Consideration of state-related cylinder foundation sinking resistance calculation method

Abstract

The application discloses a kind of state-related sinking resistance calculation methods of considering cylinder type foundation, belong to geotechnical engineering and ocean engineering field.The method includes: based on the geometric parameters of cylinder type foundation and foundation soil state parameters, determine the outside wall friction and the associated outer wall stress state parameters;Based on the outer wall stress state parameters, consider soil arch effect to determine the inner side wall friction, establish the coupling calculation relationship between inner and outer side wall friction;Determine cylinder end resistance;Based on inner, outer side wall friction and cylinder end resistance, the total sinking resistance is calculated.The application can more accurately reflect the physical mechanism of cylinder-soil interaction by establishing the coupling relationship of inner and outer wall mechanical behavior, and can optionally introduce the dynamic evolution mechanism of soil state, improve the accuracy and reliability of sinking resistance prediction.

Description

Technical Field

[0001] This invention belongs to the field of geotechnical engineering and marine engineering technology, and in particular, it is a method for calculating the settlement resistance of a cylindrical foundation considering state-dependent factors. Background Technology

[0002] Offshore wind turbine cylindrical foundations penetrate the seabed foundation using their own weight and negative pressure. Predicting the settlement resistance during this penetration process is crucial for engineering design and construction safety. Accurate resistance prediction not only facilitates successful foundation installation and prevents project failures but also allows for the rational allocation of construction equipment, cost optimization, and improved economic efficiency. Therefore, there is an urgent need to develop calculation methods that accurately reflect the physical mechanism of cylindrical foundation penetration.

[0003] Currently, the industry typically refers to and references theories and standards applied to pile foundations, such as the American Petroleum Institute (API) standards, when calculating the settlement resistance of cylindrical foundations. The total resistance is generally decomposed into three parts: outer wall friction, inner wall friction, and end resistance. The calculation of inner and outer wall friction is mainly based on various earth pressure theories, estimating the lateral earth pressure at the cylinder wall and multiplying it by the interface friction coefficient. End resistance is usually solved based on the ultimate bearing capacity theory of the foundation. These methods provide a basic calculation framework for engineering practice.

[0004] However, directly applying pile foundation theory to large-diameter, thin-walled cylindrical foundations leads to a lack of understanding of the physical mechanisms involved due to the neglect of the differences in structural form and penetration mechanism between the two. Therefore, further research and innovation are needed to address the aforementioned problems in existing technologies. Summary of the Invention

[0005] Purpose of the invention: In view of the above-mentioned problems in the prior art, this application provides a method for calculating the settlement resistance of a cylindrical foundation that considers state-related factors.

[0006] Technical solution: According to one aspect of this application, a method for calculating the settlement resistance of a cylindrical foundation considering state-related factors includes:

[0007] Obtain the geometric parameters and soil state parameters of the cylindrical foundation, and determine the outer wall friction and associated outer wall stress state parameters of the cylindrical foundation.

[0008] Based on the stress state parameters of the outer wall, the frictional resistance of the inner wall of the cylindrical foundation is determined considering the soil arching effect, and the coupling calculation relationship between the frictional resistance of the inner and outer walls is established.

[0009] Determine the end resistance of the cylindrical foundation;

[0010] The total sinking resistance is calculated based on the frictional resistance of the inner wall, the frictional resistance of the outer wall, and the resistance at the cylinder end.

[0011] Beneficial effects: By establishing a coupling relationship between the mechanical behavior of the inner and outer walls and optionally introducing a dynamic evolution mechanism of the soil state, this invention can reflect the physical mechanism of the cylinder-soil interaction, thereby improving the accuracy and reliability of settlement resistance prediction. The related technical effects will be described in detail below with reference to specific embodiments. Attached Figure Description

[0012] Figure 1 A flowchart illustrating a method for calculating the settlement resistance of a cylindrical foundation considering state-related factors, provided in an embodiment of this application.

[0013] Figure 2 This is a flowchart illustrating an example of determining the outer wall friction resistance of a cylindrical foundation, provided as an embodiment of this application.

[0014] Figure 3 A flowchart for determining the end resistance of a cylindrical foundation, provided as an embodiment of this application.

[0015] Figure 4 This is another flowchart for determining the outer wall friction of a cylindrical foundation, provided as an embodiment of this application.

[0016] Figure 5 A flowchart for determining the inner wall side pressure coefficient provided in an embodiment of this application.

[0017] Figure 6 A flowchart illustrating another method for calculating the settlement resistance of a cylindrical foundation considering state-related factors, provided in an embodiment of this application.

[0018] Figure 7 A comparison chart of frictional resistance between centrifugal model test and theoretical calculation under the conditions of wall thickness = 10cm and cylinder diameter = 6m provided in the embodiments of this application.

[0019] Figure 8 A comparison chart of end resistance between centrifugal model test and theoretical calculation under the conditions of wall thickness = 10cm and cylinder diameter = 6m provided in the embodiments of this application.

