A vibration compaction parameter control method and system for underwater block stone cushion based on vibration settlement

Abstract

The application discloses a kind of based on vibration sinking amount underwater block stone cushion vibration compaction parameter control method and system, method includes: S100, based on spring-damping-mass theory, the vibration system of block stone cushion vibration compaction is established;S200, the vibration system of block stone cushion vibration compaction is stressed analysis, obtains the overall dynamics equation of vibration device and reference vibration block stone;S300, the overall dynamics equation in step S200 is combined with the displacement of vibration system, obtains the third-order differential equation about elastic deformation;S400, the overall dynamics equation in step S200 is combined with the reaction of soil, obtains the second-order differential equation about elastic deformation;S500, the iteration algorithm based on Runge-Kutta method is prepared, differential equation is solved, and its numerical solution is obtained;S600, the output parameter in vibration process is obtained, and the input value of vibration system is adjusted according to the output parameter. Overall consideration block stone cushion in vibration compaction process elasticity, damping and plastic deformation.

Description

Technical Field

[0001] This invention belongs to the field of subgrade settlement calculation technology, and more specifically, relates to a method and system for controlling the compaction parameters of underwater boulders subgrade based on vibration settlement. Background Technology

[0002] The widespread application of vibratory compaction technology in earthwork engineering has made the study of the interaction mechanism between soil and vibratory rollers a core issue in engineering mechanics. To reveal the dynamic response of the compaction equipment and the soil, various vibratory compaction models have been proposed in existing technologies. These include the classic two-degree-of-freedom lumped mass model, which uses linear elastic vibration theory and a lumped mass-spring-damped system to describe the vibratory roller-soil system. The lumped mass is used to simulate the inertial characteristics of the roller's vibratory wheel and the soil, the spring is used to simulate the elastic response of the system, and the damping is used to simulate energy loss due to friction, internal energy dissipation, etc. This model assumes the soil is a perfectly elastic body and uses a parallel linear spring and damper model to describe the viscous and elastic response of the soil. This model is widely used due to its simplicity and clear physical meaning, but its simplification assumptions cannot describe the nonlinear and plastic deformation of the soil during vibratory compaction, thus limiting its application in practical engineering.

[0003] With a deeper understanding of the nonlinear behavior of soil, nonlinear elastic models have been proposed. These models divide the soil compaction process into two stages: contact and separation, and use piecewise linear stiffness to describe the stiffness changes of the soil. While they can reflect the nonlinear characteristics of soil, they still fail to effectively describe its plastic deformation. In practical engineering, the plastic deformation of soil, especially in the initial stage of compaction, typically exhibits strong plastic characteristics; therefore, relying solely on nonlinear viscoelastic models cannot fully characterize soil behavior.

[0004] To account for the plastic properties of soil during vibration compaction, a plastic element was introduced into the viscoelastic model, forming a viscoelastic-plastic model. This model can simultaneously consider the elastic, damping, and plastic deformation of the soil. Specifically, during vibration compaction, in addition to elastic and viscoelastic deformation, the soil also undergoes some irreversible plastic deformation. This plastic deformation directly determines the settlement during vibration compaction and is crucial to the compaction effect, deformation modulus, and shear strength of the subgrade. Therefore, the viscoelastic-plastic model can comprehensively describe the soil response during vibration compaction, especially its transition from a loose to a compacted state.

[0005] However, the viscoelastic-plastic model still faces certain challenges in practical applications. First, the complexity of the viscoelastic-plastic model makes the determination of its parameters more difficult. Especially when considering multi-stage compaction processes, the precise determination of soil parameters at each stage becomes a critical issue due to the continuous changes in soil mechanical properties. Second, the universality of the viscoelastic-plastic model is limited by the differences in plastic deformation characteristics and constitutive models among different soil types. Summary of the Invention

[0006] To address the aforementioned deficiencies or improvement needs of existing technologies, this invention provides a method and system for controlling the compaction parameters of underwater boulders cushion layers based on vibration settling. Based on the spring-damping-lumped mass theory, a viscoelastic-plastic model is used to explore the compaction mechanism of the boulders cushion layer. Through theoretical derivation and parameter determination, the applicability and reliability of the model are improved, providing more accurate predictions and guidance for engineering practice. This model can comprehensively consider the elastic, damping, and plastic deformation of the boulders cushion layer during vibration compaction, describing the transformation process of boulders from loose to dense.

