary conditions; conducting small-scale indoor physical model tests on rockfill materials of various densities using the added mass method to obtain the propagation characteristics of shock waves in each type of rockfill material under different added masses, and calibrating the rockfill material density detection simulation model based on the obtained propagation characteristics of shock waves in each type of rockfill material; conducting simulation tests on the rockfill material to be tested using the calibrated rockfill material density detection simulation model to obtain the vibration range and dominant frequency of the rockfill material under different added masses; wherein the dominant frequency of the rockfill material is the vibration dominant frequency at the center of the added mass block; and calculating the rockfill material under different added masses using the vibration range of the rockfill material under different added masses. The vibration volume of the rockfill under different added masses is calculated. The dominant vibration frequencies of the rockfill under different added masses are substituted into the relationship between the vibration mass and dominant vibration frequency to obtain the vibration mass of the rockfill under different added masses. The density of the rockfill under different added masses is calculated by combining the vibration mass and vibration volume of the rockfill under different added masses. The relationship between the vibration mass and dominant vibration frequency of the rockfill is obtained through the following steps: Simulation tests are conducted on various rockfills of different densities using a calibrated rockfill density detection simulation model to obtain the vibration range and dominant vibration frequency of each rockfill under different added masses; the corresponding vibration volume of the rockfill is calculated using the obtained vibration range; the corresponding vibration mass of the rockfill is calculated by combining the known rockfill density and the obtained vibration volume, thereby obtaining multiple sets of vibration masses and dominant vibration frequencies of the rockfill; and the relationship between the vibration mass and dominant vibration frequency of the rockfill is obtained through fitting.

[0010] In one embodiment, the mesh is divided into multi-scale meshes.

[0011] In another embodiment, the cross-scale meshing is achieved using a coupled finite element-scale boundary finite element method.

[0012] In another embodiment, the cross-scale meshing is achieved through the following steps: conducting indoor small-scale physical model tests on various rockfill materials of different densities using the added mass method to obtain the vibration range of each rockfill material under different added masses; performing statistical analysis on the obtained vibration range of each rockfill material under different added masses to obtain the coarse vibration range of the rockfill material; and using the coarse vibration range of the rockfill material to determine the size of the meshing, such that the mesh size within the coarse vibration range of the rockfill material is smaller than the mesh size outside the coarse vibration range of the rockfill material.

[0013] In another embodiment, the viscoelastic undulating boundary is added to the sides and bottom of the riprap model, and the viscoelastic undulating boundary does not affect the dynamic response inside the riprap model.

[0014] In another embodiment, the viscoelastic undulating boundary is added by the following steps: adding viscoelastic undulating boundaries to the sides and bottom of the riprap model, expanding the model range until the simulation results are the same when different boundaries are added, and the dynamic response inside the large and small range models is the same, then the added viscoelastic undulating boundary is effective.

[0015] In another embodiment, mathematical statistical methods are used to fit the obtained multiple sets of riprap mass and vibration frequency to obtain the relationship between the riprap mass and vibration frequency.

[0016] In another embodiment, the volume of the rockfill vibrating with vibration is calculated using the obtained range of rockfill vibration and the dimensions of the rockfill model.

[0017] In another embodiment, the vibration range of the riprap is the range within the simulation model from the loading point to the peak displacement of the vibration wave attenuating to a set value.

[0018] In another embodiment, the dimensions of the rockfill model, the dimensions of the additional mass block, and the load are determined based on existing indoor triaxial test results and actual dam deformation measurement results.

[0019] The beneficial effects of this invention include: After establishing a simulation model for detecting the density of riprap using the added mass method, the invention calibrates the model using the results of small-scale indoor physical model tests. This allows the simulation model to more accurately describe the mechanical properties and impact load propagation characteristics of the riprap, ensuring the reliability of the simulation results. Then, the calibrated simulation model is used to conduct simulation tests on riprap of various densities. Through these tests, the participating mass and dominant vibration frequency of multiple sets of riprap are obtained. A relationship between the participating mass and dominant vibration frequency of the riprap is then fitted. Since both the participating mass and dominant vibration frequency used to fit the relationship change with the added mass, the fitted relationship can reflect the impact effect on the riprap under different added masses. The relationship between the vibrating mass and the dominant vibration frequency of the rockfill material under varying vibrating stiffness and mass is investigated. Finally, a simulation test is conducted on the rockfill material under test using a calibrated density detection simulation model. The dominant vibration frequencies of the rockfill material under different added masses are substituted into the fitted relationship to obtain the vibrating mass of the rockfill material under different added masses. Then, combining the vibrating mass and vibrating volume of the rockfill material under different added masses, the density of the rockfill material under different added masses is calculated. It can be seen that the density of the rockfill material detected by the method of this invention is obtained under the condition that the vibrating stiffness and vibrating mass of the rockfill material at the test location change under the impact of different added masses, which is consistent with the actual situation and the density of the rockfill material detected is more accurate.