[0020] Figure 9 A comparison chart of sinking resistance obtained from centrifugal model tests and theoretical calculations under the conditions of a wall thickness of 7.5 cm and a cylinder diameter of 6 m, provided for embodiments of this application. Detailed Implementation

[0021] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0022] It should be noted that the terms "first," "second," etc., in the specification and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "including" and "having," and any variations thereof, are intended to cover non-exclusive inclusion; for example, a process, method, system, product, or apparatus that includes a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0023] To address the aforementioned issues, the applicant conducted in-depth searches and analyses, and discovered:

[0024] Correspondingly, the mechanical behavior of the inner and outer walls is treated separately. Existing methods treat the frictional resistance of the inner and outer walls as two independent physical problems, solve them separately and then superimpose them, ignoring the fact that the cylinder wall is a mechanical continuum. The constraint state of the soil on the outer side of the cylinder will inevitably affect the stress distribution of the soil inside the cylinder and the formation of the soil arching effect. The uncoupled treatment of the mechanical behavior of the inner and outer walls is inconsistent with physical reality.

[0025] Furthermore, the soil state is treated as static. Existing methods typically use initial soil state parameters before penetration, such as initial relative density, for the entire calculation, without considering the dynamic evolution of the soil's state during the shearing process of penetration, such as shear contraction or shear dilatation. This leads to a disconnect between model assumptions and actual physical processes. These problems collectively result in insufficient accuracy of existing resistance prediction methods, making it difficult to meet engineering requirements.

[0026] To solve these problems, combined with Figures 1 to 9 The present invention will be specifically described through the following embodiments.

[0027] In some embodiments, an exemplary scheme is provided for calculating the settlement resistance of a cylindrical foundation considering state-dependent factors. The calculation method disclosed in this invention abandons the traditional approach of treating the inner and outer wall frictional resistances as independent components and then superimposing them, instead establishing a closed-loop calculation framework that couples the wall mechanical behavior in two directions. This framework can more realistically reflect the physical mechanism of the cylinder-soil interaction during the penetration process of the cylindrical foundation.

[0028] Step 101: Obtain the geometric parameters and soil state parameters of the cylindrical foundation, and determine the outer wall friction and associated outer wall stress state parameters of the cylindrical foundation.

[0029] In this embodiment, the geometric parameters of the cylindrical foundation may specifically include the diameter and wall thickness of the cylindrical foundation. The soil state parameters characterize the current physical and mechanical properties of the soil, specifically including soil weight, internal friction angle, and parameters reflecting the soil's density state, such as relative density or initial void ratio. This step is used to calculate the outer wall frictional resistance. During the calculation process, intermediate physical quantities that characterize the stress state of the soil outside the cylindrical wall are generated, namely, the outer wall stress state parameters. These parameters can be used to achieve subsequent inner and outer wall coupling calculations.

[0030] Step 102: Based on the stress state parameters of the outer wall, determine the frictional resistance of the inner wall of the cylindrical foundation and establish the coupling calculation relationship between the frictional resistances of the inner and outer walls.

[0031] Alternatively, based on the stress state parameters of the outer wall, the frictional resistance of the inner wall of the cylindrical foundation is determined by considering the soil arching effect, and a coupled calculation relationship between the frictional resistances of the inner and outer walls is established.

[0032] Specifically, traditional methods for calculating the inner wall friction F _1 Previously, only the parameters of the soil plug inside the cylinder were considered, neglecting the constraint and influence of the soil outside the cylinder on the soil arching effect inside the cylinder. This invention introduces the stress state parameters of the outer wall to participate in the calculation of the frictional resistance of the inner wall, establishing a mechanical connection between the inner and outer walls. This coupling relationship is more in line with physical reality because the constraint state of the soil outside the cylinder directly affects the small deformation of the cylinder wall and the stress redistribution of the soil inside the cylinder, affecting the formation and development of the soil arching effect.

[0033] Step 103: Determine the end resistance of the cylindrical foundation.

[0034] Alternatively, the end resistance of the cylindrical foundation can be determined based on geometric parameters and soil condition parameters.

[0035] Accordingly, the resistance provided by the soil at the annular end face of the cylindrical foundation when it penetrates the soil is calculated, i.e., the end resistance. The calculation of this resistance is a necessary component of the calculation of the total settlement resistance. In this invention, the calculation of the end resistance can optionally be based on the cavity expansion theory, further considering the special physical effects under suction penetration conditions.

[0036] Step 104: Calculate the total sinking resistance based on the inner wall friction, outer wall friction, and cylinder end resistance.

[0037] The total settlement resistance is used to assess the penetrationability of the cylindrical foundation, design the construction scheme, and select construction equipment. The specific calculation process can be achieved using the following formula:

[0038] F _z =F _1 +F _2 +F _3 ;

[0039] In the formula, F _z F represents the total sinking resistance. _1 F is the frictional resistance of the inner wall; _2 F is the frictional resistance of the outer wall; _3 This represents the resistance at the cylinder end.