[0007] To achieve the above objectives, according to a first aspect of the present invention, a method for controlling the compaction parameters of an underwater boulder cushion layer based on vibration settlement is provided, specifically including the following steps:

[0008] S100. Based on the spring-damping-lumped mass theory, a vibration system for compacting the boulders cushion layer is established.

[0009] S200. Perform force analysis on the vibration system for compacting the boulders cushion layer to obtain the overall dynamic equation of the vibration device and the vibrating boulders.

[0010] S300. Combine the overall dynamic equation in step S200 with the displacement of the vibration system to obtain the third-order differential equation for elastic deformation.

[0011] S400. Combine the overall dynamic equation in step S200 with the soil reaction force to obtain the second-order differential equation for elastic deformation.

[0012] S500. Develop an iterative algorithm based on the Runge-Kutta method to solve the differential equation and obtain its numerical solution.

[0013] S600. Based on the obtained numerical solution, the output parameters of the vibration process are derived, and the input values ​​of the vibration system are adjusted according to the output parameters.

[0014] Furthermore, in step S200, under the action of the excitation force, the vibrating device and the stone cushion layer always remain in contact. At this time, the two are regarded as a whole, which includes two degrees of freedom.

[0015] The mass of the vibration system includes the mass m of the vibration device.d The mass m of the vibrating stone s Two parts;

[0016] The boulders cushion layer is modeled using a viscoelastic-plastic element, where k s k p These are the elastic modulus and plastic modulus of the spring element, respectively, c. s is the damping coefficient of the sticky pot element;

[0017] It considers the buoyancy of water, but does not consider the resistance of water.

[0018] Furthermore, the spring constant k of the spring element s The damping coefficient c of the sticky pot element s All are based on the current dynamic shear modulus G d Confirmed, specifically:

[0019]

[0020] Where, r e Let r be the equivalent radius of the tamping plate. e It is determined by its length L and width B, specifically:

[0021]

[0022] μ is Poisson's ratio of the stone, and ρ is the density of the stone.

[0023] When considering the thickness H of the rubble cushion layer and treating the area below the bottom of the cushion layer as a rigid body, the effect of the finite cushion layer thickness H on the deformation stiffness needs to be taken into account. In this case, the elastic coefficient k of the spring element... s The damping coefficient c of the sticky pot element s for:

[0024]

[0025]

[0026] Furthermore, the dynamic modulus of the stone decreases continuously as the dynamic strain increases, and the relationship between the two is as follows:

[0027]

[0028] Wherein, γ is the current dynamic shear strain of the boulders cushion layer.

[0029] τ represents the current dynamic shear stress of the boulders cushion layer.

[0030] G d The dynamic shear modulus of the rubble cushion layer.

[0031] γ rThe dynamic shear strain is the reference state for the riprap cushion layer.

[0032] τ max The dynamic shear stress is for reference conditions.

[0033] G0 is the dynamic shear modulus of the boulders cushion layer under reference conditions.

[0034] The dynamic shear modulus G0 of the boulders cushion layer in the reference state is determined based on the void ratio, specifically:

[0035]

[0036] Where e is the porosity of the rubble cushion layer.

[0037] σ′0 is the effective confining pressure of the rubble cushion layer in its initial state. It is the confining pressure of the rubble cushion layer when the vibratory hammer is placed at rest on top of the rubble cushion layer.

[0038] Furthermore, the plasticity coefficient k p From the elastic coefficient k s It is confirmed that the relationship between the two is as follows:

[0039]

[0040] Where ε is a plasticity parameter, ranging from 0 to 1. When ε = 0, the corresponding plasticity coefficient k p =0, the rubble cushion layer exhibits ideal plasticity; when ε=1, k p As it approaches infinity, the stone cushion layer exhibits perfect elasticity.

[0041] During the vibration compaction of soil and rock, the soil density gradually increases, and the plastic stiffness also increases accordingly. Its plastic parameter ε gradually increases and eventually tends towards a stable state. At this point, the plastic coefficient ε is determined by the operating time t of the vibration system, specifically:

[0042]

[0043] Where δ and β are the transformation coefficients with respect to time.