[0020] In addition, the present invention adopts a cross-scale mesh generation method, which can make full use of the fact that the region outside the vibration range has little impact on obtaining the vibration range of the rockfill. A finer mesh size is used within the coarse vibration range to ensure the accuracy of the calculation; a relatively sparse mesh size is used outside the coarse vibration range to improve the calculation efficiency without affecting the calculation accuracy. Thus, it effectively avoids the problems of large mesh size and low calculation efficiency caused by using traditional finite element meshes.

[0021] For earth and rock filling projects, the dry density of the compacted filling material has a good correlation with the construction quality and can reflect the construction quality to a certain extent. Therefore, using this invention to test the density of rockfill material can greatly improve the efficiency of dam construction material quality testing. Attached Figure Description

[0022] The above and other objects, features, and advantages of exemplary embodiments of the present invention will become readily apparent from the following detailed description taken in conjunction with the accompanying drawings. Several embodiments of the invention are illustrated in the drawings by way of example and not limitation, wherein:

[0023] Figure 1A flowchart illustrating a method for determining parameters related to the density of rockfill material in an earth-rock dam according to an embodiment of the present invention is shown.

[0024] Figure 2 A schematic diagram of two-dimensional cross-scale mesh partitioning in step 1 according to an embodiment of the present invention is shown.

[0025] Figure 3 A schematic diagram of three-dimensional cross-scale mesh partitioning in step 1 according to an embodiment of the present invention is shown.

[0026] Figure 4 A schematic diagram of a small-scale physical model test in step 2 according to an embodiment of the present invention is shown.

[0027] In the accompanying drawings, the same or corresponding reference numerals indicate the same or corresponding parts. Detailed Implementation

[0028] The principles and spirit of the invention will now be described with reference to several exemplary embodiments. It should be understood that these embodiments are given merely to enable those skilled in the art to better understand and implement the invention, and are not intended to limit the scope of the invention in any way. Rather, these embodiments are provided to make this disclosure more thorough and complete, and to fully convey the scope of this disclosure to those skilled in the art.

[0029] The principles and spirit of the present invention will be explained in detail below with reference to several representative embodiments.

[0030] In existing technologies, the process of measuring the density of riprap using the added mass method is as follows: by adding multiple levels of mass blocks, the dynamic information of the center point of the added mass blocks under different added masses is obtained. Using the superposition principle, the vibrating mass of the riprap is calculated, and then combined with the corresponding vibrating range, the density of the riprap is obtained, as detailed below:

[0031] Let the vibrating mass of the soil be M0 and the additional mass be ΔM. According to the superposition principle, we have:

[0032]

[0033] K = ω 2 ·(ΔM+M0)

[0034] When the added mass ΔM = 0, then: K = ω0 2 ·M0

[0035] In the formula, Z, Let ω and ω0 be the displacement function and acceleration function of the particle vibration, respectively; K be the dynamic stiffness of the system; ω and ω0 be the natural frequency of the system and the natural frequency of the vibrating body, respectively; and M0 be the vibrating mass of the vibrating body.

[0036] If an additional mass ΔM1 is added to the soil, an ω1 can be measured. However, this still leaves two unknowns, K and M0, in the equation, and there is no unique solution. Since the traditional method of adding mass assumes that the vibrating mass M0 of the vibrating rockfill and the dynamic stiffness K of the system remain constant under different added masses, adding two additional masses ΔM1 and ΔM2 can yield two corresponding frequencies ω1 and ω2. The equation K = ω 2 The solution is unique only when (ΔM+M0) is obtained, which yields the following formula:

[0037]

[0038] Thus, by adding mass blocks twice, the vibrating mass M0 of the vibrating pile material can be obtained.

