Method for inverting shear modulus and permeability coefficient of seabed based on wave-induced pore pressure response

Abstract

The invention relates to a method for inverting the shear modulus and permeability coefficient of a seabed based on wave-induced pore pressure response, which comprises the following steps of: firstly, constructing a three-dimensional solution model of nearly saturated seabed soil with limited thickness by taking the pore pressure response induced by the wave as an entry point, and acquiring actually measured vertical wave-induced pore pressure data by utilizing a pressure guide type pore water pressure measuring device; and searching a theoretical pore pressure curve with the highest matching degree with the actually measured pore pressure through an improved particle swarm algorithm, and outputting a seabed shear modulus and a permeability coefficient corresponding to the pore pressure curve. The invention aims to utilize a brand-new penetration point to realize low-cost and wide-applicability inversion measurement of the shear modulus and the permeability coefficient of the ocean soil, and provides a new thought for solving the problems of high cost, low efficiency and complicated operation of obtaining important parameters of the ocean soil at present.

Description

Technical Field

[0001] This invention relates to a method for inverting seabed shear modulus and permeability coefficient based on wave-induced pore pressure response, belonging to the field of marine geotechnical technology. Background Technology

[0002] In the field of marine engineering, the mechanical properties and seepage behavior of porous seabeds are key factors determining the long-term stability of marine structures (such as breakwaters, buried pipelines, and offshore platforms). The additional pore water pressure in the seabed under wave loads significantly impacts the stability of these structures. Shear modulus and permeability coefficient, as core parameters for assessing seabed stability, are crucial for the safe design of marine structures, directly affecting the evolution of pore water pressure, effective stress distribution, and liquefaction resistance under wave loads.

[0003] Therefore, when designing the foundation for offshore facilities, it is necessary to fully consider the measurement of permeability coefficient and shear modulus. The existing technology, "In-situ Soil Permeability Test Device and Method for Measuring Permeability Coefficient" (CN107014739A), proposes a method for indirectly measuring the permeability coefficient of in-situ soil through piezometric head. Although the permeability test device of this invention can measure the permeability coefficient of soil samples relatively stably, the sampling cost is high, and the sampling process causes significant disturbance to the soil, affecting the measurement results. The existing technology, "A Method and Device for Testing and Analyzing the Dynamic Shear Modulus of Marine Soil" (CN110672435A), provides a testing and analysis method for obtaining the dynamic shear modulus of marine soil. This method is based on the theoretical calculation of the dynamic shear modulus of soil using a vane shear apparatus with measured torque T and rotation angle θ. However, the above method has weak applicability to uneven soil layers and may exhibit large errors. The existing technology "A Penetration Detector for In-situ Soil Shear Modulus and Strength Weakening Test" (CN116335104A) proposes a device for measuring the in-situ soil shear modulus. This device uses a motor or hydraulic cylinder to control the speed at which T-bars are pressed into and pulled out of the soil, and measures the soil resistance to obtain the in-situ soil shear modulus. However, the penetration measurement of this device will cause a certain disturbance to the in-situ soil, and the acquisition of the shear modulus depends heavily on empirical formulas, which cannot ensure the measurement accuracy.

[0004] Therefore, a new method for measuring permeability coefficient and shear modulus is needed to address the problems of high cost and uncertain accuracy in existing marine soil parameter measurement technologies. Summary of the Invention

[0005] This invention provides a method for inverting seabed shear modulus and permeability coefficient based on wave-induced pore pressure response. It aims to achieve low-cost and widely applicable inversion measurement of marine soil shear modulus and permeability coefficient using a novel approach, providing a new solution to the current problems of high cost, low efficiency, and cumbersome operation in obtaining important marine soil parameters.

[0006] The technical solution adopted by this invention to solve its technical problem is:

[0007] A method for inverting seabed shear modulus and permeability coefficient based on wave-induced pore pressure response includes the following steps:

[0008] Step S1: Make basic assumptions about the soil properties in the seabed and construct a numerical solution model for wave-induced pore water pressure.

[0009] Step S2: By controlling the variables of the numerical solution model, obtain the theoretical values ​​of wave-induced pore water pressure of a finite-thickness seabed under different wave conditions, soil conditions and site parameters.

[0010] Step S3: Based on the theoretical numerical values ​​of wave-induced pore water pressure obtained in step S2, perform preliminary verification of the numerical solution model of step S1.

[0011] Step S4: Using a pressure-guided pore water pressure measuring device, several pore pressure measuring points are arranged at different depths on a seabed of finite thickness. By measuring the wave-induced pore water pressure under different wave conditions, several measured values ​​of wave-induced pore water pressure are obtained as a validation set. The measured values ​​of wave-induced pore water pressure do not include shear modulus and permeability coefficient.

[0012] Step S5: Using the measured values ​​of wave-induced pore water pressure obtained in step S4 as the validation set, substitute them into the numerical solution model after the preliminary validation in step S3 to calculate the wave-induced pore pressure response under different shear modulus and permeability coefficient settings.

[0013] Step S6: Based on the wave-induced pore pressure response obtained in step S5, the optimal combination of shear modulus and permeability coefficient under different wave conditions is obtained using the particle swarm optimization algorithm. The values ​​are then substituted into the numerical solution model after preliminary verification in step S3 to plot the theoretical pore pressure response curve as the seabed depth changes. The curve is then compared with the measured wave-induced pore water pressure to verify the inversion effect.

