Hyperbolic sand large-diameter single pile design method based on static sounding

Abstract

The invention relates to a hyperbolic sand large-diameter single pile design method based on static sounding, which comprises the following steps: firstly, acquiring geometric parameters of a single pile, such as pile diameter, wall thickness, penetration depth and the like, and soil body information including effective weight and conical tip resistance; then calculating initial rigidity and ultimate bearing capacity of pile-soil interaction, and determining a rigidity attenuation coefficient and a bearing capacity adjustment coefficient according to a penetration-depth ratio; integrating the parameters to establish a hyperbolic p-y spring relationship at different depths so as to accurately simulate the nonlinear behavior of the soil body; then dispersing a single pile into beam units by applying a Timoshensincaro beam-spring model, and obtaining the lateral displacement distribution of a pile body and the bearing capacity of a soil body under an external load through numerical solution; and finally, a load-displacement curve at the mud line is generated by combining the load eccentric distance, and complete prediction of the displacement response of the pile body is achieved. Compared with the prior art, by combining the static sounding data with the hyperbolic model, the design precision and reliability of the large-diameter single pile in the sandy soil are improved.

Description

Technical Field

[0001] This invention relates to the field of marine engineering technology, and in particular to a design method for large-diameter monopiles in hyperbolic sand based on static cone penetration testing. Background Technology

[0002] To address the dual challenges of depleting traditional fossil fuels and the escalating global greenhouse effect, new renewable energy sources, primarily wind, solar, and hydrogen, have become a hot topic in the energy industry. Offshore wind power, in particular, is favored worldwide due to its abundant resources, lack of land occupation, and lower noise and visual pollution. Large-diameter monopile foundations, with their mature manufacturing processes and construction methods and low production costs, will remain the preferred foundation in the development of the offshore wind power industry for a long time to come.

[0003] Large-diameter monopile foundations have long been widely used in practical engineering. However, the pile-soil interaction mechanism of large-diameter monopile foundations in sandy soil is not clear. Current design work is mainly based on the Py model recommended by the American Petroleum Institute (API) (hereinafter referred to as the API Py model). In fact, this model originated from a field test of a small-diameter flexible pile. The geometric characteristics of the test pile are completely different from those of large-diameter monopile foundations, and the number of tests was insufficient. The API Py model method was initially applied to the design of small-diameter flexible piles for offshore oil and gas platforms. These foundations mainly bear the vertical loads transmitted by the superstructure, while large-diameter monopile foundations for offshore wind power mainly bear the horizontal loads brought by wind, waves, and currents. Existing studies have confirmed that directly applying this method to the design of large-diameter monopile foundations for offshore wind power will significantly overestimate the initial stiffness of the pile-soil interaction of large-diameter monopile foundations in sandy soil, posing potential risks to actual engineering projects.

[0004] The prior art CN120409089A relates to a numerical simulation method for the stiffness of a single pile in an offshore wind turbine considering long-term cycling and scouring. This method analyzes the stiffness and deformation characteristics of a single pile by establishing a three-dimensional finite element model. However, the numerical model of this method does not fully utilize the symmetry of the pile-soil structure for simplified calculations, and lacks a comprehensive consideration of the coupling effect between scouring depth and soil stiffness attenuation, making it difficult to accurately predict the cumulative deformation and dynamic response of the foundation under long-term cyclic loading.

[0005] Therefore, developing specialized design methods for pile-soil interaction mechanisms in large-diameter monopile foundations in sandy soil can improve design reliability, ensure the normal use of large-diameter monopile foundations, and has significant practical engineering implications. Summary of the Invention

[0006] The purpose of this invention is to provide a specialized design method for the pile-soil interaction mechanism of large-diameter monopile foundations in sandy soil, thereby improving design reliability and ensuring the normal use of large-diameter monopile foundations in actual engineering projects.

[0007] The objective of this invention can be achieved through the following technical solutions: This invention provides a design method for large-diameter monopiles in hyperbolic sandy soil based on static cone penetration testing, comprising the following steps: S1. Obtain the geometric information of a single pile in the actual project, including pile diameter, wall thickness, load eccentricity, penetration depth, and elastic modulus of the pile material. S2. Obtain soil information for the engineering site, including effective unit weight at different depths and cone tip resistance of static cone penetration tests; S3. Based on the soil information, calculate the initial stiffness of the pile-soil interaction; S4. Calculate the ultimate bearing capacity of pile-soil interaction; S5. Based on the ratio of the penetration depth to the pile diameter of a single pile, determine the stiffness attenuation coefficient and the ultimate bearing capacity adjustment coefficient of the py model. S6. By integrating the initial stiffness of pile-soil interaction, the ultimate bearing capacity of pile-soil interaction, the stiffness attenuation coefficient, and the ultimate bearing capacity adjustment coefficient, a hyperbolic py-spring relationship at different depths is obtained. S7. Using the Timoshenko beam-spring model, based on the wall thickness and elastic modulus of the pile material obtained in S1, the single pile is discretized into beam elements, and the py spring is used to calculate the lateral displacement of the pile body and the bearing capacity provided by the soil under external load. S8. Based on the pile lateral displacement distribution and soil bearing capacity results obtained in S7, and combined with the load eccentricity obtained in S1, calculate the load-displacement curve at the mudline, thereby realizing a complete predictive design of the pile displacement response.