[0044] Furthermore, in step S200, the overall dynamic equation of the vibration device and the vibrating stone is:

[0045]

[0046] Where z represents the displacement of the vibrating device and the vibrating stone block.

[0047] F0sinwt is the excitation force acting on the system.

[0048] F 浮 The buoyancy force experienced by the vibrating device and the vibrating stone in the water.

[0049] w is the angular velocity of the eccentric block.

[0050] F0 is the amplitude of the excitation force.

[0051] t is the running time of the vibration system.

[0052] F R This is the soil reaction force.

[0053] Furthermore, in step S300, the displacement of the vibration system is the displacement z of the vibration device and the vibrating stone, which is equal to the elastic deformation z of the stone cushion layer. e Plastic deformation of the rubble cushion layer z p The sum is:

[0054] z = z e +z p (5)

[0055] Combining equations (1) and (5), we obtain the elastic deformation z. e The third-order differential equation:

[0056]

[0057] Among them, F d The coefficients α2, α1, and α0 are respectively:

[0058] F d =F0sin wt+m d g+m s gF 浮 (7)

[0059]

[0060] Furthermore, in step S400, when the excitation force enters the unloading stage, the soil in the vibration system only undergoes elastic deformation, the vibration device is in contact with the soil, and the system has two degrees of freedom.

[0061] Since plastic deformation cannot be recovered at this point, the relationship between the displacement of the vibration device and elastic and plastic deformation is as follows:

[0062] z = z e +z p,max (9)

[0063] Among them, z p,max For the plastic deformation in the previous elastic-plastic stage, which is a constant, we can differentiate equation (9) to obtain:

[0064]

[0065] At this time, the soil reaction force FR for:

[0066]

[0067] Combining equations (1), (9), (10), and (11), we obtain the elastic deformation z of the soil. e The second-order differential equation:

[0068]

[0069] Furthermore, in step S500, the plasticity coefficient k of the rubble cushion layer... p As the compaction process continues, the plastic deformation that the soil can undergo becomes smaller and smaller;

[0070] When k p When it reaches infinity, its effect is negligible; at this point, the soil reaction force F... R The formula for calculation is,

[0071]

[0072] The formula for calculating displacement is:

[0073] z = z e (14)

[0074] From equation (3), we get:

[0075]

[0076] The vibration equation of equation (15) is in the form of:

[0077]

[0078] Let the steady-state response of equation (16), i.e. the displacement relationship during underwater vibration, be defined as:

[0079]

[0080] Where A is the amplitude of the vibration system.

[0081] The phase angle of the vibrating system.

[0082] Q indicates that the device is constantly on due to displacement.

[0083] According to a second aspect of the present invention, a compaction parameter control system for underwater boulder cushion layers based on vibration settling amount is provided, comprising:

[0084] System establishment module: used to establish a vibration system for compacting the boulders cushion layer based on the spring-damping-lumped mass theory;

[0085] Force analysis module: used to perform force analysis on the vibration system of the compaction of the boulders cushion layer, and obtain the overall dynamic equation of the vibration device and the vibrating boulders;

[0086] The first combining module is used to combine the overall dynamic equation in step S200 with the displacement of the vibration system to obtain a third-order differential equation for elastic deformation.

[0087] The second combining module is used to combine the overall dynamic equation in step S200 with the soil reaction force to obtain a second-order differential equation for elastic deformation.

[0088] The solution module is used to develop iterative algorithms based on the Runge-Kutta method to solve differential equations and obtain their numerical solutions.

[0089] Parameter feedback module: It is used to obtain the output parameters of the vibration process based on the obtained numerical solution, and adjust the input value of the vibration system according to the output parameters.

[0090] In summary, compared with the prior art, the above-described technical solutions conceived by this invention can achieve the following beneficial effects:

[0091] 1. The control method of this invention is based on the spring-damping-lumped mass theory and uses a viscoelastic-plastic model to explore the vibration compaction mechanism of the boulders cushion layer. Through theoretical derivation and calculation parameter determination, the applicability and reliability of the model are improved, providing more accurate predictions and guidance for engineering practice. This model can comprehensively consider the elastic, damping, and plastic deformation of the boulders cushion layer during vibration compaction, describing the transformation process of the boulders from loose to dense.