[0014] Furthermore, in step S1, the basic assumptions made about the soil properties in the seabed include assuming a soil matrix in a sedimentary seabed located in front of a breakwater, which is subjected to a short-peak wave system generated by obliquely incident and reflected waves.

[0015] Meanwhile, it is assumed that the seabed is porous, homogeneous, and hydraulically isotropic; the soil skeleton and pore fluids are compressible; there is phase lag in pore pressure in very fine sediments, but the soil skeleton follows Hooke's law; and the flow in porous media is controlled by Darcy's law.

[0016] Furthermore, the constructed numerical solution model for wave-induced pore pressure includes governing equations, namely, a combination of Biot's three-dimensional consolidation theory and Verruijt's storage equations:

[0017]

[0018] In formula (1), the crest of the composite wave is defined as propagating along the positive x-direction parallel to the wall, the y-direction is perpendicular to the wall, the z-direction is the positive direction measured upwards from the water-soil interface, P is the wave-induced pore water pressure, and k x Let k be the permeability coefficient in the x-direction. y Let k be the permeability coefficient in the y-direction. z ε is the permeability coefficient in the z-direction, n′ is the soil porosity, ε is the volumetric strain, t is the time, and β is the compressibility of the pore fluid.

[0019] The equilibrium equations relating soil displacement, volumetric strain, and pore pressure are as follows:

[0020]

[0021]

[0022] In formulas (2)-(6), G is the soil shear modulus, ξ is the soil displacement in the x-direction, ζ is the soil displacement in the y-direction, χ is the soil displacement in the z-direction, K' is the apparent bulk modulus of pore water, and K w P is the true bulk modulus of water. wo S represents the absolute pore water pressure. r Soil saturation;

[0023] The relationship between effective stress in soil and soil displacement and volumetric strain includes:

[0024]

[0025] In formulas (7)-(12), σ' x σ' is the effective normal stress component in the x-direction. y Let σ′ be the effective normal stress component in the y-direction. z τ′ is the effective normal stress component in the z-direction. xy Let τ′ be the shear stress in the y-direction on a plane perpendicular to the x-axis. xz Let τ′ be the shear stress in the z-direction on a plane perpendicular to the x-axis. yx Let τ′ be the shear stress in the x-direction on a plane perpendicular to the y-axis. yz Let τ′ be the shear stress in the z-direction on a plane perpendicular to the y-axis. zx Let τ′ be the shear stress in the x-direction on a plane perpendicular to the z-axis. zy This represents the shear stress in the y-direction on a plane perpendicular to the z-axis.

[0026] For homogeneous soil matrices, the boundary conditions that must be met at the rigid, impermeable bottom and the mudline include:

[0027] Assuming the displacement at the seabed bottom at z = -d is zero, and d is the seabed thickness, then...

[0028] ξ,ζ,χ=0 (13),

[0029] If there is no vertical flow across the horizontal boundary, and z = -d, then...

[0030]

[0031] At the interface between water and soil, the effective normal stress and shear stress in the vertical direction are zero, i.e., z = 0.

[0032] σ z =τ yz =τ xz =0 (15),

[0033] When z = 0, the formula for calculating the pore water pressure at the boundary of the upper soil layer is:

[0034] P=p0cos(nay)cos(max-ωt) (16)

[0035] In formula (16), P0 is the amplitude factor, ω is the angular frequency, a is the wave number, and a = 2π / L. The relationship between the amplitude factor and the first-order wave pressure of the segment crest theory is as follows:

[0036]

[0037] In formula (17), γ w H is the unit weight of pore water, H is the height of the short peak wave, and h is the water depth.

[0038] Based on formulas (1)-(17), the final calculation formulas for soil displacement and wave-induced pore water pressure are obtained, namely...

[0039]

[0040]

[0041] In formulas (18)-(21), ι is a complex variable, and C1-C6 are the result coefficients, respectively;

[0042] Furthermore, in steps S2-S3, based on the numerical solution model constructed in step S1, under the condition that other variables remain unchanged, several different orders of magnitude of shear modulus and permeability coefficient are selected to study the influence of the two variables, shear modulus and permeability coefficient, on the pore water pressure distribution in the vertical direction of the porous seabed, and to preliminarily verify the numerical solution model of step S1.

[0043] Furthermore, in step S4, in the wave-induced pore pressure response experiment of a finite-thickness seabed using a pressure-conducting pore water pressure measuring device, the effective wave height and the corresponding wave period are calculated using statistical methods, and the measured values ​​of wave-induced pore water pressure at different measuring points are obtained under the working condition.

[0044] Furthermore, in step S5, the two parameters of shear modulus and permeability coefficient are left blank, and the vertical wave-induced pore pressure response under different combinations is continuously calculated within the range that conforms to the actual working conditions.

[0045] Furthermore, the feature is that: within the range that conforms to actual working conditions, that is, the reasonable range of variation of the shear modulus and permeability coefficient of the seabed is obtained based on existing seabed data; when using the particle swarm optimization algorithm in step S6, the upper and lower limits of the actual shear modulus and permeability coefficient are input; at the beginning of the search, a global search is performed; and after the number of searches reaches a preset value, a local search is performed.

[0046] By employing the above technical solutions, the present invention has the following beneficial effects compared to the prior art:

[0047] 1. The method for inverting seabed shear modulus and permeability coefficient based on wave-induced pore pressure response provided by this invention obtains pore pressure data at in-situ measuring points by arranging pore pressure gauges, and then inverts the permeability coefficient from the pore pressure, which greatly reduces the disturbance to the original soil and solves the problem of data monitoring at the same measuring point at different times.