[0039] After calculating the vibrating mass M0 based on the superposition principle, the vibrating volume V can be calculated based on the obtained vibration range and model box dimensions. Then, according to the density calculation formula, the density of the vibrating rockfill can be obtained as follows:

[0040]

[0041] As can be seen from the above process, the existing traditional method of adding mass calculates the density of the vibrating rockfill under the assumption that the vibrating mass and dynamic stiffness of the system remain unchanged under different added masses. Since these assumptions do not conform to reality, the difference between the assumptions and reality will inevitably affect the accuracy of the test results.

[0042] This invention addresses this issue by enabling the high-precision calculation of the density of the rockfill material under impact when it is subjected to different masses, taking into account changes in the vibration stiffness and mass of the rockfill material at the test site.

[0043] After introducing the basic principles of the present invention, various non-limiting embodiments of the present invention will be described in detail below.

[0044] According to embodiments of the present invention, a method for determining parameters related to the density of rockfill material in earth-rock dams using the added mass method is proposed. Furthermore, any quantity of elements in the accompanying drawings is for illustrative purposes only and not for limitation, and any naming is for distinction only and has no limiting meaning.

[0045] The following is for reference. Figure 1 This invention describes a method for determining parameters related to the density of rockfill material in earth-rock dams using the added mass method, according to an exemplary embodiment of the present invention. It should be noted that the embodiments of the present invention can be applied to any applicable scenario. The method described in this invention can be used in any application scenario involving the detection of rockfill material density.

[0046] Figure 1A flowchart illustrating a method for determining parameters related to the density of rockfill material in an earth-rock dam according to an embodiment of the present invention is shown.

[0047] In step 1, the riprap density detection simulation model using the added mass method is established by combining the determined dimensions of the riprap model, the dimensions of the added mass block and the load, as well as the mesh generation and viscoelastic wave boundary.

[0048] The rockfill model is determined based on the actual type (crushed stone, gravel) and gradation of the rockfill. In this embodiment, the mass-elastic model with added mass method is used as the basis, and the influence of rockfill damping is ignored. The vibration of the rockfill is equivalent to a single-degree-of-freedom undamped free vibration system.

[0049] In this embodiment, the dimensions of the rockfill model, the dimensions of the additional mass block, and the magnitude of the load are determined based on existing indoor triaxial test results and actual dam deformation measurement results.

[0050] The mesh generation in this embodiment is a multi-scale mesh generation. Specifically, a finite element-scale boundary finite element coupled mesh generation method is used to generate the multi-scale mesh. A schematic diagram of the two-dimensional multi-scale mesh generation is shown below. Figure 2 As shown, a schematic diagram of three-dimensional multi-scale mesh generation is as follows: Figure 3 As shown, the specific process of cross-scale mesh generation is as follows:

[0051] Small-scale indoor physical model tests were conducted on various rockfill materials of different densities using the added mass method to obtain the vibration range of each rockfill material under different added masses. Statistical analysis was performed on the obtained vibration range of each rockfill material under different added masses to obtain the approximate vibration range of the rockfill material. The size of the mesh was determined using the approximate vibration range of the rockfill material, so that the mesh size within the approximate vibration range of the rockfill material is smaller than the mesh size outside the approximate vibration range of the rockfill material.

[0052] This cross-scale meshing method fully utilizes the characteristic that the region outside the vibration range has little impact on obtaining the vibration range of the rockfill. A finer mesh size is used within the coarse vibration range to ensure the accuracy of the calculation; a relatively sparse mesh size is used outside the coarse vibration range to improve the calculation efficiency without affecting the calculation accuracy. Thus, it effectively avoids the problems of large mesh size and low calculation efficiency caused by using traditional finite element meshes.

[0053] As another implementation method, if the focus is on calculation accuracy, a grid division method with the same grid size inside and outside the coarse vibration range can also be adopted.

[0054] In this embodiment, viscoelastic undulating boundaries are added to the sides and bottom of the riprap model, and these boundaries do not affect the dynamic response within the model. Specifically, the addition of viscoelastic undulating boundaries is achieved through the following steps:

[0055] Viscoelastic wave boundaries were added to the sides and bottom of the riprap model, and the effectiveness of the boundaries was verified. First, a working condition similar to the theoretical solution was studied to expand the model range and eliminate the influence of boundary type on the simulation results. When the simulation results were the same when different boundaries were added to the model within this model range, it can be considered that the addition of the boundary does not affect the simulation results. This working condition is consistent with the actual situation, and the simulation result can be considered as the theoretical solution. This result was compared with the original model result. When the results were consistent, it indicates that the dynamic response inside the model of different sizes is basically the same under the influence of the boundary. It can be considered that the viscoelastic wave boundary applied to the small-scale model can effectively absorb and bounce vibration waves and can effectively simulate the propagation of vibration waves in an infinite domain, thus verifying the effectiveness of the boundary.