[0040] In other embodiments, alternative technical solutions for dynamically determining the soil state parameters are described. This overcomes the limitation of treating soil state parameters (such as relative density) as static values ​​that remain constant during penetration. By establishing an iterative evolution model related to the degree of shear mobilization, this method can simulate the shear contraction or dilatation effects that may occur in the soil under penetration shear, solving for a soil state that more closely matches physical reality at each penetration depth, providing input for subsequent resistance calculations.

[0041] The soil state parameters are dynamically determined at a given penetration depth through iterative calculations until convergence conditions are met. This iterative calculation process can be broken down into the following steps:

[0042] Step 201: Calculate the shear mobilization ratio based on the foundation soil state parameters obtained in the previous iteration;

[0043] The calculation of the shear mobilization ratio specifically includes:

[0044] Based on the foundation soil state parameters obtained from the previous iteration, the ultimate skin friction and the current mobilization skin friction are determined respectively.

[0045] Calculate the ratio of the current mobilization friction to the ultimate friction to obtain the shear mobilization ratio.

[0046] The soil condition parameters can be optionally specified as the relative density D of the soil. _r Before the iteration begins, the initial relative compaction of the soil is used as the initial value for the 0th iteration, denoted as D. _r_0 In the k-th iteration, based on the relative density D obtained in the previous round... _r_k Determine two physical quantities.

[0047] Among them, the ultimate skin friction refers to the resistance of soil in state D. _r_k This is the maximum frictional resistance that the cylinder-soil interface can exert. This value can be calculated using the method described in the subsequent embodiments, assuming that the shear strength of the soil has been utilized.

[0048] Current mobilization frictional resistance refers to the actual frictional resistance generated at the cylinder-soil interface under the current penetration load and displacement conditions. This value is related to the overall stress state and deformation coordination.

[0049] The shear mobilization ratio, also known as the ratio of the two, is a dimensionless parameter between 0 and 1, used to quantify the degree to which soil is sheared under its current state. The closer it is to 1, the higher the degree of soil mobilization, and the greater the likelihood of changes in its internal structure and state. Its calculation process can be expressed as follows:

[0050] R _mob =F _mob / F _lim ;

[0051] In the formula, R _mob For shear mobilization ratio; F _mob For current mobilization friction resistance; F _lim This represents the ultimate frictional resistance.

[0052] Step 202: Based on the shear mobilization ratio, update the foundation soil state parameters for the current iteration.

[0053] Specifically, the updated foundation soil state parameters for the current iteration are as follows:

[0054] The shear mobilization ratio is input into the state evolution function to adjust the state parameters of the foundation soil.

[0055] The state evolution function is a mathematical model used to describe how relative compaction changes with shear mobilization ratio. Optionally, this state evolution function can take an exponential asymptotic form, as follows:

[0056] D _r_k+1 =D _r_k +ΔD _r_max ×(1-exp(-β×R _mob ));

[0057] In the formula, D _r_k+1 The relative density corresponding to the (k+1)th round, i.e., the density obtained in the current iteration; D _r_k Corresponding to the k-th round, i.e., the relative density of the previous iteration; ΔD _r_max Corresponding to the maximum potential change in relative density, this parameter characterizes the maximum possible change in the relative density of soil from its initial state to its ultimate shear state. For loose sandy soils prone to shear shrinkage, ΔD _r_max For dense sandy soils prone to dilatation, ΔD is a positive value. _r_max The value is negative, and its specific value can be determined through indoor unit tests; exp corresponds to the natural exponential function; β corresponds to the state evolution rate coefficient, which is a material parameter used to control the rate of change of relative density, and can also be calibrated experimentally, for example, its value range can be 1.5-2.5; R _mob Corresponding shear mobilization ratio.

[0058] Furthermore, determine the newly calculated D_r_k+1 Compared to the previous round D _r_k Does it meet the preset convergence conditions? For example, it can be determined whether the absolute value of the difference between the two is less than a small preset threshold, such as 0.001. If the convergence conditions are met, the iteration terminates, and the final converged relative compaction is used as the foundation soil state parameter determined at that penetration depth for subsequent calculation of total settlement resistance. If not, then D... _r_k+1 As new input, return to the previous step and begin the next iteration.

[0059] In some alternative implementations, the state evolution function can also be other functions that reflect D. _r With R _mob Functions that grow nonlinearly and tend to saturate, such as hyperbolic or piecewise functions. Furthermore, in more complex numerical models, the shear mobilization ratio can be replaced by other physical quantities that characterize the degree of soil shear, such as equivalent shear strain.

[0060] In some alternative implementations, the following boundary conditions and exception handling mechanisms can be set for the iterative process:

[0061] Accordingly, an upper limit is set for the number of iterations. If the number of iterations exceeds the preset maximum number of iterations, such as 100, and the convergence condition is still not met, the iteration is terminated, and the relative density obtained from the last iteration is used as the output result. At the same time, the non-convergence flag is recorded for subsequent analysis.