[0048] 2. The method for inverting seabed shear modulus and permeability coefficient based on wave-induced pore pressure response provided by this invention inverts marine soil parameters through the pore pressure response of measuring points. This method is applicable to different types of soil layers, solves the problem of inaccurate measurement of dynamic shear modulus of heterogeneous soil layers, and has a low measurement cost, making it more economical to obtain the dynamic shear modulus of marine soil.

[0049] 3. The method for inverting seabed shear modulus and permeability coefficient based on wave-induced pore pressure response provided by this invention uses easily measurable pore pressure data to invert seabed shear modulus and visualizes the inversion results, which not only reduces measurement costs but also improves measurement accuracy. Attached Figure Description

[0050] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0051] Figure 1 This is a schematic diagram of an incident breakwater with a wave inclination angle of θ and its reflected wave provided by the present invention.

[0052] Figure 2In the preferred embodiment provided by this invention, the vertical distribution of |p| / P0 with z / d is related to the soil permeability coefficient k. z Relationship;

[0053] Figure 3 This is the relationship between the vertical distribution of |p| / P0 with z / d and the soil shear modulus G in the preferred embodiment provided by the present invention;

[0054] Figure 4 This is a diagram showing the arrangement of experimental measurement points in a preferred embodiment of the present invention;

[0055] Figure 5 This is a schematic diagram illustrating the change of wavefront elevation over time using the zero-point crossing method in a preferred embodiment of the present invention.

[0056] Figure 6 This is a schematic diagram showing the change of pore water pressure over time at four vertical measuring points in a preferred embodiment of the present invention.

[0057] Figure 7 This is a flowchart of the particle swarm algorithm in a preferred embodiment of the present invention;

[0058] Figure 8 This is a comparison diagram of theoretical pore pressure curves and measured pore pressure points under different wave conditions in a preferred embodiment of the present invention. Detailed Implementation

[0059] The present invention will now be described in further detail with reference to the accompanying drawings. In the description of this application, it should be understood that the terms "left side," "right side," "upper part," "lower part," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. "First," "second," etc., do not indicate the importance of the components, and therefore should not be construed as a limitation of the present invention. The specific dimensions used in this embodiment are only for illustrating the technical solution and do not limit the scope of protection of the present invention.

[0060] As described in the background section, existing methods for measuring shear modulus and permeability coefficient largely rely on simplified theoretical models or laboratory tests, making it difficult to accurately reflect the true mechanical behavior of undisturbed soil in complex marine environments, especially the dynamic response under the coupling effect of three-dimensional wave fields and finite-thickness soil. Furthermore, existing measurement methods still face significant challenges in practical applications. Traditional permeability coefficient measurements often rely on laboratory tests, requiring indirect analysis through sampling. However, the sampling process inevitably disturbs the undisturbed soil structure, leading to parameter distortion, and the high cost of repeated sampling is difficult to meet the economic requirements of large-scale engineering projects. For obtaining shear modulus, the conventional vane shear tester method, based on the assumption of homogeneity and isotropy, can deduce dynamic parameters through torque and rotation angle. However, under the conditions of widely existing layered or heterogeneous soil layers in marine environments, the simplified assumptions of its theoretical model contradict the complexity of actual soil behavior, significantly increasing the measurement error. Furthermore, while penetration testing technology correlates penetration resistance with shear modulus through empirical formulas, the universality of empirical models is severely limited due to the nonlinear characteristics of soil constitutive relations and the diversity of stress paths under dynamic loads. In particular, measurement accuracy is difficult to guarantee under wave cyclic loading. This limitation has become a major bottleneck restricting the safety design and disaster prevention of marine engineering.

[0061] To address this, this invention proposes a method for inverting seabed shear modulus and permeability coefficient based on wave-induced pore pressure response. Its greatest innovation lies in establishing an inversion model for marine soil shear modulus and permeability coefficient by taking wave-induced pore pressure response as the starting point. This innovative design, cross-validated by theoretical and measured pore pressure solutions, demonstrates that the inversion model can accurately invert the shear modulus and permeability coefficient of marine soil, providing a new solution to the current problems of high cost and low accuracy in obtaining shear modulus and permeability coefficient.

[0062] Before describing the specific methods of this application, it is necessary to clarify that to successfully reverse the method provided in this application, an existing pressure-conducting pore water pressure measuring device (publication number CN118483291B) needs to be used during implementation. This device was developed by the research group of the inventors of this application. Compared with traditional pore pressure measuring instruments, this device has a simple structure, consisting of a measuring point setting platform and a data processing platform. Only the measuring point setting platform and the pressure-conducting pipe need to be buried in the sand of the seabed. The data processing platform (the part for data measurement, processing, and conversion) is set up independently outside the seabed environment, resulting in low replacement costs. The measuring point setting platform can freely adjust the position of the measuring points according to needs. By reasonably setting the position and number of measuring points, the pore water pressure distribution in the target area of ​​the seabed soil can be monitored in an array form, obtaining measuring point information in real time and accurately. This device not only reduces experimental costs but also improves experimental accuracy. Through the above-mentioned pressure-conducting pore water pressure measuring device, experimental values ​​of pore pressure response used as comparative data under wave-induced conditions can be obtained at low cost and with high accuracy.