[0056] In step 2, indoor small-scale physical model tests were conducted on various rockfill materials with different densities using the added mass method to obtain the propagation characteristics of shock waves in each type of rockfill material under different added masses. Based on the obtained propagation characteristics of shock waves in each type of rockfill material, the simulation model for rockfill material density detection was calibrated.

[0057] The calibrated simulation model for detecting the density of rockfill can more accurately describe the mechanical properties of rockfill and the propagation characteristics of shock waves.

[0058] A schematic diagram of conducting small-scale physical model experiments using the added mass method is shown below. Figure 4 As shown in the figure, the weight and height of the hammer, the dimensions of the model box, and the dimensions of the additional mass block are all set according to actual needs. The stress of the hammer falling from the set height onto the rockfill is the load magnitude. For example, the load magnitude, model box dimensions, and additional mass block dimensions for small-scale physical model tests can be determined based on existing indoor triaxial test results, dam deformation measurement results, etc.

[0059] The specific process of conducting small-scale physical model experiments using the added mass method is as follows:

[0060] First, the test setup was carried out. Specifically, rockfill was laid inside the model box, and after laying, it was compacted multiple times. Multiple dynamic monitoring points were selected inside the rockfill, and vibration sensors were installed at each dynamic monitoring point. By installing vibration sensors inside the rockfill, the effective propagation range of the shock wave was roughly determined. Then, a layer of fine sand was laid flat on the rockfill inside the model box, and an additional mass block was placed on top. An acceleration sensor was placed at the center of the additional mass block.

[0061] After the test setup is completed, the heavy hammer is hoisted to a fixed height and then horizontally dropped onto the pile of rocks next to the additional mass block. The dynamic information change at the center position of the additional mass block is measured by an acceleration sensor for future reference.

[0062] Based on this approach, physical model tests were conducted on various rockfill materials with different densities using the added mass method. For each density of rockfill material, the propagation characteristics of shock waves under different added masses were measured by gradually adding additional mass blocks. This allows for the calibration of the rockfill density detection simulation model using the obtained shock wave propagation characteristics for each type of rockfill material. Simultaneously, the attenuation degree of the peak displacement of the vibration wave at each dynamic monitoring point under different added masses can be measured. Based on the attenuation degree of the peak displacement of the vibration wave, the vibration range of each type of rockfill material under different added masses can be determined. Furthermore, by combining multiple sets of vibration ranges of rockfill materials, a coarse vibration range of the rockfill material can be obtained through statistical analysis for mesh generation. Additionally, the dynamic information of the center position of the added mass block under different added masses can be measured for each type of rockfill material. Based on the dynamic information of the center position of the added mass block, the dominant vibration frequency at the center of the added mass block can be determined as the dominant vibration frequency of the rockfill material.

[0063] In step 3, the calibrated rockfill density detection simulation model is used to conduct simulation tests on the rockfill under test to obtain the vibration range and dominant frequency of the rockfill under different added masses; wherein, the vibration range of the rockfill is the range from the loading point to the displacement peak of the vibration wave decaying to the set value within the simulation model, and the dominant frequency of the rockfill is the dominant frequency of the vibration at the middle position of the added mass block;

[0064] Specifically, for the rockfill material to be tested, dynamic information of all positions inside the simulation model and the vibration dominant frequency of the middle position of the added mass block are obtained by gradually adding additional mass blocks. The displacement peak attenuation degree of the vibration wave at all positions inside the model is obtained from the dynamic information of all positions inside the simulation model. The range from the loading point to the displacement peak attenuation of the vibration wave to a set value (which is set according to actual needs) is taken as the effective propagation range of the vibration wave, which is the vibration range of the rockfill material.

[0065] In step 4, the vibration range of the rock pile under different added masses is used to calculate the vibration volume of the rock pile under different added masses.