[0092] 2. The control method of this invention addresses the limitation of traditional viscoelastic models in characterizing plastic deformation by introducing a plastic spring element. The plasticity coefficient describes the transformation process of the boulders from loose to dense. The model decomposes the total displacement into elastic and plastic deformation. During the loading stage, the boulder cushion layer undergoes both elastic and plastic deformation simultaneously, resulting in a third-order differential equation. During the unloading stage, the boulder cushion layer only undergoes plastic deformation, resulting in a second-order differential equation. The Runge-Kutta method is used to numerically solve these piecewise differential equations, overcoming the complexity of analytical solutions.

[0093] 3. The control method of the present invention determines the amplitude and frequency of the excitation force based on the mass of the eccentric block of the hydraulic vibratory hammer, the product of the eccentricity and the angular frequency; it proposes to assume that the mass of the vibrating stone is α times the mass of the vibrating device, and its value range is generally between 0 and 0.5; based on the dynamic shear modulus of the stone pad and the size of the tamping plate, the elastic coefficient and damping coefficient of the pad are determined, and the influence of the pad thickness on the stiffness is corrected; by introducing the plastic parameter ε related to the compaction time, the growth law of the plastic coefficient with the compaction process is described.

[0094] 4. The control method of the present invention, through viscoelastic-plastic model and numerical calculation, realizes the quantitative analysis of the compaction process of the boulders cushion layer, clarifies the influence law of excitation parameters and cushion layer characteristics, and provides a theoretical basis for optimizing the compaction process. In the future, the parameter calibration can be optimized by combining field test data to further improve the model prediction accuracy and universality. Attached Figure Description

[0095] Figure 1 This is a flowchart illustrating a method for controlling the compaction parameters of an underwater boulders cushion layer based on the amount of vibration settling, according to an embodiment of the present invention.

[0096] Figure 2 This is a schematic diagram of a two-degree-of-freedom viscoelastic-plastic model in an embodiment of the present invention;

[0097] Figure 3 This is a schematic diagram of the forces acting on the vibration system in an embodiment of the present invention;

[0098] Figure 4 This is a schematic diagram of the force on the viscoelastic-plastic model in an embodiment of the present invention;

[0099] Figure 5 This is a schematic diagram of the force distribution of the viscoelastic-plastic model when the plasticity coefficient of the boulders cushion layer is infinite in an embodiment of the present invention.

[0100] Figure 6 This is a schematic diagram showing the dynamic shear stress and dynamic shear strain relationship of the boulders cushion layer backbone curve in an embodiment of the present invention;

[0101] Figure 7 This is a schematic diagram illustrating the relationship between plasticity parameters and the number of rolling passes in an embodiment of the present invention;

[0102] Figure 8 This is a schematic diagram illustrating the influence of coefficient β on the plasticity parameter and the growth law of the plasticity coefficient in an embodiment of the present invention;

[0103] Figure 9 This is a schematic diagram illustrating the influence of the coefficient δ on the growth law of the plasticity parameter and the plasticity coefficient in an embodiment of the present invention. Detailed Implementation

[0104] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0105] Example 1

[0106] like Figure 1As shown, this embodiment of the invention provides a method for controlling the compaction parameters of an underwater boulder cushion layer based on vibration settling volume, specifically including the following steps:

[0107] S100. Based on the spring-damping-lumped mass theory, a vibration system for compacting the boulders cushion layer is established.

[0108] S200. Perform force analysis on the vibration system for compacting the boulders cushion layer to obtain the overall dynamic equation of the vibration device and the vibrating boulders.

[0109] S300. Combine the overall dynamic equation in step S200 with the displacement of the vibration system to obtain the third-order differential equation for elastic deformation.

[0110] S400. Combine the overall dynamic equation in step S200 with the soil reaction force to obtain the second-order differential equation for elastic deformation.

[0111] S500. Develop an iterative algorithm based on the Runge-Kutta method to solve the differential equation and obtain its numerical solution.

[0112] S600. Based on the obtained numerical solution, the output parameters of the vibration process are derived, and the input values ​​of the vibration system are adjusted according to the output parameters.

[0113] In step S100, the vibration system for compacting the boulders cushion layer includes a vibration device, vibrating boulders, springs, and dampers. The vibration device includes a vibratory hammer, a resonant beam, and a tamping plate. The vibratory hammer generates excitation force by rotating an eccentric block, which acts on the boulders cushion layer through the resonant beam and the tamping plate.