[0063] The following section details the method provided in this application for inverting seabed shear modulus and permeability coefficient based on wave-induced pore pressure response, including the following steps:

[0064] Step S1 involves making basic assumptions about the soil properties in the seabed and constructing a numerical solution model for wave-induced pore water pressure. Currently, many different theories of wave-induced pore pressure have been proposed based on various assumptions about the physical properties of the seabed and pore fluids. This study considers a soil matrix in a sedimentary seabed located in front of a breakwater, which is subjected to a short-peak wave system generated by obliquely incident and reflected waves. It is assumed that the peaks of the composite waves propagate along the positive x-direction parallel to the wall; the y-direction is perpendicular to the wall; and the z-direction is the positive direction measured upwards from the water-soil interface (mudline), used to study the soil response caused by waves in a porous seabed. For wave propagation and the calculation of wave pressure at the "seabed," the measured value of z is zero at the still water level (SWL). The seabed thickness is d, and the water depth is h. This study mainly discusses wave reflection in breakwaters with sloping sides. Figure 1 The diagram shows an incident breakwater (1a) with a wave inclination angle of θ and its reflected wave (1b) in a Cartesian coordinate system.

[0065] In addition, some basic assumptions about soil properties are necessary: ​​a soil matrix in a sedimentary seabed located in front of a breakwater is assumed to be subjected to a short-peak wave system generated by obliquely incident and reflected waves; the seabed is assumed to be porous, homogeneous, and hydraulically isotropic; the soil skeleton and pore fluids are compressible; pore pressure exhibits phase lag in very fine sediments, but the soil skeleton obeys Hooke's law; and flow in porous media is governed by Darcy's law.

[0066] Based on these assumptions, the governing equations describing wave-induced soil response under anisotropic and unsaturated conditions include a combination of Biot's three-dimensional consolidation theory and Verruijt's storage equations:

[0067]

[0068] In formula (1), the crest of the composite wave is defined as propagating along the positive x-direction parallel to the wall, the y-direction is perpendicular to the wall, the z-direction is the positive direction measured upwards from the water-soil interface, P is the wave-induced pore water pressure, and k x Let k be the permeability coefficient in the x-direction. y Let k be the permeability coefficient in the y-direction. z ε is the permeability coefficient in the z-direction, n′ is the soil porosity, ε is the volumetric strain, t is the time, and β is the compressibility of the pore fluid.

[0069] The equilibrium equations relating soil displacement, volumetric strain, and pore pressure are as follows:

[0070]

[0071] In formulas (2)-(6), G is the soil shear modulus, ξ is the soil displacement in the x-direction, ζ is the soil displacement in the y-direction, χ is the soil displacement in the z-direction, K' is the apparent bulk modulus of pore water, and K w P is the true bulk modulus of water. wo S represents the absolute pore water pressure. r Soil saturation;

[0072] The concept of effective stress in soil and Hooke's law derive the relationship between effective stress and soil displacement and volumetric strain, including:

[0073]

[0074]

[0075] In formulas (7)-(12), σ' x σ' is the effective normal stress component in the x-direction. y Let σ′ be the effective normal stress component in the y-direction. z τ′ is the effective normal stress component in the z-direction. xy Let τ′ be the shear stress in the y-direction on a plane perpendicular to the x-axis. xz Let τ′ be the shear stress in the z-direction on a plane perpendicular to the x-axis. yx Let τ′ be the shear stress in the x-direction on a plane perpendicular to the y-axis. yz Let τ′ be the shear stress in the z-direction on a plane perpendicular to the y-axis. zxLet τ′ be the shear stress in the x-direction on a plane perpendicular to the z-axis. zy This represents the shear stress in the y-direction on a plane perpendicular to the z-axis.

[0076] For homogeneous soil matrices, a mathematical expression for the soil response under short-peak wave action can be derived, but it requires satisfying certain appropriate boundary conditions at the rigid, impermeable bottom and the mudline. For a finite porous bed of thickness d located above an impermeable rigid bottom, the following boundary conditions apply:

[0077] (1) Assuming the displacement at the bottom of the seabed at z = -d is zero, and d is the thickness of the seabed, then

[0078] ξ,ζ,χ=0 (13)

[0079] (2) If there is no vertical flow across the horizontal boundary, then z = -d.

[0080]

[0081] (3) At the interface between water and soil, the effective normal stress and shear stress in the vertical direction are zero, i.e., z = 0.

[0082]

[0083] (4) When z = 0, the formula for calculating the pore water pressure at the boundary of the upper soil layer is:

[0084] P=p0cos(nay)cos(max-ωt)(16)

[0085] In formula (16), P0 is the amplitude factor, ω is the angular frequency, a is the wave number, and a = 2π / L;

[0086] (5) The relationship between the amplitude factor and the first-order wave pressure in the segment crest theory is as follows:

[0087]

[0088] In formula (17), γ w H is the unit weight of pore water, H is the height of the short peak wave, and h is the water depth.

[0089] Based on formulas (1)-(17), the soil displacement and pore water pressure under the incident and reflected waves are first calculated by decomposition, and then the final calculation formulas for soil displacement and wave-induced pore water pressure are obtained through the superposition principle, i.e.

[0090]

[0091]

[0092] In formulas (18)-(21), ι is a complex variable, and C1-C6 are the result coefficients. The result coefficients can be referred to the derivation results of Jeng, DS & Hsu, JRC (1996). Wave-induced soil response in a nearly saturated sea-bed of finite thickness. Geotechnique 46, No.3, 427-440.