[0008] Furthermore, in S1, the pile diameter is the cross-sectional diameter of a single pile; The wall thickness is the thickness of the hollow pile body wall; The load eccentricity distance is the vertical distance between the point of application of the horizontal load and the mudline. The penetration depth is the total depth to which the pile is driven into the soil.

[0009] Furthermore, in S2, the specific process of obtaining soil information at the engineering site includes: The cone tip resistance at different depths was obtained by in-situ static cone penetration testing. The cone tip resistance is used to reflect the compaction and strength characteristics of the site soil. The effective unit weight is derived by combining geotechnical test results or field measurement data; When using seismic static cone penetration testing, the small strain shear modulus is obtained simultaneously; otherwise, the small strain shear modulus is indirectly derived through the relationship between cone tip resistance and effective stress.

[0010] Furthermore, the specific process in S3 for calculating the initial stiffness of the pile-soil interaction based on the soil information includes: First, the small-strain shear modulus is derived from the cone tip resistance of static penetration test and the effective stress of the site soil. Then, the initial stiffness is calculated based on the derived small-strain shear modulus. When the small-strain shear modulus of the site soil is obtained directly through seismic static cone penetration testing, the initial stiffness of the pile-soil interaction is directly calculated based on the small-strain shear modulus.

[0011] Furthermore, in S4, the specific process for calculating the ultimate bearing capacity of pile-soil interaction includes: Using the cone tip resistance and effective stress value of the site soil obtained in S2, the ultimate bearing capacity parameters are derived through calibration relationships.

[0012] Furthermore, small strain shear modulus G max The calculation method is as follows: in, ρ T The total density of the site soil, in kg / m³ 3 ; V s The shear wave velocity of the site soil is expressed in m / s. q c This refers to the cone tip resistance, expressed in MPa. This represents the effective stress of the soil at the site, expressed in MPa. Ultimate bearing capacity p u The calculation method is as follows: in, D The diameter of the pile is in meters (m). q c This refers to the cone tip resistance, expressed in kPa. This represents the effective stress of the soil at the site, expressed in kPa.

[0013] Furthermore, in S5, the specific process of determining the stiffness attenuation coefficient and ultimate bearing capacity adjustment coefficient of the py model based on the ratio of the penetration depth to the pile diameter includes: The penetration depth ratio is calculated based on the penetration depth and pile diameter obtained in S1. Then, the cone tip resistance data obtained in S2 is combined with the normalized cone tip resistance data to obtain the normalized cone tip resistance. Finally, based on the correspondence between the penetration depth ratio and the normalized cone tip resistance, the corresponding stiffness attenuation coefficient and ultimate bearing capacity adjustment coefficient are determined by querying the preset curve.

[0014] Specifically, the penetration ratio is calculated based on the penetration depth and pile diameter obtained in S1. The penetration ratio is defined as the ratio of penetration depth to pile diameter. This parameter is used to quantify the relative embedment of the pile in the soil, thereby reflecting the constraint effect of the soil on the pile and the deformation characteristics of the pile. A higher penetration ratio usually indicates that the pile penetrates deeper into the soil, and the lateral constraint provided by the soil is stronger, which helps to reduce the flexible deformation of the pile. Then, the cone tip resistance data obtained in S2 is combined. The cone tip resistance is a soil strength index obtained through static cone penetration testing, which directly characterizes the shear strength and compaction state of the soil. However, the original cone tip resistance is greatly affected by the test depth and soil stratification. Therefore, normalization is performed, such as dividing the cone tip resistance by the effective overburden pressure or performing logarithmic standardization, to obtain the normalized cone tip resistance, so as to eliminate depth-related bias and make the data comparable, thereby highlighting the intrinsic mechanical properties of the soil.

[0015] Specifically, based on the correspondence between the penetration ratio and the normalized cone tip resistance—a relationship established through extensive experimental research and numerical simulations—it can reveal the law of stiffness decay with load cycles in pile-soil interaction and the trend of ultimate bearing capacity variation with soil conditions. For example, in sandy soil, a higher normalized cone tip resistance results in denser soil and slower stiffness decay, while an increased penetration ratio enhances overall stability. Finally, by querying preset curves—empirical charts or functions pre-calibrated through regression analysis or machine learning methods—the penetration ratio and normalized cone tip resistance are directly mapped to the corresponding stiffness decay coefficient and ultimate bearing capacity adjustment coefficient. The stiffness decay coefficient is used to correct the bending stiffness of the pile to simulate performance degradation under long-term cyclic loading, while the ultimate bearing capacity adjustment coefficient optimizes the predicted bearing capacity value to adapt to uncertainties in actual engineering.

[0016] Furthermore, in S6, the specific process of integrating the initial stiffness of pile-soil interaction, ultimate bearing capacity of pile-soil interaction, stiffness attenuation coefficient, and ultimate bearing capacity adjustment coefficient to obtain the hyperbolic py-spring relationship at different depths includes: By integrating the initial stiffness of pile-soil interaction calculated in S3, the ultimate bearing capacity of pile-soil interaction calculated in S4, and the stiffness attenuation coefficient and ultimate bearing capacity adjustment coefficient determined in S5, a hyperbolic curve describing pile-soil interaction based on static cone penetration testing is established. p-y A spring, its expression is: in: pThe reaction force provided per meter of soil, expressed in kN / m; y This represents the lateral displacement of the pile, expressed in meters (m). k ini The initial stiffness of the large-diameter single pile in the engineering site is expressed in kPa. p u This represents the ultimate bearing capacity of a large-diameter single pile in terms of pile-soil interaction, expressed in kN / m. m This is the stiffness attenuation coefficient; A This is the adjustment coefficient for the ultimate bearing capacity.