[0066] The vibration-affected volume of the riprap is calculated using the obtained vibration-affected range of the riprap and the dimensions of the riprap model. For example, assuming the vibration-affected range of the riprap is a circle with a radius of 1m, then as long as the height of the riprap model is known, the vibration-affected volume corresponding to that range can be calculated using the cylinder volume formula.

[0067] In step 5, the vibration dominant frequency of the rock pile under different added masses is substituted into the relationship between the participating mass and the vibration dominant frequency of the rock pile to obtain the participating mass of the rock pile under different added masses.

[0068] In this embodiment, the relationship between the vibrating mass of the riprap and the dominant vibration frequency is obtained through the following steps:

[0069] Simulation tests were conducted on various rockfill materials with different densities using a calibrated rockfill density detection simulation model. The vibration range and dominant frequency of each rockfill material under different added masses were obtained. The vibration range of the rockfill material was combined with the size of the rockfill model to calculate the corresponding vibration volume of the rockfill material. The vibration mass of the rockfill material was calculated by combining the known rockfill density and the obtained vibration volume of the rockfill material. Thus, the vibration mass and dominant frequency of multiple sets of rockfill materials were obtained. The relationship between the vibration mass and the dominant frequency of the rockfill material was obtained by fitting.

[0070] For example, fitting methods can employ methods such as the least squares method from mathematical statistics.

[0071] Specifically, during the simulation experiment, for each density of riprap, by gradually adding additional mass blocks, the dynamic information of all positions inside the simulation model under different added masses and the vibration dominant frequency of the middle position of the additional mass block are obtained; from the dynamic information of all positions inside the simulation model, the displacement peak attenuation degree of the vibration wave at all positions inside the model is obtained, and the range from the loading point to the displacement peak attenuation of the vibration wave to the set value is taken as the effective propagation range of the vibration wave, that is, the vibration range of the riprap.

[0072] In step 6, the density of the rockfill material under different added masses is calculated by combining the vibrating mass and vibrating volume of the rockfill material under different added masses.

[0073] Assuming the vibrating mass and vibrating volume of the rockfill have been determined, the density of the rockfill can be calculated using the density calculation formula.

[0074] The effectiveness of the method of the present invention will be verified through specific cases below.

[0075] A 40kg heavy hammer is selected as the load and dropped freely from a height of 0.3m. The contact surface between the hammer and the riprap is a circular base with a diameter of 0.2m. The Young's modulus E of the riprap material is 1000MPa, and the Poisson's ratio μ is 0.35, taken as 2100kg / m². 3 2200kg / m 3 2300kg / m 3Three densities of riprap were used for validation. The load was applied to the top center of the model, and dynamic calculations were performed. The model size was initially 2m × 2m, later expanded to 10m × 10m. Viscoelastic boundaries were applied to the model, and their effectiveness was verified. Within this model range, the boundaries had no effect on the dynamic response results; vibration waves could propagate freely within this range, consistent with actual conditions. Therefore, the simulation results for this range are identical to the theoretical solution, and the simulation results can be considered as the theoretical solution. The mesh size was 0.05m × 0.05m, which meets the wave propagation accuracy requirements.

[0076] First, by gradually increasing the mass of the riprap, the vibration range of the riprap under different added masses was determined. The vibration range was defined as the area from the loading point to the point where the displacement peak decayed to 60%. Then, the vibration mass was calculated using the method of this invention based on the known density parameters and the obtained vibration range.

[0077] The density of the riprap is 2100 kg / m³ 3 The dominant vibration frequency f and the calculated vibrating mass under different added masses are shown in Table 1:

[0078] Table 1 shows that the density of the riprap is 2100 kg / m³. 3 Time-estimated parametric mass

[0079]

[0080] As shown in Table 1, the additional first-level mass block is 55.05 kg, the additional second-level mass block is 110.1 kg, the additional third-level mass block is 165.15 kg, and so on, with the additional seventh-level mass block being 385.35 kg.

[0081] The density of the riprap is 2200 kg / m³ 3 The dominant vibration frequency f and the calculated vibrating mass under different added masses are shown in Table 2:

[0082] Table 2 shows the density of the riprap is 2200 kg / m³. 3 Time-estimated parametric mass

[0083]

[0084] Through 2100kg / m 3 2200kg / m 3 The dominant vibration frequencies of the two types of riprap densities and the calculated participating masses were used to fit the relationship between the dominant vibration frequency f and the participating mass M using the least squares method:

[0085] M = 0.212269331f + 66.34839706

[0086] Using the fitted relationship between the dominant vibration frequency f and the vibrating mass M, combined with the 2300 kg / m² under different added masses... 3 The dominant vibration frequency of the riprap is calculated to be 2300 kg / m² under the corresponding additional mass. 3 The vibratory mass of the riprap, combined with the corresponding additional mass of 2300 kg / m 3 The vibration range of the riprap is calculated under different additional masses of 2300 kg / m. 3 The density of the riprap is calculated, and the calculated density value is compared with the actual value to obtain the density error.