[0093] Step S2: By controlling the variables of the numerical solution model, theoretical values ​​of wave-induced pore water pressure on a finite-thickness seabed under simulated wave-induced conditions are obtained under different wave conditions, soil conditions, and site parameters. Step S3: The numerical solution model of Step S1 is preliminarily verified based on the theoretical values ​​of wave-induced pore water pressure obtained in Step S2.

[0094] Steps S2-S3 ultimately aim to verify the constructed numerical solution model to preliminarily confirm its feasibility and improve the accuracy of subsequent inversion results. Since this application mainly studies the theoretical numerical values ​​of wave-induced pore water pressure under finite-thickness seabed under different wave conditions, soil conditions, and experimental conditions, this paper only discusses the variation and attenuation of wave-induced pore water pressure with respect to the vertical z-axis. There are various verification methods. This application adopts the method of controlling model variables and changing the soil permeability coefficient under constant wave conditions (wave height, wave period, incident wave angle), soil conditions (shear modulus, Poisson's ratio, porosity, saturation, seabed thickness, etc.) and water depth, and observing the variation of pore water pressure in the vertical direction. To eliminate the influence of dimensions, the vertical axis is z / d, where z is the depth below the seabed and d is the seabed thickness; the horizontal axis is |p| / P0, where |p| is the maximum instantaneous pore water pressure of the soil and P0 is calculated by formula (17). Based on this numerical model, four sets of shear modulus and permeability coefficients of different orders of magnitude were selected to study the effects of these two variables on the vertical pore water pressure distribution of the porous seabed, while ensuring that other variables remained constant. Figure 2 The soil permeability coefficient k can be observed in the middle. z Changes in magnitude have a significant impact on the distribution of vertical pore pressure, relative to the permeability coefficient. Figure 3 As shown, the shear modulus has little effect on the distribution of vertical pore pressure.

[0095] Next, a wave-induced pore pressure response experiment of a finite-thickness seabed is conducted, namely step S4. Several pore pressure measurement points are arranged at different depths of the finite-thickness seabed using a pressure-conducting pore water pressure measurement device. By measuring the wave-induced pore water pressure under different wave conditions, several measured values ​​of wave-induced pore water pressure are obtained as a validation set. The measured values ​​of wave-induced pore water pressure do not include shear modulus and permeability coefficient.

[0096] The research background provided in this application is breakwaters, especially sloping breakwaters, whose main function is to reduce the impact of waves on the breakwater, maintain the stability of the port water level, and ensure the safe berthing of ships. The instability of sloping breakwaters due to soil liquefaction under wave action has always been a challenging engineering problem. Therefore, studying the dynamic characteristics of the seabed soil surrounding sloping breakwaters under wave action is of great significance for evaluating the stability of sloping breakwaters. In step S4, with the sloping breakwater in place, multiple pore pressure measuring points are arranged at different depths in the finite-thickness seabed using a pressure-conducting pore water pressure measuring device. By measuring the wave-induced pore water pressure under different wave conditions, the vertical pore pressure response of the seabed soil under different conditions is studied, and the measured pore pressure values ​​are further compared and verified with the theoretical values ​​of the numerical model.

[0097] Specifically, the first step is to determine the wave generator and wave height meter. The wave generator is an essential piece of equipment for wave physics model experiments. It uses a wave generator to drive a wave-generating plate, causing the water in the tank to move and generate the waves required for the experiment, based on given input wave elements. For measuring wave height and wave period, this experiment uses a capacitive wave height meter. A capacitive wave height meter typically consists of a capacitor wire, a support frame, and measurement conversion circuit components. Since the physical characteristics, diameter, and insulation thickness of the wire used in the selected wave height meter are fixed, the capacitance is only proportional to the length of the sensor in the water. Changes in water level cause changes in capacitance, which in turn cause corresponding voltage changes. By establishing the relationship between water level and voltage, and recording the voltage signal, the water level change can be deduced, ultimately obtaining the process of water surface change over time during wave motion. The wave height meter in this experiment uses a sampling frequency of 50Hz.

[0098] After selecting the appropriate equipment, a pressure-conducting pore water pressure measuring device is used. Figure 4As shown, this experiment used quartz sand with a median particle size of 0.18 mm to arrange the seabed in the experimental tank. The seabed thickness was d = 0.3 m, with a soil porosity of n' = 0.42 and a Poisson's ratio of μ = 0.33. The experimental water depth was h = 0.292 m. To simulate more realistic ocean wave conditions, a breakwater with an inclination angle of 1:1.5 was installed in the tank. Wave height meters were installed at distances of 0.1 m, 0.7 m, 1.3 m, and 1.9 m from the toe of the breakwater. Using a pressure-conducting pore water pressure measuring device, four pressure-conducting pipes were installed at the bottom of the seabed where each wave height meter was located as pore pressure measuring points. The four measuring points were located at distances of 0.02 m, 0.08 m, 0.14 m, and 0.20 m below the seabed, respectively. The wave height of the wave generator varies from H to 0.10 m, and the wave period varies from 1.0 s to 1.3 s. This study mainly discusses six wave condition combinations under the conditions of H = 0.06 m, 0.08 m, 0.10 m, and T = 1.0 s and 1.3 s.

[0099] The pressure-conducting pore water pressure measuring device also includes a data processing platform. During data processing, wave parameters are first acquired, and the wave surface elevation data recorded by the wave height meter as a function of time is exported to the computer system. Data preprocessing is then performed to filter out recording wavebands that are less affected by interference. Figure 5 The wave surface elevation over a period of time was statistically determined using the zero-point crossing method. In order to make the statistical wave height more accurately reflect the measured situation, H1 / 3, i.e., the effective wave height and the corresponding wave period T, was calculated using statistical methods.