[0017] Furthermore, in S7, the Timoshenko beam-spring model is applied. Based on the wall thickness and elastic modulus of the pile material obtained in S1, the single pile is discretized into beam elements. The specific process of calculating the lateral displacement of the pile body and the bearing capacity provided by the soil under external load using the py spring includes: Based on the wall thickness and elastic modulus of the pile material obtained in S1, the cross-sectional stiffness characteristics of the Timoshenko beam element are calculated. Based on the aforementioned cross-sectional stiffness characteristics, a single pile is systematically discretized into multiple Timoshenko beam elements along the penetration depth direction to construct a pile-soil system calculation model. Based on the hyperbolic py spring relationship established in S6 at different depths, a corresponding soil spring is set at each beam element node. Based on the established pile-soil system calculation model, the pile response under external load is solved systematically using numerical methods to obtain the lateral displacement distribution and soil bearing capacity data along the depth direction.

[0018] Specifically, in step S7, the Timoshenko beam-spring model is applied to simulate the mechanical behavior of a single pile in the soil. This model achieves high-precision analysis by integrating the structural characteristics of the pile body and the interaction with the soil. First, based on the wall thickness and the elastic modulus of the pile body material obtained in S1, the cross-sectional stiffness characteristics of the Timoshenko beam element are calculated, including the moment of inertia and bending stiffness. These parameters are determined by the cross-sectional geometry by the wall thickness, and the bending and shear stiffness of the beam element are derived by combining the elastic modulus, thus accurately characterizing the structural response capability of the pile body. Next, based on the cross-sectional stiffness characteristics, the single pile is systematically discretized into multiple Timoshenko beam elements along the penetration depth direction. Each element represents a small segment of the pile body, and the pile-soil system calculation model is constructed by connecting nodes. This discretization method allows the continuous pile body to be transformed into a discrete system under the finite element framework, which is convenient for numerical processing.

[0019] Specifically, in step S7, based on the hyperbolic Py-spring relationship established in S6 at different depths, corresponding soil springs are set at each beam element node. The hyperbolic Py-spring simulates the lateral resistance of the soil to the pile through the force-displacement relationship. Its parameters are determined by the soil strength and deformation characteristics, ensuring that the spring can reflect the nonlinear soil behavior. Finally, based on the established pile-soil system calculation model, the pile response under external loads is systematically solved using numerical methods. Numerical methods such as iterative methods or matrix solvers process the equilibrium equations, calculating the displacement and force at each node, thereby obtaining the lateral displacement distribution and soil bearing capacity data along the depth direction. The displacement distribution reveals the pile deformation mode, and the bearing capacity data quantifies the soil's supporting capacity, providing key inputs for design.

[0020] Furthermore, in S8, based on the pile lateral displacement distribution and soil bearing capacity results obtained in S7, and combined with the load eccentricity obtained in S1, the load-displacement curve at the mudline is calculated, thereby realizing the specific process of pile displacement response, including: Based on the pile lateral displacement distribution and soil bearing capacity results obtained from S7 calculations, displacement response data at the mudline are directly extracted to provide initial input for load-displacement analysis. Based on the load eccentricity obtained from S1, the actual load conditions at the mudline are determined, and the transmission path and bending moment distribution of the external load are determined. By gradually applying external loads at different levels and iteratively solving the problem using the Timoshenko beam-spring model, the displacement value at the mudline under each load level is recorded, forming a corresponding data sequence of load and displacement. Based on the corresponding load-displacement data sequence, a load-displacement curve at the mudline is constructed, and the load-displacement curve is used to predict the displacement response of the pile body under horizontal load in actual engineering, thus completing the design verification.

[0021] Specifically, in step S8, based on the pile lateral displacement distribution and soil bearing capacity results obtained in S7, the displacement response data at the mudline is first directly extracted. This data comes from the numerical solution output of the Timoshenko beam-spring model, providing key displacement indices for the pile-soil interaction as initial input for load-displacement analysis, ensuring that subsequent calculations are based on the actual deformation state. Combined with the load eccentricity distance obtained in S1, which defines the position of the external load application point relative to the mudline, the actual load application conditions at the mudline are determined through geometric relationships, including the distribution of horizontal force and bending moment. This clarifies the transmission path of the external load and the evolution of the bending moment along the pile, which is crucial for accurately simulating the bending behavior of the pile.

[0022] Specifically, in step S8, different levels of external load are applied progressively, and the Timoshenko beam-spring model is used for iterative solution. Under each load increment, the model updates nodal displacements and forces through equilibrium equations and the nonlinear relationship of the spring. The displacement value at the mudline is recorded at each load level, forming a load-displacement data sequence that captures the pile's response from the elastic to the plastic stage. Based on this load-displacement data sequence, a load-displacement curve at the mudline is constructed. The curve transforms discrete data points into a continuous function using interpolation or fitting methods, visually demonstrating the nonlinear relationship between load and displacement. This is used to predict the displacement response of the pile under horizontal loads in actual engineering projects. Design verification is completed by comparing the displacement limits under the design load, ensuring the stability and safety of the pile foundation.