[0062] Next, constraints are set on the range of variation in relative density. After each iteration update, D is checked. _r_k+1 Is it within the physically reasonable range, i.e., 0≤D? _r_k+1 ≤1. If it exceeds this range, it will be corrected to the boundary value.

[0063] Furthermore, for extreme cases of the state parameter ψ, when the absolute value of ψ exceeds a preset threshold, such as 0.3, the exponential function involved in subsequent calculations can be truncated to avoid numerical overflow.

[0064] In other embodiments, specific methods for determining the outer wall friction resistance are provided. Based on experimentally verified experience and semi-empirical formulas, a state equation directly related to the relative density of the foundation soil is introduced to modify the earth pressure calculation theory and predict the outer wall friction resistance of the cylindrical foundation.

[0065] In this embodiment, determining the outer wall friction of the cylindrical foundation specifically includes:

[0066] Step 301: Call the state equation related to the relative compaction in the foundation soil state parameters to determine the outer wall earth pressure coefficient.

[0067] Accordingly, the dimensionless parameter, namely the outer wall earth pressure coefficient, is calculated. This coefficient reflects the lateral stress level of the soil at the outer wall during the penetration of the cylindrical foundation. The outer wall earth pressure coefficient ξ is... _1 The calculation process is as follows:

[0068] ξ _1 =A _1 ×D _r +A _2 ×ψ(D _r );

[0069] In the formula, ξ _1 A is the coefficient of earth pressure on the outer wall; _1 The equation of state considering the compaction of the foundation soil and the friction coefficient of the cylinder-foundation interface; D _r The relative density of the foundation soil can be determined by a dynamic iteration method, or taken as the initial value in simplified calculations; A _2 ψ(D) is the shape equivalence coefficient for the cylindrical foundation. This coefficient mainly reflects the influence of the geometric characteristics of the cylindrical foundation as a large-diameter, thin-walled structure on the soil stress field. Based on experimental data and numerical simulation results, this coefficient can generally be taken as -0.75; _r ) is another state equation that considers the density of the foundation soil.

[0070] Furthermore, the state equation A _1 and ψ(D) _r The formula is an empirical relation derived from fitting a large amount of experimental data, and its specific form is as follows:

[0071] A _1 =1-0.5×μ;

[0072] In the formula, A _1 The equation of state is given; μ is the friction coefficient at the cylinder-foundation interface.

[0073] ψ(D _r )=D _r ×(1-D _r );

[0074] In the formula, ψ(D) _r ) represents the state equation; D _r This refers to the relative density of the foundation soil.

[0075] The friction coefficient μ at the cylinder-foundation interface in the above formula is also closely related to the compaction state of the soil. In this embodiment, its value can be determined by the following linear relationship:

[0076] μ=a _1 +a _2 ×D _r ;

[0077] In the formula, μ is the friction coefficient of the cylinder-foundation interface; a _1 This is the basic value of the friction coefficient, corresponding to the ideal loosest state, i.e., D. _r The interfacial friction coefficient when a = 0; _2 The interfacial friction coefficient varies with the relative density D _r The rate of increase with increasing density reflects the physical phenomenon that denser soil particles have tighter interlocking, leading to increased interfacial friction. _1 and a _2 The specific values ​​are related to factors such as the roughness of the cylinder wall and the mineral composition and shape of the soil particles, and need to be calibrated through indoor interfacial shear tests. For example, for quartz sand and steel cylinder walls in a marine environment, a _1 The value of a can range from 0.15 to 0.20. _2 The value range can be 0.18-0.22.

[0078] Step 302: Calculate the outer wall friction resistance based on the outer wall earth pressure coefficient.

[0079] The earth pressure coefficient ξ on the outer wall was determined. _1 Then, the total outer wall friction F can be calculated by integrating the effective lateral stress on the outer side of the cylinder wall. _2 Assuming the soil weight γ remains constant along the depth, its calculation process can be expressed as follows:

[0080] F _2 =∫0 h [μ×ξ _1 ×γ×z]×(π×(d _1 +2t))dz=(1 / 2)×μ×ξ _1 ×γ×h 2 ×π×(d _1 +2t);

[0081] In the formula, F _2 The outer wall frictional resistance; ∫0 h ξ represents the integral along the penetration depth from 0 to h; μ is the friction coefficient at the cylinder-foundation interface; _1 γ is the coefficient of earth pressure on the outer wall; z is the effective unit weight of the foundation soil; π is the integral variable representing depth; d is the radius of the circle. _1 t is the inner diameter of the cylindrical foundation; h is the wall thickness of the cylindrical foundation; and h is the total penetration depth of the cylindrical foundation.

[0082] By following the steps described above, the calculation of the outer wall friction resistance based on empirical formulas can be completed. Although the method provided in this embodiment relies on empirical parameters, its physical concepts are clear, and the calculation process is relatively simple. It can provide a fast and effective prediction method when the parameters are known in the preliminary engineering design.