[0114] like Figure 2 , 3 As shown, in step S200, under the action of the excitation force, the vibrating device and the stone cushion layer remain in contact. At this point, they are considered as a single unit, comprising two degrees of freedom. The mass of the vibration system includes the mass m of the vibrating device. d The mass m of the vibrating stone s Two parts. The boulders cushion layer is modeled using a viscoelastic-plastic element, where k s k p These are the elastic modulus and plastic modulus of the spring element, respectively, c. s Let be the damping coefficient of the sticky pot element. The buoyancy of the water is considered, but the water resistance is neglected.

[0115] The overall dynamic equation of the vibrating device and the vibrating stone is:

[0116]

[0117] Where z represents the displacement of the vibrating device and the vibrating stone block.

[0118] F0sinwt is the excitation force acting on the system.

[0119] F 浮 The buoyancy force experienced by the vibrating device and the vibrating stone in the water.

[0120] w is the angular velocity of the eccentric block.

[0121] F0 is the amplitude of the excitation force.

[0122] t is the running time of the vibration system.

[0123] F R This is the soil reaction force.

[0124] The amplitude F0 of the excitation force is:

[0125]

[0126] Where A0 is the nominal vibration amplitude of the vibration system.

[0127] B and L are the length and width of the ramming plate, respectively;

[0128] The nominal vibration amplitude A0 of the vibration system is:

[0129] A0 = M e w 2 (3)

[0130] Among them, M e It is the product of the mass of the eccentric block and the eccentricity.

[0131] like Figure 4 As shown, the soil reaction force F R for:

[0132]

[0133] Among them, z e The elastic deformation of the rubble cushion layer,

[0134] z p This refers to the plastic deformation of the boulders cushion layer.

[0135] In step S300, the displacement of the vibration system is the displacement z of the vibration device and the vibrating stone, which is equal to the elastic deformation z of the stone cushion layer. e Plastic deformation of the rubble cushion layer z p The sum is:

[0136] z = z e +z p (5)

[0137] Combining equations (1) and (5), we obtain the elastic deformation z.e The third-order differential equation:

[0138]

[0139] Among them, F d The coefficients α2, α1, and α0 are respectively:

[0140] F d =F0sin wt+m d g+m s gF 浮 (7)

[0141]

[0142] In step S400, when the excitation force enters the unloading stage, the soil in the vibration system only undergoes elastic deformation, the vibrating device is in contact with the soil, and the system has two degrees of freedom. At this time, since plastic deformation cannot be recovered, the relationship between the displacement of the vibrating device and the elastic and plastic deformations is as follows:

[0143] z = z e +z p,max (9)

[0144] Among them, z p,max For the plastic deformation in the previous elastic-plastic stage, which is a constant, we can differentiate equation (9) to obtain:

[0145]

[0146] At this time, the soil reaction force F R for:

[0147]

[0148] Combining equations (1), (9), (10), and (11), we obtain the elastic deformation z of the soil. e The second-order differential equation:

[0149]

[0150] The vibrating device is initially in a static state, i.e., undergoing elastic deformation due to gravity. During the initial compaction, the system is in the elastoplastic stage, and the soil spring reaction force gradually increases. R As plastic deformation gradually develops, and the soil spring reaction force begins to decrease, the system changes from loading to unloading, transitioning from the elastoplastic stage to the elastic stage. This indicates that the soil spring reaction force F at the next moment in the elastoplastic stage... R,next The soil spring reaction force F is greater than the current moment. R,now The soil spring reaction force F at the next moment of the elastic phase R,next The soil spring reaction force F is less than the current moment. R,now .

[0151] like Figure 5 As shown, in step S500, the plasticity coefficient k of the rubble cushion layer... p As the compaction process continues, the plastic deformation that the soil can undergo decreases. When k p When it reaches infinity, its effect is negligible; at this point, the soil reaction force F... R The formula for calculation is,

[0152]

[0153] The formula for calculating displacement is:

[0154] z = z e (14)

[0155] From equation (3), we get:

[0156]

[0157] The vibration equation of equation (15) is in the form of:

[0158]

[0159] Let the steady-state response of equation (16), i.e. the displacement relationship during underwater vibration, be defined as:

[0160]

[0161] After rearranging equations (7) and (17) to obtain equation (16), we get:

[0162]

[0163] For all operating times t of the vibration system, equation (18) must hold, therefore the following relationship must be satisfied:

[0164]

[0165] k s Q = m d g+m s gF 浮 (twenty one)

[0166] Based on the above relationships, we obtain the following:

[0167]

[0168] Where A is the amplitude of the vibration system.