[0023] Compared with the prior art, the present invention has the following beneficial effects: 1) This invention fundamentally solves the industry problem of inaccurate prediction of the initial stiffness of pile-soil interaction in large-diameter single piles due to the traditional API specification method, which relies on small-diameter flexible pile tests, by innovatively establishing a hyperbolic Py-spring model based on in-situ test data. The core advantage of this invention lies in greatly simplifying the acquisition of complex soil parameters. It only requires relying on the cone tip resistance provided by static cone penetration testing as a core indicator to accurately calibrate four key control parameters: initial stiffness of pile-soil interaction, ultimate bearing capacity, stiffness attenuation coefficient, and ultimate bearing capacity adjustment coefficient. This parameter determination method not only avoids the cumbersome indoor geotechnical tests and the uncertainties of empirical parameter selection, but also truly reflects the in-situ soil characteristics of the engineering site, effectively overcoming the shortcomings of traditional methods in terms of poor applicability under different geological conditions.

[0024] 2) By introducing the Timoshenko beam-spring model, the deformation characteristics of rigid piles with large diameter single piles are fully considered, making the calculation of the lateral displacement of the pile body more consistent with the rigid rotational failure mode in actual engineering, and providing a reliable theoretical basis and technical support for the design of single pile foundations for large-scale infrastructure such as offshore wind power.

[0025] 3) From the perspective of engineering application value, the widespread use of the method of this invention will bring about a comprehensive improvement in the quality and efficiency of engineering design. Since all parameters can be obtained directly or indirectly through on-site CPT testing, designers do not need to rely on complex numerical simulations or a large number of empirical formulas, significantly shortening the design cycle and lowering the technical threshold. The method of this invention has been verified through numerous on-site tests and numerical simulations, covering various geometric dimensions and soil conditions from model piles to actual engineering piles, proving its good applicability and prediction accuracy in sandy soil sites with different relative density.

[0026] 4) By accurately predicting the stiffness and bearing capacity decay process of pile-soil interaction, this invention allows for more precise control of the deformation behavior of single pile foundations under long-term horizontal loads in engineering design. This avoids material waste caused by conservative design and eliminates safety hazards caused by prediction deviations, achieving the best balance between safety and economy. It has important practical significance for promoting the sustainable development of the offshore wind power industry. Attached Figure Description

[0027] Figure 1(a) and Figure 1(b) are respectively p-y Model parameters m and A The method for obtaining the value; Figure 2 For Timoshenko beam-spring model; Figure 3 The CPT cone tip resistance corresponding to each model pile q c ; Figures 4(a) and 4(b) show the comparison between the predicted curves and experimental data of the proposed design method for large-diameter single piles in hyperbolic sand based on static cone penetration test. Figure 5 This is a flowchart illustrating the design method for large-diameter single piles in hyperbolic sand based on static cone penetration testing in this invention. Detailed Implementation

[0028] This invention relates to a design method for large-diameter hyperbolic sandy soil piles based on static cone penetration testing, and particularly to a hyperbolic pile design method based on static cone penetration testing. p-y A spring is used to accurately predict the initial stiffness, ultimate bearing capacity, and stiffness decay process of large-diameter single piles in sandy soil. This invention is based on a hyperbolic spring-like spring based on static cone penetration testing (CPT). p-y Springs and Timoshenko beam-spring model, p-y All four control parameters of the spring: initial stiffness of pile-soil interaction ( k ini Ultimate bearing capacity of pile-soil interaction ( p u Stiffness attenuation coefficient ( m ) and ultimate bearing capacity adjustment coefficient ( AAll parameters require only in-situ CPT test results for determination. This method comprehensively considers field tests and numerical simulation tests of single piles with different test sites and geometric dimensions, possessing sufficient universality. The single pile horizontal loading test involved in parameter calibration conforms to the rigid rotational failure mode of large-diameter single piles in actual engineering, making it targeted for the design of large-diameter single pile foundations. The only input parameter required by this method is the CPT cone tip resistance provided by in-situ testing, simplifying the parameter acquisition process, ensuring high reliability, and fully reflecting the physical properties of the in-situ soil at the engineering site. Compared with existing design methods, this method is more targeted for the design of large-diameter single piles in sandy soil, and the predicted initial stiffness, ultimate bearing capacity, and stiffness decay process of large-diameter single pile pile-soil interaction show a higher degree of agreement with experimental data.

[0029] Overall, this invention obtains cone tip resistance data based on static cone penetration testing. First, the penetration ratio is calculated by dividing the penetration depth by the pile diameter. This ratio is then normalized using the cone tip resistance to eliminate depth deviation, resulting in a normalized cone tip resistance as a soil strength index. Next, the relationship between the penetration ratio and the normalized cone tip resistance is used to query a preset curve to determine the stiffness attenuation coefficient and the ultimate bearing capacity adjustment coefficient. These coefficients are used to correct pile stiffness and bearing capacity predictions to adapt to the nonlinear behavior of sandy soil. Then, the Timoshenko beam-spring model is applied, calculating the beam element section stiffness based on wall thickness and elastic modulus. A single pile is discretized into multiple elements along its depth, and a hyperbolic Py spring is used to simulate soil resistance. The hyperbolic model captures the nonlinear response of the soil through the force-displacement relationship. Subsequently, external loads were applied step by step using numerical methods, and the equilibrium equations were solved iteratively to obtain data on the lateral displacement distribution of the pile and the bearing capacity of the soil. The load-displacement curve at the mudline was calculated by combining the load eccentricity. This curve was used to predict the displacement response of the pile under horizontal loads. Finally, the design verification was completed to ensure the stability and safety of the single pile in the sandy soil.