[0087] Table 3 shows that the density of the riprap is 2300 kg / m³. 3 Time-estimated para-vibration mass

[0088]

[0089] As can be seen from Table 3, under the condition of adding three or more mass blocks, the density error calculated by using the relationship between the vibration main frequency f and the participating mass M obtained by fitting can be controlled within about two percent. Moreover, as the number of added mass blocks increases, the accuracy of the method of the present invention also becomes higher and higher. After adding four or more mass blocks, the measurement accuracy of the method of the present invention is extremely high, which meets the usage requirements.

[0090] In summary, the density of the rockfill material detected by the method of the present invention is obtained under the condition that the vibration stiffness and vibration mass of the rockfill material at the test location change when subjected to impact with different added masses. This is consistent with the actual situation, and the detected density of the rockfill material is more accurate.

[0091] Those skilled in the art will recognize that embodiments of the present invention can be implemented as a system, method, or computer program product. Therefore, this disclosure can be specifically implemented as entirely hardware, entirely software (including firmware, resident software, microcode, etc.), or a combination of hardware and software, generally referred to herein as a "circuit," "module," "unit," or "system." Furthermore, in some embodiments, the present invention can also be implemented as a computer program product contained in one or more computer-readable media, which includes computer-readable program code.

[0092] Any combination of one or more computer-readable media may be used. A computer-readable medium can be a computer-readable signal medium or a computer-readable storage medium. A computer-readable storage medium can be, for example,, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples (not exhaustive) of a computer-readable storage medium may include: an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof. In this document, a computer-readable storage medium can be any tangible medium that contains or stores a program that can be used by or in connection with an instruction execution system, apparatus, or device.

[0093] Computer-readable signal media may include data signals propagated in baseband or as part of a carrier wave, carrying computer-readable program code. Such propagated data signals may take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. Computer-readable signal media may also be any computer-readable medium other than computer-readable storage media, capable of transmitting, propagating, or transmitting programs for use by or in connection with an instruction execution system, apparatus, or device. The program code contained on the computer-readable medium may be transmitted using any suitable medium, including but not limited to wireless, wireline, optical fiber, RF, etc., or any suitable combination thereof.

[0094] Computer program code for performing the operations of this invention can be written in one or more programming languages ​​or a combination thereof, including object-oriented programming languages ​​such as Java, Smalltalk, and C++, as well as conventional procedural programming languages ​​such as "C" or similar programming languages. The program code can be executed entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving remote computers, the remote computer can be connected to the user's computer via any type of network (including a local area network (LAN) or a wide area network (WAN)), or it can be connected to an external computer (e.g., via the Internet using an Internet service provider).

[0095] These computer program instructions can be stored in a computer-readable medium that enables a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable medium produce a product comprising an instruction apparatus that implements the functions / operations specified in the boxes of a flowchart and / or block diagram.

[0096] Computer program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other device to cause a series of operational steps to be performed on the computer, other programmable data processing apparatus, or other device to produce a computer-implemented process, such that the instructions that execute on the computer or other programmable apparatus can provide a process for implementing the functions / operations specified in the boxes of a flowchart and / or block diagram.

[0097] It should be noted that although several steps in determining the relevant parameters of the density of rockfill material for earth-rock dams using the added mass method are mentioned in the detailed description above, this division is not mandatory. In fact, according to embodiments of the present invention, the features and functions of two or more steps described above can be embodied in one step. Conversely, the features and functions of one step described above can be further divided and embodied by multiple steps.