[0100] Next, the wave-induced pore water pressure data is processed. Due to the unique structure and multiple signal conversions of the pore water pressure gauge, the measured data often deviates from the actual or expected values. Therefore, to ensure the accuracy and reliability of the pore water pressure gauge's measurement performance before and after the experiment, calibration coefficients for each pore pressure measurement point channel need to be obtained through calibration experiments. Multiplying the signal value of different pore pressure measurement point channels by the corresponding calibration coefficients yields the actual pore pressure values ​​at different measurement points. In this embodiment, pore pressure response waveforms for four different measurement point channels are obtained. Figure 6 The amplitude of pore water pressure variation in the vertical direction over time can be observed. To standardize the data format, the effective wave height method, similar to the wave surface elevation method mentioned above, is used. This involves statistically analyzing the pore pressure using the zero-point method and sorting it from largest to smallest. The first third of the largest instantaneous pore water pressures are then averaged to obtain the effective instantaneous pore water pressure at different measuring points.

[0101] Because the initial pore pressure response is relatively unstable, and prolonged sampling time can lead to seabed liquefaction under wave-induced effects, only a portion of the more stable pore pressure response values ​​are extracted. Taking four pore pressure measurement points 1.9m from the breakwater toe as an example, the experimental data are shown in Table 1 below:

[0102] Table 1

[0103] Test H / s P1 / k P2 / k P3 / k P4 / k 1 0. 0 0.12 0.08 90.05 90.04 2 0. 3 0.16 90.13 50.09 30.07 3 0. 0 0.14 00.10 0.06 80.04 4 0. 3 0.23 70.17 70.12 0.09 5 0. 0 0.16 30.12 00.07 70.05 6 0. 3 0.27 80.21 40.14 40.11

[0104] As can be observed from Table 1, under the condition that other conditions remain unchanged, the pore water pressure induced by waves increases continuously below the shallow seabed as the wave height and wave period increase, and decreases continuously with the increase of vertical depth.

[0105] The three-dimensional numerical model of the finite-thickness seabed established above allows for easy calculation of the vertical distribution of wave-induced pore pressure below the seabed. Furthermore, measured wave-induced pore pressure data under different wave conditions were obtained using a pressure-conducting pore water pressure measurement device. Changes in wave-induced pore water pressure directly reflect soil properties and liquefaction status, serving as a good criterion for evaluating soil property parameters. Therefore, wave-induced pore water pressure can be used as a starting point. The shear modulus and permeability coefficient parameters in the theoretical numerical model can be left undefined, and the vertical wave-induced pore pressure response under different combinations can be calculated within a realistic range. Continuing with step S5, the measured wave-induced pore water pressure values ​​obtained in step S4 are used as a validation set and substituted into the numerical model after preliminary validation in step S3 to calculate the wave-induced pore pressure response under different shear modulus and permeability coefficient settings. The closer the theoretical combination of shear modulus and permeability coefficient is to the actual soil parameters, the closer the theoretical and measured values ​​of wave-induced pore water pressure are. Therefore, based on the least squares method, the objective function is set to minimize the difference between the theoretical pore pressure and the measured pore pressure.

[0106] Because the shear modulus and permeability coefficient vary considerably, traditional search algorithms cannot achieve efficient search calculations. Therefore, it is necessary to introduce intelligent optimization algorithms to solve this complex problem. Given the complexity of this problem and its dynamic nature, an algorithm based on intuition or experience is needed to provide a feasible solution for minimizing the objective function under these constraints, within acceptable computational time and space requirements. Therefore, in step S6 of this application, based on the wave-induced pore pressure response obtained in step S5, the optimal combination of shear modulus and permeability coefficient under different wave conditions is obtained using a particle swarm optimization algorithm.

[0107] The flowchart for the particle swarm optimization algorithm in this step is as follows: Figure 7 As shown in the diagram, in a brief introduction, we first define the initialization parameters: number of particles x = 200; individual learning factor c1 = 2; social learning factor c2 = 2; velocity inertia weight w = 0.9; variable n = 2; and the velocity v of the i-th particle at the d-th iteration. i d The position x of the i-th particle at the d-th iteration. i dThe fitness, i.e., the objective value, is f(x) at position x; the best position pbest reached by the i-th particle up to the d-th iteration. i d The best position gbest that all particles have traversed up to the d-th iteration. d The core formula is as follows:

[0108]

[0109] In formula (22), r1 and r2 are random numbers in the range [0,1].

[0110] To address the problem requiring a solution, and to reduce the computational load of the model and improve search efficiency, two approaches are taken. First, based on existing soil data, a reasonable range of variation for soil shear modulus and permeability coefficient can be obtained. By inputting the upper and lower limits of the actual site shear modulus and permeability coefficient, the computational range can be narrowed. Second, a global search strategy is preferred at the beginning of the search, but after a certain number of searches, it can be switched to a local search strategy to obtain the optimal solution. Therefore, certain improvements are made to the particle swarm optimization (PSO) parameters. Adaptive inertia weights are used to optimize the PSO algorithm, enabling the model to dynamically adjust the inertia weights during the search process, thereby avoiding getting trapped in local optima while accelerating the convergence speed.