[0030] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. Component models, material names, connection structures, circuit structures, control methods, algorithms, and other features not explicitly described in this technical solution are considered common technical features disclosed in the prior art.

[0031] Example 1 This embodiment provides a specialized design method for the pile-soil interaction mechanism of large-diameter monopile foundations in sandy soil, improving design reliability and ensuring the normal use of large-diameter monopile foundations in actual engineering projects.

[0032] The design method for large-diameter monopiles in hyperbolic sandy soil based on static cone penetration testing is mainly based on a hyperbolic cone penetration testing method. p-y Springs and Timoshenko beam-spring model, based on the hyperbolic type of static cone penetration test. p-y The specific model is shown in Table 1 and Figure 1: Table 1. Design method for large-diameter monopiles in hyperbolic sandy soil based on static cone penetration test. The following details the design method for large-diameter monopiles in hyperbolic sand based on static cone penetration testing. (See also...) Figure 5 This includes the following steps: S1. Obtaining the geometric information of a single pile in actual engineering must include the pile diameter ( D ), wall thickness ( t Load eccentricity ( e ), penetration depth ( L ), Elastic modulus of pile material ( E pile ).

[0033] S2. Obtain the actual site soil information, which must include the effective unit weight of the site soil at different depths. γ The static cone penetration test (CPT) data must include the cone tip resistance of the CPT. q c If a seismic cone caliper (CPT) is used to perform CPT, then the small strain shear modulus of the site soil needs to be obtained. G max ).

[0034] The soil information at the test site in step S2 can be obtained entirely through in-situ static cone penetration testing. The parameters are easy to obtain, highly reliable, and fully reflect the physical properties of the in-situ soil at the test site.

[0035] S3. Calculate the initial stiffness of the pile-soil interaction of a large-diameter single pile at the engineering site. k ini If a seismic cone penetration test (CPT) is conducted to directly obtain the small strain shear modulus of the site soil (…), then… G max ), directly calculate the initial stiffness of pile-soil interaction ( k ini Specifically, as shown in equation (1): (1) in, G max It is the small-strain shear modulus (kPa) of the site soil. This calculation method is based on the analytical solution of the pile-soil interaction theory of large-diameter single pile under horizontal load, and has sufficient reliability.

[0036] If a seismic cone penetration test (CPT) is not performed, the small strain shear modulus of the site soil must be calculated and determined. G maxSpecifically, as shown in equation (2): (2) In the formula: ρ T The total density of the site soil (kg / m³) 3 ); V s The site soil shear wave velocity (m / s); q c CPT cone tip resistance (MPa); σ v ′ represents the effective stress (MPa) of the soil at the site.

[0037] Determine the small strain shear modulus of the site soil according to equation (2). G max After that, the initial stiffness of the pile-soil interaction is further calculated using equation (1). k ini ).

[0038] S4. Calculate the ultimate bearing capacity of large-diameter single piles in the engineering site based on pile-soil interaction. p u Specifically, as shown in equation (3): (3) In the formula: D Pile diameter (m); q c The CPT cone tip resistance (kPa); σ v ′ represents the effective stress (kPa) of the soil at the site.

[0039] Step S4: Ultimate bearing capacity of large-diameter single piles in the engineering site due to soil-pile interaction ( p u Based on numerous model rigid and semi-rigid pile field tests and rigid pile finite element numerical simulation test results, the calibration was performed, among which the rigid and semi-rigid pile field tests covered the relative compaction of the site soil ( D r From 64% to 100%, pile diameter ( D From 0.127m to 2.000m, the ratio of penetration depth to pile diameter ( L / D The relative compaction of the soil at the site covered by the finite element numerical simulation test of rigid piles ranged from 1.64 to 14.79. D r From 20% to 80%, pile diameter ( D From 4m to 10m, the ratio of penetration depth to pile diameter ( L / DThe test results, ranging from 3 to 7.5, are widely representative, and the calibration results are universally applicable. The test results used for calibration are widely representative, and the failure modes conform to the common rotational failure modes of rigid and semi-rigid piles for large-diameter monopiles. The parameter calibration results are targeted for the design of large-diameter monopiles in actual engineering projects and are universally applicable to different actual engineering sites.

[0040] S5. Calculate the penetration depth of a single pile ( L ) and pile diameter ( D The ratio of () L / D Figure 1 shows the locations at different depths of the engineering site. p-y Model stiffness attenuation coefficient ( m ) and ultimate bearing capacity adjustment coefficient ( A ), the horizontal axis in Figure 1 The normalized cone tip resistance is calculated as shown in equation (4): (4) In the formula: p a Standard atmospheric pressure is taken as 98.1 kPa; q c The CPT cone tip resistance (kPa); σ v ′ represents the effective stress (kPa) of the soil at the site.