Claims

1. A method for determining the parameters related to the density of rockfill of earth and rockfill dams by the method of additional mass, characterized in that, The method includes: By combining the determined dimensions of the riprap model, the dimensions of the added mass block and the magnitude of the load, as well as the mesh division and viscoelastic wave boundary, a simulation model for riprap density detection using the added mass method is established. Indoor small-scale physical model tests were conducted on various rockfill materials with different densities using the added mass method to obtain the propagation characteristics of shock waves in each type of rockfill material under different added masses. Based on the obtained propagation characteristics of shock waves in each type of rockfill material, the simulation model for detecting the density of the rockfill material was calibrated. The calibrated simulation model for detecting the density of the rockfill was used to conduct simulation tests on the rockfill under test to obtain the vibration range and dominant frequency of the rockfill under different added masses; wherein, the dominant frequency of the rockfill is the vibration frequency of the middle position of the added mass block; By utilizing the vibration range of the rockfill material under different added masses, the vibration volume of the rockfill material under different added masses can be calculated respectively. Substitute the dominant vibration frequency of the rockfill material under different added masses into the relationship between the participating mass and the dominant vibration frequency to obtain the participating mass of the rockfill material under different added masses. By combining the vibrating mass and vibrating volume of the rockfill material under different added masses, the density of the rockfill material under different added masses can be calculated. The relationship between the vibrating mass and the dominant vibration frequency of the riprap is obtained through the following steps: Simulation tests are conducted on various riprap with different densities using a calibrated riprap density detection simulation model to obtain the vibrating range and dominant vibration frequency of each riprap under different added masses; the corresponding vibrating volume of the riprap is calculated using the obtained vibrating range; the corresponding vibrating mass of the riprap is calculated by combining the known riprap density and the obtained vibrating volume, thereby obtaining the vibrating mass and dominant vibration frequency of multiple sets of riprap; and the relationship between the vibrating mass and the dominant vibration frequency of the riprap is obtained by fitting.

2. The method for detecting the density-related parameters of the rockfill of an earth-rockfill dam by the added-mass method according to claim 1, characterized in that, The mesh is divided into multi-scale meshes.

3. The method for detecting the density-related parameters of the rockfill of the earth-rockfill dam by the added-mass method according to claim 2, characterized in that, The multi-scale mesh generation is achieved using a coupled finite element-scale boundary finite element method.

4. The method for detecting the density-related parameters of the rockfill of the earth-rockfill dam by the added-mass method according to claim 3, characterized in that, The cross-scale meshing is achieved through the following steps: small-scale indoor physical model tests are conducted on various rockfill materials of different densities using the added mass method to obtain the vibration range of each type of rockfill material under different added masses; statistical analysis is performed on the obtained vibration range of each type of rockfill material under different added masses to obtain a coarse vibration range of the rockfill material; the size of the meshing is determined using the coarse vibration range of the rockfill material, ensuring that the mesh size within the coarse vibration range of the rockfill material is smaller than the mesh size outside the coarse vibration range of the rockfill material.

5. The method for determining the density-related parameters of the rockfill of earth-rockfill dams by the added-mass method according to claim 4, characterized in that, The viscoelastic wave boundary is added to the sides and bottom of the riprap model, and the viscoelastic wave boundary does not affect the dynamic response inside the riprap model.

6. The method for detecting the density-related parameters of the rockfill of the earth-rockfill dam by the added-mass method according to claim 5, characterized in that, The viscoelastic undulating boundary is added through the following steps: add viscoelastic undulating boundaries to the sides and bottom of the rockfill model, expand the model range, until the simulation results are the same when different boundaries are added, and the dynamic response inside the large and small range models is the same, then the added viscoelastic undulating boundary is effective.

7. The method for detecting the density-related parameters of the rockfill of the earth-rockfill dam by the added-mass method according to claim 6, characterized in that, The relationship between the vibration mass and the main frequency of the rockfill is obtained by fitting the obtained groups of rockfill vibration mass and main frequency by using mathematical statistics method.

8. The method for detecting the density-related parameters of the rockfill of the earth-rockfill dam by the added-mass method according to claim 7, characterized in that, The rockfill vibration volume is calculated by using the obtained rockfill vibration range and the size of the rockfill model.

9. The method for detecting the density-related parameters of the rockfill of the earth-rockfill dam by the added-mass method according to claim 8, characterized in that, The rockfill vibration range is from the loading point to the range where the displacement peak value of the vibration wave in the simulation model attenuates to a set value.

10. The method for determining the parameters related to the density of rockfill of earth and rockfill dams by the method of added mass according to any one of claims 1 to 9, characterized in that, The size of the rockfill model, the size of the additional mass block and the load size are determined according to the existing indoor triaxial test results and the measured results of dam deformation.

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