[0111] Right now

[0112]

[0113] In formula (23), ω min It is the pre-given minimum inertia coefficient, ω max It is the pre-defined maximum inertia coefficient; f average d =∑f(x) i d f / n, which is the average fitness of all particles in the d-th iteration; max d =max{f(x1) d ),f(x2 d f(x) n d )}, which is the maximum fitness of all particles in the d-th iteration.

[0114] Based on the numerical model of the finite thickness seabed and the measured pore pressure response data, the optimal combination values ​​of shear modulus and permeability coefficient under six different wave conditions were obtained through the improved particle swarm optimization search described above, as shown in Table 2.

[0115] Table 2

[0116] Test H / m T / s G / 10^6N / mkz / 10^-4cm / serror 1 0.06 1.0 1.760 1.390 0.043 2 0.06 1.3 1.792 1.175 0.054 3 0.08 1.0 1.766 1.215 0.015 4 0.08 1.3 1.783 1.051 0.044 5 0.10 1.0 1.761 1.390 0.053 6 0.10 1.3 1.765 0.957 0.075

[0117] As can be seen from Table 2, the shear modulus G changes relatively stably under different wave conditions, and the permeability coefficient varies from 0.957×10-4cm / s to 1.390×10-4cm / s, which is within a reasonable range, and the maximum norm error is only 0.075.

[0118] Through six sets of comparative experiments under different wave conditions, the optimal combination of shear modulus and permeability coefficient obtained from the above table was substituted into the numerical solution model after preliminary verification in step S3 to plot the theoretical pore pressure response curve under the change of seabed depth, and compared with the measured values ​​of wave-induced pore water pressure to verify the inversion effect.

[0119] In a preferred embodiment, such as Figure 8 As shown, 8a-8b represent wave condition combinations under the conditions of H=0.06m and T=1.0s and 1.3s, 8c-8d represent wave condition combinations under the conditions of H=0.08m and T=1.0s and 1.3s, and 8e-8f represent wave condition combinations under the conditions of H=0.10m and T=1.0s and 1.3s. Under the six different wave condition conditions, the searched shear modulus remains almost unchanged with the change of wave condition conditions, while the permeability coefficient changes within a reasonable range. Moreover, the measured pore pressure values ​​are basically on the theoretical pore pressure curve. Therefore, the model error and visualization can verify that the inversion model has considerable effect and high accuracy, and can accurately invert the seabed shear modulus and permeability coefficient under real ocean conditions.

[0120] In summary, the method for inverting seabed shear modulus and permeability coefficient based on wave-induced pore pressure response provided in this application constructs a three-dimensional solution model for near-saturated seabed soil of finite thickness, using the wave-induced pore pressure response as the starting point. Within a reasonable range, the shear modulus and permeability coefficient of the soil are inverted by inputting specified parameters of the research measurement points using the soil's pore pressure response. An improved particle swarm optimization algorithm is used to search for the theoretical pore pressure curve with the highest matching degree with the measured pore pressure, and the seabed shear modulus and permeability coefficient corresponding to this pore pressure curve are output. Compared with existing soil sample experimental measurements, this method has the advantages of low cost, strong reproducibility, and wide applicability. The inversion effect is supported by experimental data, demonstrating scientific validity, rationality, and accuracy.

[0121] Those skilled in the art will understand that, unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains. It should also be understood that terms such as those defined in general dictionaries should be understood to have the meaning consistent with their meaning in the context of the prior art, and should not be interpreted in an idealized or overly formal sense unless defined as herein.

[0122] The meaning of "and / or" as used in this application includes situations where each exists alone or both exist simultaneously.

[0123] The term "connection" as used in this application can mean a direct connection between components or an indirect connection between components through other components.

[0124] Based on the above-described preferred embodiments of the present invention, and through the foregoing description, those skilled in the art can make various changes and modifications without departing from the inventive concept. The technical scope of this invention is not limited to the contents of the specification, but must be determined according to the scope of the claims.

Claims

1. A method for inverting seabed shear modulus and permeability coefficient based on wave-induced pore pressure response, characterized in that: Includes the following steps: Step S1: Make basic assumptions about the soil properties in the seabed and construct a numerical solution model for wave-induced pore water pressure. Step S2: By controlling the variables of the numerical solution model, obtain the theoretical values ​​of wave-induced pore water pressure of a finite-thickness seabed under different wave conditions, soil conditions and site parameters. Step S3: Based on the theoretical numerical values ​​of wave-induced pore water pressure obtained in step S2, perform preliminary verification of the numerical solution model of step S1. Step S4: Using a pressure-guided pore water pressure measuring device, several pore pressure measuring points are arranged at different depths on a seabed of finite thickness. By measuring the wave-induced pore water pressure under different wave conditions, several measured values ​​of wave-induced pore water pressure are obtained as a validation set. The measured values ​​of wave-induced pore water pressure do not include shear modulus and permeability coefficient. Step S5: Using the measured values ​​of wave-induced pore water pressure obtained in step S4 as the validation set, substitute them into the numerical solution model after the preliminary validation in step S3 to calculate the wave-induced pore pressure response under different shear modulus and permeability coefficient settings. Step S6: Based on the wave-induced pore pressure response obtained in step S5, the optimal combination of shear modulus and permeability coefficient under different wave conditions is obtained using the particle swarm optimization algorithm. The values ​​are then substituted into the numerical solution model initially verified in step S3 to plot the theoretical pore pressure response curve as the seabed depth changes. The curve is then compared with the measured wave-induced pore water pressure to verify the inversion effect.