[0083] As an example, an alternative approach to determining the outer wall skin friction is provided. It incorporates critical state theory into the analytical model of settlement resistance. State parameters are used instead of relative density as indicators of soil state. This reduces the model's dependence on site-specific empirical parameters and explains the shear contraction or dilatation behavior of sands with different densities during shearing processes, and their impact on outer wall skin friction, thus improving the model's scientific validity and engineering extrapolation.

[0084] Specifically, determining the skin friction of the outer wall of the cylindrical foundation includes:

[0085] Step 401: Obtain the current void ratio in the foundation soil state parameters.

[0086] The void ratio, a physical quantity characterizing the ratio of pore volume to soil particle volume, is a fundamental parameter describing the compaction state of soil. In this invention, the current void ratio e can be determined by the relative compaction degree D of the foundation soil. _r The conversion is as follows:

[0087] e=(e _max -D _r ×(e _max -e _min ));

[0088] In the formula, e is the current void ratio; e _max e represents the maximum void ratio of the foundation soil, corresponding to the loosest state; _min D represents the minimum void ratio of the foundation soil, corresponding to its densest state; _r represents the relative density of the foundation soil, and its value can optionally be determined by a dynamic iterative method, reflecting the state evolution of the soil during penetration. Where e _max and e _min These are all basic physical properties of soil, which can be determined through indoor tests.

[0089] Step 402: Calculate the critical state porosity under the current stress level.

[0090] The critical state void ratio refers to the void ratio corresponding to the steady state of soil under sustained shear deformation, where the volume and stress remain constant. It is not a fixed value, but a function related to the current average effective stress p'. Optionally, the critical state void ratio can be determined by the following critical state line equation:

[0091] e _c =Γ-λ×ln(p' / p _a );

[0092] In the formula, e _c The critical porosity is given by: ln (critical state porosity); ln (natural logarithm); p' (mean effective stress); p_a For reference atmospheric pressure, 100 kPa is usually taken; Γ is the reference pressure, i.e., p' = p _a Γ is the critical state void ratio; λ is the slope of the critical state line in the e-ln(p') coordinate space, and e is the soil void ratio. Γ and λ are two material parameters characterizing the critical state properties of a specific soil, which can be calibrated through a series of triaxial drained shear tests.

[0093] Based on this, the average effective stress can be estimated according to the depth of the current calculation point and the lateral pressure coefficient, for example:

[0094] p'=(1 / 3)×(σ' _v +2×K×σ' _v ) = (1 / 3) × (1 + 2 × K) × γ' × z;

[0095] In the formula, p' is the average effective stress; σ' _v γ is the effective vertical stress; K is the lateral pressure coefficient during static or penetration process; γ' is the effective unit weight of the soil; z is the depth of the calculation point.

[0096] Step 403: Determine the state parameter ψ based on the difference between the current porosity and the critical state porosity.

[0097] The state parameter ψ is defined as the difference between the current void ratio and the critical state void ratio under the same stress level. It reflects the degree and direction of the soil's current state deviating from its final stable state. Its calculation formula is:

[0098] ψ=ee _c ;

[0099] In the formula, ψ is the state parameter; e represents the current porosity; e _c This indicates the critical porosity.

[0100] When ψ>0, it indicates that the soil is in a loose critical state and tends to undergo volume compression during shearing, i.e., shear contraction; when ψ<0, it indicates that the soil is in a dense critical state and tends to undergo volume expansion during shearing, i.e., shear dilatation; when ψ=0, it indicates that the soil is exactly in a critical state.

[0101] Step 404: Determine the earth pressure coefficient of the outer wall based on the state parameter ψ.

[0102] By establishing a direct functional relationship between the external earth pressure coefficient and state parameters, the soil dilatation and contraction behaviors are intrinsically coupled to the calculation of lateral stress. Optionally, this relationship can be expressed in exponential form, specifically:

[0103] ξ _1 =K _base×exp(-n×ψ);

[0104] In the formula, ξ _1 K represents the coefficient of earth pressure on the outer wall. _base ψ represents the reference earth pressure coefficient, whose value is mainly related to the roughness of the cylinder wall and the internal friction angle of the soil, and is dimensionless; exp represents the natural exponential function; n represents a positive material constant used to control the sensitivity of the earth pressure coefficient to changes in state parameters, and also needs to be calibrated by test; ψ represents the state parameter.

[0105] For dense sand (ψ<0), the dilatation effect causes soil particles to push against each other during shear slip, generating additional normal stress in the direction perpendicular to the shear plane, which increases the coefficient of earth pressure on the outer wall and makes exp(-n×ψ)>1. Conversely, for loose sand (ψ>0), the contraction effect causes the soil skeleton to tend to be compacted, the lateral stress is relatively reduced, which reduces the coefficient of earth pressure on the outer wall and makes exp(-n×ψ)<1.