[0041] At different depths of the engineering site in step S5 p-y Model stiffness attenuation coefficient ( m ) and ultimate bearing capacity adjustment coefficient ( A ), determined solely by the penetration depth of a single pile ( L ) and pile diameter ( D The ratio of () L / D ) and CPT cone resistance of the site soil q c Direct calibration, without relying on additional parameters, is a simple and reliable method.

[0042] At different depths of the engineering site in step S5 p-y Model stiffness attenuation coefficient ( m ) and ultimate bearing capacity adjustment coefficient ( A Based on the calibration results of a large number of rigid pile finite element numerical simulation tests, the test scope covers the relative compaction of the site soil ( D r From 20% to 80%, pile diameter ( D From 4m to 10m, the ratio of penetration depth to pile diameter ( L / DThe test results used for calibration, ranging from 3 to 7.5, are widely representative. The failure mode conforms to the common rotational failure mode of rigid piles for large-diameter monopiles. The parameter calibration results are targeted for the design of large-diameter monopiles in actual engineering projects and are universally applicable to different actual engineering sites.

[0043] S6. Based on S3 to S5, obtain the hyperbolic cone pattern at different depths using static cone penetration. p-y All four parameters of the spring: initial stiffness of pile-soil interaction ( k ini Ultimate bearing capacity of pile-soil interaction ( p u Stiffness attenuation coefficient ( m ) and ultimate bearing capacity adjustment coefficient ( A ), calculate the depth of the engineering site at different depths p-y The relationship is shown in equation (5): (5) In the formula: p The reaction force provided per linear meter of soil (kN / m); y The lateral displacement of the pile body is in meters (m).

[0044] The hyperbolic type based on static cone penetration in step S6 p-y All four parameters of the spring: initial stiffness of pile-soil interaction ( k ini Ultimate bearing capacity of pile-soil interaction ( p u Stiffness attenuation coefficient ( m ) and ultimate bearing capacity adjustment coefficient ( A The cone tip resistance is entirely provided by the static cone penetration test (CPT) of the site soil. q c It directly calibrates the geometric information of a single pile, without relying on other parameters, simplifying the calibration process, ensuring high reliability, and providing clear physical meaning.

[0045] Hyperbolic type based on static cone penetration p-y All four parameters of the spring are provided solely by the cone tip resistance from the static cone penetration test (CPT) of the site soil. q c The geometric information of the single pile is directly used for calibration. This form... p-y The process of obtaining spring parameters is simplified, fully reflecting the physical properties of the in-situ soil at the engineering site. Compared with the existing design methods for large-diameter single piles, it has a better fitting effect on the initial stiffness, ultimate bearing capacity, and stiffness decay process of large-diameter single piles in sandy soil, enhances the universality of prediction, and has a better predictive ability for a wider range of practical engineering projects.

[0046] S7. The Timoshenko beam-spring model is used to calculate the lateral displacement of the pile body and the bearing capacity provided by the foundation soil at different depths under external loads. Specifically, as follows... Figure 2 As shown, the large-diameter monopile is discretized into a set of Timoshenko beam elements, based on the hyperbolic cone penetration test at different depths as organized in S6. p-y The spring calculation determines the bearing capacity provided by the site soil at each beam element node location.

[0047] The Timoshenko beam element in step S7 is specifically designed to describe the behavior of short beams, fully considering transverse shear deformation, and can effectively calculate the lateral displacement of large-diameter single piles caused by horizontal loads.

[0048] S8. Calculate the load-displacement curve at the mudline to provide predictive design for pile displacement at the mudline under external loads.

[0049] Application Example 1 This application example is selected from a set of centrifuge (Ng) model pile horizontal loading tests. The geometric information of the model pile (including model dimensions and prototype dimensions) and the test soil bed information are summarized in Tables 2 and 3, respectively: Table 2. Geometric information of a single pile in the model (model dimensions) Table 2 (continued). Geometric information of a single pile in the model (prototype dimensions) Table 3. Site Soil Information The CPT data of each test point on the model pile in the centrifuge model test are as follows: Figure 3 As shown.

[0050] First, based on Tables 2 and 3, the information on the test soil bed and the geometric information of the model piles were obtained. After the information was compiled, the initial stiffness of the pile-soil interaction of each model pile in the centrifuge test was calculated. k ini ) and ultimate bearing capacity ( p u After the calculation is completed, the ratio of the penetration depth of the model pile to the pile diameter is used as the basis for the calculation. L / D Determine the location of soil at different depths in the test bed. p-y Model stiffness attenuation coefficient ( m ) and ultimate bearing capacity adjustment coefficient ( A Finally, the locations at different depths were determined. p-y The model was used to calculate the relationship between lateral displacement and soil reaction at different depths along the pile under external load, as well as the load-displacement curve at the pile head, using the Timoshenko beam-spring model.

[0051] The following is the actual operation process provided in this example according to the specific steps of the design method: S1. Based on Table 2, compile the geometric information of each single pile in the centrifuge model test. The pile diameter of each model pile (… D ), wall thickness ( t ), load eccentricity ( e ), penetration depth ( L ), Elastic modulus of pile material ( E pile The specific values ​​are shown in Table 2.

[0052] S2, based on Table 3 and Figure 3 The soil bed information for this centrifuge model test was compiled. The test was conducted in a uniform soil layer, and the effective unit weight of the soil within the test design range was ( ). γ’ The value is a constant of 17.00 kN / m. 3 The envelope of CPT cone tip resistance at each test point of the model pile ( q c )like Figure 3 As shown.