2. The method for inverting seabed shear modulus and permeability coefficient based on wave-induced pore pressure response according to claim 1, characterized in that: In step S1, the basic assumptions made about the soil properties in the seabed include assuming a soil matrix in a sedimentary seabed located in front of a breakwater, which is subjected to a short-peak wave system generated by obliquely incident and reflected waves. Meanwhile, it is assumed that the seabed is porous, homogeneous, and hydraulically isotropic; the soil skeleton and pore fluids are compressible; there is phase lag in pore pressure in very fine sediments, but the soil skeleton follows Hooke's law; and the flow in porous media is controlled by Darcy's law.

3. The method for inverting seabed shear modulus and permeability coefficient based on wave-induced pore pressure response according to claim 1, characterized in that: The constructed numerical solution model for wave-induced pore pressure includes governing equations, namely, a combination of Biot's three-dimensional consolidation theory and Verruijt's storage equations: In formula (1), the crest of the composite wave is defined as propagating along the positive x-direction parallel to the wall, the y-direction is perpendicular to the wall, the z-direction is the positive direction measured upwards from the water-soil interface, P is the wave-induced pore water pressure, and k x Let k be the permeability coefficient in the x-direction. y Let k be the permeability coefficient in the y-direction. z ε is the permeability coefficient in the z-direction, n′ is the soil porosity, ε is the volumetric strain, t is the time, and β is the compressibility of the pore fluid. The equilibrium equations relating soil displacement, volumetric strain, and pore pressure are as follows: In formulas (2)-(6), G is the soil shear modulus, ξ is the soil displacement in the x-direction, ζ is the soil displacement in the y-direction, χ is the soil displacement in the z-direction, K' is the apparent bulk modulus of pore water, and K w P is the true bulk modulus of water. wo S represents the absolute pore water pressure. r Soil saturation; The relationship between effective stress in soil and soil displacement and volumetric strain includes: In formulas (7)-(12), σ' x σ' is the effective normal stress component in the x-direction. y σ' is the effective normal stress component in the y-direction. z τ′ is the effective normal stress component in the z-direction. xy Let τ′ be the shear stress in the y-direction on a plane perpendicular to the x-axis. xz Let τ′ be the shear stress in the z-direction on a plane perpendicular to the x-axis. yx Let τ′ be the shear stress in the x-direction on a plane perpendicular to the y-axis. yz Let τ′ be the shear stress in the z-direction on a plane perpendicular to the y-axis. zx Let τ′ be the shear stress in the x-direction on a plane perpendicular to the z-axis. zy This represents the shear stress in the y-direction on a plane perpendicular to the z-axis. For homogeneous soil matrices, the boundary conditions that must be met at the rigid, impermeable bottom and the mudline include: Assuming the displacement at the seabed bottom at z = -d is zero, and d is the seabed thickness, then... ξ,ζ,χ=0 (13) If there is no vertical flow across the horizontal boundary, and z = -d, then... At the interface between water and soil, the effective normal stress and shear stress in the vertical direction are zero, i.e., z = 0. s z ′=τ yz ′=τ xz ′=0 (15) When z = 0, the formula for calculating the pore water pressure at the boundary of the upper soil layer is: P=p0cos(nay)cos(max-ωt) (16) In formula (16), P0 is the amplitude factor, ω is the angular frequency, a is the wave number, and a = 2π / L. The relationship between the amplitude factor and the first-order wave pressure in the wave crest theory is as follows: In formula (17), γ w H is the unit weight of pore water, H is the height of the short peak wave, and h is the water depth. Based on formulas (1)-(17), the final calculation formulas for soil displacement and wave-induced pore water pressure are obtained, namely... In formulas (18)-(21), ι is a complex variable, and C1-C6 are the result coefficients.

4. The method for inverting seabed shear modulus and permeability coefficient based on wave-induced pore pressure response according to claim 1, characterized in that: In steps S2-S3, based on the numerical solution model constructed in step S1, under the condition that other variables remain unchanged, several different orders of magnitude of shear modulus and permeability coefficient are selected to study the influence of the two variables, shear modulus and permeability coefficient, on the pore water pressure distribution in the vertical direction of the porous seabed, and to preliminarily verify the numerical solution model of step S1.

5. The method for inverting seabed shear modulus and permeability coefficient based on wave-induced pore pressure response according to claim 1, characterized in that: In step S4, in the wave-induced pore pressure response experiment of a finite-thickness seabed using a pressure-conducting pore water pressure measuring device, the effective wave height and the corresponding wave period are calculated using statistical methods, and the measured values ​​of wave-induced pore water pressure at different measuring points are obtained under the working conditions.

6. The method for inverting seabed shear modulus and permeability coefficient based on wave-induced pore pressure response according to claim 1, characterized in that: In step S5, the shear modulus and permeability coefficient are left blank, and the vertical wave-induced pore pressure response under different combinations is continuously calculated within the range that conforms to the actual working conditions.

7. The method for inverting seabed shear modulus and permeability coefficient based on wave-induced pore pressure response according to claim 6, characterized in that: Within the range that conforms to actual working conditions, that is, based on existing seabed data, the reasonable range of variation of seabed shear modulus and permeability coefficient is obtained. When using the particle swarm optimization algorithm in step S6, the upper and lower limits of the actual shear modulus and permeability coefficient are input. At the same time, a global search is performed at the beginning of the search, and a local search is performed after the number of searches reaches a preset value.

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