[0106] Step 405: Calculate the outer wall friction resistance based on the outer wall earth pressure coefficient.

[0107] Alternatively, obtain the earth pressure coefficient of the outer wall and calculate the frictional resistance of the outer wall.

[0108] After determining the external earth pressure coefficient based on the physical mechanism, the total external wall friction can be calculated by substituting it into the following integral formula:

[0109] F _2 =(1 / 2)×μ×ξ _1 ×γ×h 2 ×π×(d _1 +2t);

[0110] In summary, the method provided in this embodiment constructs a calculation model for external wall friction by introducing critical state theory. This model can capture the differences in mechanical response of soils with different densities during the penetration process, providing a theoretical basis for the design and construction of cylindrical foundations.

[0111] As another example, an exemplary scheme integrating multiple physical mechanisms is described to determine the frictional resistance of the inner wall. This embodiment not only considers the soil arching effect caused by the relative displacement between the cylinder and the soil during the penetration of the cylindrical foundation, but also couples multiple physical mechanisms such as the constraint effect of the external soil, the gradual development process of the principal stress rotation angle, and the seepage effect under suction construction conditions to construct a predictive model for the frictional resistance of the inner wall.

[0112] The determination process of the inner wall friction resistance can be broken down into the following aspects. Accordingly, at the foundation calculation framework level, determining the inner wall friction resistance of the cylindrical foundation specifically includes:

[0113] The inner wall lateral pressure coefficient is determined based on the principal stress rotation angle, which reflects the soil arching effect.

[0114] The frictional resistance of the inner wall is calculated based on the inner wall pressure coefficient.

[0115] The principal stress rotation angle is determined based on the stress state parameters of the outer wall.

[0116] In other words, the inner wall lateral pressure coefficient is determined by using the principal stress rotation angle to reflect the soil arching effect.

[0117] This gives us the frictional resistance generated by the inner wall.

[0118] The principal stress rotation angle is obtained based on the stress state parameters of the outer wall.

[0119] Specifically, the frictional resistance of the inner wall can be calculated by integrating the shear stress on the inner wall along the depth, and its basic calculation formula can be expressed as:

[0120] F _1 =∫0 h [μ×K _1 ×γ×z]×(π×d _1 )dz=(1 / 2)×μ×K _1 ×γ×h 2 ×π×d _1 ;

[0121] In the formula, F _1 The frictional resistance is the inner wall friction; ∫0 h The integral represents the distance from 0 to h along the penetration depth; μ is the friction coefficient at the cylinder-foundation interface; K _1 γ is the inner wall lateral pressure coefficient; γ is the effective unit weight of the foundation soil; z is the integral variable, representing depth; π is pi; d _1 denoted as the inner diameter of the cylindrical foundation; h is the total penetration depth of the cylindrical foundation.

[0122] Among them, the inner wall side pressure coefficient K _1 Used to calculate F _1 This reflects the enhancing effect of the soil arching effect on the lateral stress inside the cylinder. In this invention, K _1 The determination of θ is closely related to the principal stress rotation angle θ, and their relationship can be described by the following formula:

[0123] K _1 =(σ _1 +σ _3 -(σ _1 -σ _3 )×cos(2θ)) / (σ _1 +σ _3 +(σ _1 -σ _3)×cos(2θ));

[0124] In the formula, K _1 σ is the pressure coefficient on the inner wall side; _1 The maximum principal stress; σ _3 The minimum principal stress is θ, which is the principal stress rotation angle.

[0125] Further, the principal stress rotation angle is determined, specifically including:

[0126] The outer wall constraint ratio is determined as the outer wall stress state parameter;

[0127] Based on the external wall constraint ratio, the principal stress rotation angle is corrected;

[0128] The external wall constraint ratio is determined by calculating the ratio of the normal stress to the vertical stress of the outer wall of the cylindrical foundation.

[0129] Accordingly, the external wall constraint ratio is defined as the ratio of the normal stress to the vertical stress at the outer wall of the cylindrical foundation, and its calculation formula can be expressed as:

[0130] η _out =σ _h / σ _v ;

[0131] In the formula, η _out σ is the outer wall constraint ratio; _h σ is the normal stress of the outer wall; _v This represents the vertical stress on the outer wall. The outer wall constraint ratio quantifies the strength of the constraint exerted by the external soil on the cylinder wall. In the calculation of the principal stress rotation angle θ, η can be used... _out As a correction factor, for example, the base rotation angle θ calculated in subsequent steps. _base Multiplied by η _out The relevant function f(η) _out ), to obtain the final result used to calculate K _1 The rotation angle, i.e., θ = θ _base ×f(η _out This transfers the constraint effect of the outer wall to the calculation of the soil arch of the inner wall.