[0169] The phase angle of the vibrating system.

[0170] Q indicates that the device is constantly on due to displacement.

[0171] In step S600, the output parameters of the vibration process are obtained through the displacement relationship during the underwater vibration process. The output parameters of the vibration process include the velocity during the vibration process, the work done by the vibration system on the rock cushion layer, and the work done by the underwater vibration system on the rock cushion layer per unit time.

[0172] The velocity during the vibration process is:

[0173]

[0174] The work done by the vibration system on the boulders cushion layer is:

[0175]

[0176] The work done by the underwater vibration system on the boulders cushion layer per unit time is:

[0177]

[0178] The spring element's elastic coefficient k s The damping coefficient c of the sticky pot element s All are based on the current dynamic shear modulus G d Confirmed, specifically:

[0179]

[0180] Where, r e Let r be the equivalent radius of the tamping plate. e It is determined by its length L and width B, specifically:

[0181]

[0182] μ is the Poisson's ratio of the stone, and ρ is the density of the stone.

[0183] When considering the thickness H of the boulders cushion layer and treating the area below the bottom of the cushion layer as a rigid body, the effect of the finite cushion layer thickness H on the deformation stiffness needs to be taken into account. In this case, the elastic coefficient k of the spring element... s The damping coefficient c of the sticky pot element s for:

[0184]

[0185] like Figure 6 As shown, the dynamic modulus of the stone decreases continuously with the increase of dynamic strain, and the relationship between the two is as follows:

[0186]

[0187] Wherein, γ is the current dynamic shear strain of the boulders cushion layer.

[0188] τ is the current dynamic shear stress of the boulders cushion layer.

[0189] G d The dynamic shear modulus of the rubble cushion layer.

[0190] γ r The dynamic shear strain is the reference state for the riprap cushion layer.

[0191] τ max The dynamic shear stress is for reference conditions.

[0192] G0 is the dynamic shear modulus of the boulders cushion layer under reference conditions.

[0193] The dynamic shear modulus G0 of the boulders cushion layer in the reference state is determined based on the void ratio, specifically:

[0194]

[0195] Where e is the porosity of the rubble cushion layer.

[0196] σ′0 is the effective confining pressure of the rubble cushion layer in its initial state. It is the confining pressure of the rubble cushion layer when the vibratory hammer is placed at rest on top of the rubble cushion layer.

[0197] The plasticity coefficient k p From the elastic coefficient k s It is confirmed that the relationship between the two is as follows:

[0198]

[0199] Where ε is a plasticity parameter, ranging from 0 to 1. When ε = 0, the corresponding plasticity coefficient k p =0, the rubble cushion layer exhibits ideal plasticity; when ε=1, k p As it approaches infinity, the stone cushion layer exhibits perfect elasticity.

[0200] like Figure 7 As shown, during the vibration compaction of soil and rock, the soil density gradually increases, and the plastic stiffness also increases accordingly. Its plastic parameter ε gradually increases and eventually tends towards a stable state. At this point, the plastic coefficient ε is determined by the operating time t of the vibration system, specifically:

[0201]

[0202] Where δ and β are the transformation coefficients with respect to time.

[0203] The ε represented by equation (36) has a trend of low initial value, rapid growth in the early stage, slow growth thereafter, and finally stable convergence to 1.

[0204] like Figure 8 As shown, when δ is fixed, the effect of changing the coefficient β on the growth law of plastic parameters and plastic coefficient is observed. It can be seen that the smaller β is, the faster ε reaches a higher level. When δ is 0 and β is 10, after 60 seconds of vibration, k... p It can reach k s Hundreds of times.

[0205] like Figure 9 As shown, when β is fixed, the effect of changing the coefficient δ on the plasticity parameter and the growth law of the plasticity coefficient shows that the larger δ is, the higher the initial value of ε is. When δ is 5 and β is 20, k p The initial value is k s 0.67 times.