[0053] S3. Calculate the initial stiffness of the pile-soil interaction in the centrifuge test model. k ini The test soil bed did not undergo vibration cone CPT, so the minimum strain modulus of the test soil bed at each depth was calculated according to equation (2). G max Then, use equation (1) to further calculate the initial stiffness of the pile-soil interaction at each depth along the pile body. k ini ).

[0054] S4. Calculate the ultimate bearing capacity of the pile-soil interaction in the centrifuge test model. p u Use equation (3) to calculate the ultimate bearing capacity at each depth along the pile body. p u ).

[0055] S5. Calculate the penetration depth of a single pile in the model ( L ) and pile diameter ( D The ratio of () L / D Figure 1 shows the locations at different depths of the test soil bed. p-y Model stiffness attenuation coefficient ( m ) and ultimate bearing capacity adjustment coefficient ( A ).

[0056] S6. Based on S3 to S5, obtain the hyperbolic curves of each model's single pile at different depths based on static cone penetration tests. p- y All four parameters of the spring: initial stiffness of pile-soil interaction (k ini Ultimate bearing capacity of pile-soil interaction ( p u Stiffness attenuation coefficient ( m ) and ultimate bearing capacity adjustment coefficient ( A ), calculate the values ​​of each model pile at different depths along the pile body in the test soil bed. p- y relation.

[0057] S7. The Timoshenko beam-spring model is used to calculate the lateral displacement of the pile at different depths under external load and the bearing capacity provided by the test soil bed. In this example, the portion of each model pile below the mud surface is divided into 42 Timoshenko beam elements along the depth, resulting in a total of 43 beam element nodes. Here, model pile 1 is used as an example to demonstrate the hyperbolic curve at each beam element node based on static cone penetration testing. p-y The values ​​of all four parameters of the spring are summarized in Table 4: Table 4. Nodes of each beam element in model pile 1 p-y Spring parameters The nodes in Table 4 p-y Substituting the spring parameters into equation (5) yields the hyperbolic curves at various depths based on static cone penetration. p-y The spring is used to calculate the bearing capacity provided by the test soil bed at each beam element node location.

[0058] S8. Calculate the displacement-load curves of each model pile at the pile head to provide a prediction of the single pile displacement at the pile head under external load, as shown in Figure 4(a) and Figure 4(b) (model piles 1 and 2, respectively). The circles in the figures are the test data points, and the red solid line is the pile load-displacement curve at the pile head predicted by the hyperbolic large-diameter single pile design method for sand based on static cone penetration proposed in this invention.

[0059] The above description of the embodiments is provided to enable those skilled in the art to understand and use the invention. It will be apparent to those skilled in the art that various modifications can be made to these embodiments, and the general principles described herein can be applied to other embodiments without inventive effort. Therefore, the present invention is not limited to the above embodiments, and any improvements and modifications made by those skilled in the art based on the disclosure of the present invention without departing from the scope of the invention should be within the protection scope of the present invention.

Claims

1. A static cone-based design method for large-diameter single piles in sand with hyperbolic curves, characterized in that, The method comprises the following steps: S1, obtaining geometric information of a single pile in an actual project, including pile diameter, wall thickness, load eccentric distance, penetration depth, and pile body material elastic modulus; S2, obtaining soil information of the project site, including effective specific weight at different depths and cone tip resistance of static sounding test; S3, calculating initial stiffness of pile-soil interaction based on the soil information; S4, calculating ultimate bearing capacity of pile-soil interaction; S5, determining stiffness attenuation coefficient and ultimate bearing capacity adjustment coefficient of the p-y model according to the ratio of the penetration depth of the single pile to the pile diameter; S6, integrating the initial stiffness of pile-soil interaction, the ultimate bearing capacity of pile-soil interaction, the stiffness attenuation coefficient, and the ultimate bearing capacity adjustment coefficient to obtain hyperbolic p-y spring relationship at different depths; S7, applying the Timoshenko beam-spring model, discretizing the single pile into beam elements based on the wall thickness and the pile body material elastic modulus obtained in S1, and calculating lateral displacement of the pile body and bearing capacity provided by the soil under external load by using the p-y spring; S8, calculating load-displacement curve at the mud line based on the lateral displacement distribution of the pile body and the bearing capacity of the soil obtained in S7, and combining the load eccentric distance obtained in S1, so as to realize complete prediction design of the displacement response of the pile body.

2. A static cone-based design method for large-diameter single piles in sand with hyperbolic soil behavior according to claim 1, characterized in that, In S1, the pile diameter is the cross-sectional diameter of the single pile; The wall thickness is the thickness of the wall of the hollow pile body; The load eccentric distance is the vertical distance between the horizontal load action point and the mud line; The penetration depth is the total depth of the pile body into the soil.

3. A static cone-based design method for large-diameter single piles in sand with hyperbolic soil behavior according to claim 1, characterized in that, In S2, the specific process of obtaining the soil information of the project site comprises: Obtaining the cone tip resistance at different depths through in-situ static sounding test, which is used to reflect the compactness and strength characteristics of the site soil; Deriving the effective specific weight in combination with the soil test results or field measurement data; When using seismic static sounding, synchronously obtaining the small-strain shear modulus, otherwise indirectly deriving the small-strain shear modulus through the relationship between the cone tip resistance and the effective stress.