[0132] Furthermore, the principal stress rotation angle is determined by one or more methods selected from the group consisting of:

[0133] Optionally, the reference rotation angle is determined based on the internal friction angle of the foundation soil;

[0134] Determine the state-related correction function based on the relative density of the foundation soil;

[0135] The principal stress rotation angle is calculated based on the reference rotation angle and the state-related correction function;

[0136] Optionally, the critical principal stress rotation angle can be determined based on the internal friction angle of the foundation soil.

[0137] The soil arch depth development function is determined based on the penetration depth and the critical development depth of the soil arch effect.

[0138] Determine the state-related correction function based on the relative density of the foundation soil;

[0139] The principal stress rotation angle is calculated based on the critical principal stress rotation angle, the soil arch depth development function, and the state-related correction function.

[0140] Optionally, the reference rotation angle for interface condition constraints is determined based on the interface friction angle and the internal friction angle of the foundation soil;

[0141] Determine the depth development function;

[0142] Determine the state-related correction function based on the state parameters of the critical state theory;

[0143] The principal stress rotation angle is calculated based on the reference rotation angle, the depth development function, and the state-related correction function.

[0144] Accordingly, the calculation is based on the reference rotation angle and the state-related correction function, and its formula can be described as follows:

[0145] θ _base =θ _ref ×η(D _r );

[0146] In the formula, θ _base Based on the rotation angle; θ _ref The principal stress rotation angle under the reference state is calculated as follows:

[0147] θ _ref =45°-φ / 2; where φ is the internal friction angle of the foundation soil;

[0148] η(D _r ) is the state-dependent correction function, which is calculated as follows:

[0149] η(D _r )=1+κ×(D _r -D _r_ref ); where κ is the state sensitivity coefficient, and D _r D represents the relative density of the foundation soil. _r_ref For reference relative density, 0.50 can be taken.

[0150] Another possible method is to use the following formula:

[0151] θ _base =θ _cr ×ψ(h)×η(D_r );

[0152] In the formula, θ _cr The critical principal stress rotation angle is θ. _cr =(45°-φ / 2), where ψ(h) is the soil arch depth development function, calculated as ψ(h)=1-exp(-λ×h / h) _cr ), where h is the penetration depth of the cylinder, h _cr The critical development depth of the soil arching effect; η(D) _r ) is a state-dependent correction function, but its sensitivity coefficient κ can take negative values.

[0153] Another possible method has the following specific formula:

[0154] θ _base =θ _base_interface ×ψ(h)×η(ψ _state );

[0155] In the formula, θ _base_interface The reference rotation angle, which takes into account the effect of interface roughness, can be calculated using the following formula:

[0156] θ _base_interface =(45°-φ / 2)×(1+C _δ ×(δ / φ));

[0157] Where δ is the friction angle at the cylinder-soil interface, C _δ Corresponding interface friction correction coefficient;

[0158] ψ(h) is the depth development function; η(ψ) _state The state-related correction function is based on critical state theory, and its specific form can be:

[0159] η(ψ _state )=1+A×tanh(B×(ψ _state -ψ _ref ));

[0160] Where, ψ _state For the corresponding state parameters, tanh corresponds to the hyperbolic tangent function, A and B correspond to the model parameters, and ψ _ref Corresponding reference state parameters.

[0161] Based on this, the principal stress rotation angle is determined, including:

[0162] The principal stress rotation angle calculated by the method is determined as the limiting rotation angle;

[0163] The soil arch formation rate factor is determined based on the relative density of the foundation soil.

[0164] For the calculation point on the inner wall, the principal stress rotation angle at the calculation point is calculated based on the limit rotation angle, the soil arch formation rate factor, and the relative cumulative displacement associated with the calculation point.

[0165] Specifically, the calculated θ _base This can be considered as the limiting rotation angle θ that can be reached after the soil arching effect is fully developed at the current penetration depth. _lim Near the bottom of the cylinder, the soil arching effect has not yet formed due to the small cumulative displacement. Therefore, the actual principal stress rotation angle θ(z') at any calculation point can be determined by the following dynamic evolution model:

[0166] θ(z')=θ _lim ×(1-exp(-z' / (S _f ×d _1 )));

[0167] In the formula, θ(z') is the actual principal stress rotation angle at the calculation point; θ _lim is the limiting rotation angle; exp is the natural exponential function; z' is the vertical distance from the calculation point to the bottom of the cylinder, which can be regarded as the equivalent relative cumulative displacement; S _f This is the soil arch formation rate factor, which is related to soil density, for example, S. _f =S _f0 ×(1-D _r ), indicating that the denser the soil, the higher the density. _r The larger the rate factor S is, the greater the rate factor S is. _f The smaller the size, the faster the earth arch forms; d _1 S is the inner diameter of the cylinder; _f0 This represents the corresponding initial value.

[0168] Based on this, to account for the influence of suction penetration, the inner wall side pressure coefficient is determined, which further includes:

[0169] Based on the real-time negative pressure applied at the top of the cylinder and the state parameters of the foundation soil, the seepage weakening factor is determined.