[0206] In step S600, it is also necessary to determine whether the compaction of the boulders cushion layer meets the design and construction requirements based on the value of the displacement z of the vibration device, and then adjust the input values ​​and parameters.

[0207] Example 2

[0208] This invention provides a control system for the compaction parameters of an underwater boulder cushion layer based on vibration settling, comprising:

[0209] System establishment module: used to establish a vibration system for compacting the boulders cushion layer based on the spring-damping-lumped mass theory;

[0210] Force analysis module: used to perform force analysis on the vibration system of the compaction of the boulders cushion layer, and obtain the overall dynamic equation of the vibration device and the vibrating boulders;

[0211] The first combining module is used to combine the overall dynamic equation in step S200 with the displacement of the vibration system to obtain a third-order differential equation for elastic deformation.

[0212] The second combining module is used to combine the overall dynamic equation in step S200 with the soil reaction force to obtain a second-order differential equation for elastic deformation.

[0213] The solution module is used to develop iterative algorithms based on the Runge-Kutta method to solve differential equations and obtain their numerical solutions.

[0214] Parameter feedback module: It is used to obtain the output parameters of the vibration process based on the obtained numerical solution, and adjust the input value of the vibration system according to the output parameters.

[0215] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for controlling the compaction parameters of an underwater boulders cushion layer based on vibration settlement, characterized in that, Specifically, the following steps are included: S100. Based on the spring-damping-lumped mass theory, a vibration system for compacting the boulders cushion layer is established. S200. Perform force analysis on the vibration system for compacting the boulders cushion layer to obtain the overall dynamic equation of the vibration device and the vibrating boulders. S300. Combine the overall dynamic equation in step S200 with the displacement of the vibration system to obtain the third-order differential equation for elastic deformation. S400. Combine the overall dynamic equation in step S200 with the soil reaction force to obtain the second-order differential equation for elastic deformation. S500. Develop an iterative algorithm based on the Runge-Kutta method to solve the differential equation and obtain its numerical solution. S600. Based on the obtained numerical solution, the output parameters of the vibration process are obtained, and the input values ​​of the vibration system are adjusted according to the output parameters. In step S200, under the action of excitation force, the vibrating device and the stone cushion layer always remain in contact. At this time, the two are regarded as a whole, which includes two degrees of freedom. The mass of the vibration system includes the mass of the vibration device. And the quality of the vibrating stone Two parts; The boulders cushion layer is modeled using a viscoelastic-plastic element, in which... , These are the elastic modulus and plastic modulus of the spring element, respectively. is the damping coefficient of the sticky pot element; And the buoyancy of water is considered, but the water resistance is not considered; The spring element's elastic coefficient Damping coefficient of the sticky pot element All are based on the current dynamic shear modulus Confirmed, specifically: （28） （29） in, Let be the equivalent radius of the tamping plate. By its length and width Confirmed, specifically: （30） Poisson's ratio for the block stone The density of the stone; When considering the thickness H of the rubble cushion layer and treating the area below the bottom of the cushion layer as a rigid body, the effect of the finite cushion layer thickness H on the deformation stiffness needs to be taken into account. In this case, the elastic coefficient of the spring element... Damping coefficient of the sticky pot element for: （31） （32） 2. The method for controlling the compaction parameters of an underwater boulders cushion layer based on vibration settling volume according to claim 1, characterized in that, The dynamic modulus of the stone decreases continuously as the dynamic strain increases, and the relationship between the two is as follows: （33） in, This represents the current dynamic shear strain of the riprap cushion layer. The current dynamic shear stress of the rubble cushion layer. The dynamic shear modulus of the rubble cushion layer. The dynamic shear strain is the reference state for the riprap cushion layer. The dynamic shear stress is for reference conditions. The dynamic shear modulus is given as a reference state for the riprap cushion layer. The dynamic shear modulus of the boulders cushion layer under reference conditions Determined based on the porosity ratio, specifically: （34） in, The porosity of the rubble cushion layer. To determine the effective confining pressure of the rubble cushion layer in its initial state, the confining pressure of the rubble cushion layer is measured when a vibratory hammer is placed statically on top of the rubble cushion layer.