4. A static cone-based design method for large-diameter single piles in sand with hyperbolic soil behavior according to claim 3, characterized in that, In S3, the specific process of calculating the initial stiffness of pile-soil interaction based on the soil information comprises: First, deriving the small-strain shear modulus through the cone tip resistance of the static sounding and the effective stress of the site soil, and then calculating the initial stiffness based on the derived small-strain shear modulus; When directly obtaining the small-strain shear modulus of the site soil through seismic static sounding, directly calculating the initial stiffness of pile-soil interaction based on the small-strain shear modulus.

5. A static cone-based design method for large-diameter single piles in sand with hyperbolic soil behavior according to claim 4, characterized in that, In S4, the specific process of calculating the ultimate bearing capacity of pile-soil interaction comprises: Deriving the ultimate bearing capacity parameter through the calibration relationship by using the cone tip resistance and the effective stress value of the site soil obtained in S2.

6. A static cone-based design method for large-diameter single piles in sand with hyperbolic soil behavior according to claim 5, characterized in that, Small strain shear modulus G max The calculation is as follows: wherein, In S5, the specific process of determining the stiffness attenuation coefficient and the ultimate bearing capacity adjustment coefficient of the p-y model according to the ratio of the penetration depth of the single pile to the pile diameter comprises: T G is the total density of the site soil, in kg / m 3 ; V s V is the shear wave velocity of the site soil, in m / s; q c R is the tip resistance, in MPa; σ is the effective stress of the site soil, in MPa; ultimate bearing capacity p u The calculation is as follows: wherein, D is the pile diameter in m; q c is the tip resistance in kPa; is the effective stress of the site soil in kPa.

7. The static cone-based design method for large-diameter single piles in sand with hyperbolic curves according to claim 1, wherein Calculating the penetration depth ratio based on the penetration depth and the pile diameter obtained in S1, then obtaining the normalized cone tip resistance through normalization processing in combination with the cone tip resistance data obtained in S2, and finally determining the corresponding stiffness attenuation coefficient and ultimate bearing capacity adjustment coefficient by querying the preset curve according to the corresponding relationship between the penetration depth ratio and the normalized cone tip resistance. ​ 8. A static cone-based design method for large-diameter single piles in sand with hyperbolic soil models according to claim 1, characterized in that, In S6, the initial stiffness of pile-soil interaction, the ultimate bearing capacity of pile-soil interaction, the stiffness attenuation coefficient, and the ultimate bearing capacity adjustment coefficient are integrated to obtain the specific process of the hyperbolic p-y spring relationship at different depths, which includes: The initial stiffness of pile-soil interaction calculated by S3, the ultimate bearing capacity of pile-soil interaction calculated by S4, and the stiffness attenuation coefficient and the ultimate bearing capacity adjustment coefficient determined by S5 are integrated to establish a hyperbolic curve type formula capable of describing the pile-soil interaction based on static sounding p-y a spring, the expression of which is: wherein: p is the counterforce provided per meter of soil, in kN / m; y is the lateral displacement of the pile, in m; k ini is the initial stiffness of the pile-soil interaction for large diameter single piles in an engineering site, in kPa; p u is the ultimate bearing capacity of the pile-soil interaction for large diameter single piles, in kN / m; m is the stiffness decay coefficient; A is the ultimate bearing capacity adjustment coefficient.

9. A static cone-based design method for large-diameter single piles in sand with hyperbolic soil models according to claim 1, characterized in that, In S7, the single pile is discretized into beam elements based on the wall thickness and the elastic modulus of the pile body material obtained in S1 by applying the Timoshenko beam-spring model, and the lateral displacement of the pile body and the bearing capacity provided by the soil under external load are calculated using the p-y spring, which includes: Based on the wall thickness and the elastic modulus of the pile body material obtained in S1, the cross-sectional stiffness characteristics of the Timoshenko beam element are calculated; Based on the cross-sectional stiffness characteristics, the single pile is systematically discretized into multiple Timoshenko beam elements along the penetration depth direction to construct a pile-soil system calculation model; Based on the hyperbolic p-y spring relationship at different depths established in S6, the corresponding soil springs are set at each beam element node; Based on the established pile-soil system calculation model, the pile body response under external load is systematically solved by numerical method to obtain the lateral displacement distribution and soil bearing capacity data along the depth direction.

10. A static cone-based design method for large-diameter single piles in sand with hyperbolic soil behavior according to claim 1, characterized in that, In S8, based on the pile body lateral displacement distribution and soil bearing capacity results obtained in S7, and combined with the load eccentricity distance obtained in S1, the load-displacement curve at the mud line is calculated to realize the specific process of the pile body displacement response, which includes: Based on the pile body lateral displacement distribution and soil bearing capacity results obtained in S7, the displacement response data at the mud line is directly extracted to provide initial input for load-displacement analysis; Combined with the load eccentricity distance obtained in S1, the actual load action condition at the mud line is determined, and the transmission path and bending moment distribution of the external load are determined; By gradually applying different levels of external load and using the Timoshenko beam-spring model for iterative solution, the displacement value at the mud line under each load level is recorded to form a corresponding data sequence of load-displacement; Based on the corresponding data sequence of load-displacement, the load-displacement curve at the mud line is constructed, and the load-displacement curve is used to predict the displacement response of the pile body under horizontal load in actual engineering, and the design verification is completed.

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