3. The method for controlling the compaction parameters of an underwater boulders cushion layer based on vibration settling volume according to claim 2, characterized in that, The plasticity coefficient From the elasticity coefficient It is confirmed that the relationship between the two is as follows: （35） in, This is a plasticity parameter, with a value ranging from 0 to 1. When = 0, the corresponding plasticity coefficient =0, the rubble cushion layer exhibits ideal plasticity; when When =1, As it approaches infinity, the stone cushion layer exhibits perfect elasticity. During the vibration compaction process of soil and rock materials, the soil density gradually increases, and the plastic stiffness also increases accordingly, as does its plasticity parameter. It gradually increases and eventually tends to a stable state; at this point, the plasticity coefficient... The time t during which the vibration system operates is determined, specifically: （36） in, and These are the transformation coefficients with respect to time.

4. The method for controlling the compaction parameters of an underwater boulders cushion layer based on vibration settling volume according to claim 3, characterized in that, In step S200, the overall dynamic equation of the vibration device and the vibrating stone is: （1） in, For the displacement of the vibrating device and the vibrating stone, The excitation force acting on the system, The buoyancy force experienced by the vibrating device and the vibrating stone in the water. The angular velocity of the eccentric block is... The amplitude of the excitation force, t is the running time of the vibration system. This is the soil reaction force.

5. The method for controlling the compaction parameters of an underwater boulders cushion layer based on vibration settling volume according to claim 4, characterized in that, In step S300, the displacement of the vibration system is the displacement of the vibration device and the vibrating block. It is equal to the elastic deformation of the stone cushion layer. Plastic deformation of the rubble cushion layer The sum is: （5） Combining equations (1) and (5), we obtain the information regarding elastic deformation. The third-order differential equation: （6） in, With coefficient , , They are respectively: （7） （8） 6. The method for controlling the compaction parameters of an underwater boulders cushion layer based on vibration settling volume according to claim 5, characterized in that, In step S400, when the excitation force enters the unloading stage, the soil in the vibration system only undergoes elastic deformation, the vibration device is in contact with the soil, and the system has two degrees of freedom. Since plastic deformation cannot be recovered at this point, the relationship between the displacement of the vibration device and elastic and plastic deformation is as follows: （9） in, For the plastic deformation in the previous elastic-plastic stage, which is a constant, we can differentiate equation (9) to obtain: （10） At this time, the soil reaction force for: （11） The elastic deformation of the soil is obtained by combining equations (1), (9), (10) and (11). The second-order differential equation: （12） 7. The method for controlling the compaction parameters of an underwater boulders cushion layer based on vibration settling volume according to claim 6, characterized in that, In step S500, the plasticity coefficient of the rubble cushion layer As the compaction process continues, the plastic deformation that the soil can undergo becomes smaller and smaller; when When it reaches infinity, its effect is negligible; at this point, the soil reaction force... The formula for calculation is, （13） The formula for calculating displacement is: （14） From equation (3), we get: （15） The vibration equation of equation (15) is in the form of: （16） Let the steady-state response of equation (16), i.e. the displacement relationship during underwater vibration, be defined as: （17） in, The amplitude of the vibration system. The phase angle of the vibrating system. The light is constantly on due to displacement.

8. A control system for the compaction parameters of an underwater boulders cushion layer based on vibration settlement, used to implement the method for controlling the compaction parameters of an underwater boulders cushion layer based on vibration settlement as described in any one of claims 1-7, characterized in that, include: System establishment module: used to establish a vibration system for compacting the boulders cushion layer based on the spring-damping-lumped mass theory; Force analysis module: used to perform force analysis on the vibration system of the compaction of the boulders cushion layer, and obtain the overall dynamic equation of the vibration device and the vibrating boulders; The first combining module is used to combine the overall dynamic equation in step S200 with the displacement of the vibration system to obtain a third-order differential equation for elastic deformation. The second combining module is used to combine the overall dynamic equation in step S200 with the soil reaction force to obtain a second-order differential equation for elastic deformation. The solution module is used to develop iterative algorithms based on the Runge-Kutta method to solve differential equations and obtain their numerical solutions. Parameter feedback module: It is used to obtain the output parameters of the vibration process based on the obtained numerical solution, and adjust the input value of the vibration system according to the output parameters.

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