[0170] The pressure coefficient of the inner wall side is corrected based on the seepage weakening factor.

[0171] In other words, the seepage weakening factor is obtained based on the real-time negative pressure value applied to the top of the cylinder and the state parameters of the foundation soil.

[0172] Based on this, the pressure coefficient of the inner wall side is corrected.

[0173] The determination of the seepage weakening factor is based on the real-time negative pressure value, the effective unit weight of the soil, the current height of the soil plug in the cylinder, and the state-sensitive seepage coefficient related to the state parameters of the foundation soil.

[0174] During suction penetration, the negative pressure inside the cylinder generates an upward seepage gradient within the soil plug, weakening the effective stress of the soil skeleton. This invention introduces a seepage weakening factor to quantify this effect. The formula for calculating this factor is:

[0175] ζ=1-(p _s / (γ'×h _plug ))×(1+k _s ×(D _r -D _rc ));

[0176] In the formula, ζ is the seepage weakening factor; p _s γ' is the real-time negative pressure applied to the top of the cylinder; h is the effective unit weight of the soil; _plug k represents the current height of the soil plug inside the cylinder. _s D is the state-sensitive seepage coefficient, a parameter reflecting the sensitivity of soil compaction to seepage attenuation. _r D represents relative density. _rc The critical relative density is usually taken as 0.5.

[0177] After calculating the seepage weakening factor, the inner wall side pressure coefficient K was... _1 Make corrections, namely:

[0178] K _1_final =K _1 ×ζ;

[0179] In the formula, K _1_final K is the coefficient of internal wall lateral pressure ultimately used to calculate the internal wall friction coefficient. _1 ζ represents the pressure coefficient of the inner wall side without considering the effect of seepage; ζ is the seepage weakening factor.

[0180] In this embodiment, multiple physical mechanisms, such as coupling between inner and outer walls, various rotation angle algorithms, dynamic evolution, and seepage effects, are integrated into the calculation framework of inner wall friction, forming a prediction method that conforms to physical reality.

[0181] As another example, an alternative approach to determining the end resistance of a cylindrical foundation is provided. A model based on the theory of cylindrical cavity expansion is used to calculate the resistance encountered when the annular end face of the cylindrical foundation penetrates the soil. Furthermore, for the special case of suction-assisted penetration, the weakening effect of negative pressure seepage on the effective stress of the soil at the end of the foundation is introduced, making the prediction of the end resistance more comprehensive and accurate.

[0182] Specifically, determining the end resistance of the cylindrical foundation includes:

[0183] Calculate the initial expansion stress;

[0184] The expansion stress is calculated based on the initial expansion stress and parameters reflecting the elastic-plastic strain characteristics of the foundation soil.

[0185] The end resistance of the cylinder is calculated based on this (expansion stress).

[0186] In other words, the initial expansion stress is calculated based on the soil state parameters and the penetration depth of the cylindrical foundation;

[0187] The expansion stress is calculated based on the initial expansion stress and parameters reflecting the elastic-plastic strain characteristics of the foundation soil.

[0188] The end resistance of the cylinder is calculated based on this (expansion stress).

[0189] Specifically, the cylinder end resistance F _3 The calculation can be expressed as the product of the area of ​​the annular end face of the cylindrical foundation and the expansion stress f, which can be described by the following formula:

[0190] F _3 =f×(π / 4)×((d _1 ) 2 -(d _1 -2t) 2 );

[0191] In the formula, F _3 ρ is the end resistance of the cylinder; f is the expansion stress; π is pi; d _1 t is the inner diameter of the cylindrical foundation; t is the thickness of the cylindrical wall.

[0192] The calculation of the expansion stress f can be performed using the following formula:

[0193] f=f _0 +(ff _0 )×(1-exp(-R / R _u ));

[0194] In the formula, f is the final expansion stress; _0 R is the initial expansion stress; exp is the natural exponential function; R and R _u Specifically, R and R are parameters that reflect the elastoplastic strain characteristics of foundation soil. _u These correspond to the magnitudes of elastic strain and plastic strain in the foundation soil under ideal conditions, respectively, and their values ​​can be determined through geotechnical tests or empirical relationships.

[0195] Furthermore, the initial expansion stress f _0 The formula for calculating can be expressed as:

[0196] f _0 =K _p ×γ×h;

[0197] In the formula, f _0 K represents the initial expansion stress. _pThe passive earth pressure coefficient can be optionally calculated using Rankine's earth pressure theory, i.e., K. _p =tan 2 (45°+φ / 2), where φ is the internal friction angle of the foundation soil; γ is the effective unit weight of the foundation soil; and h is the penetration depth of the cylindrical foundation.

[0198] Based on this, the initial expansion stress can also be calculated using the following method:

[0199] The local hydraulic gradient at the top of the cylinder is determined based on the real-time negative pressure applied at the top of the cylinder.

[0200] The initial expansion stress is corrected based on the local hydraulic gradient at the end of the cylinder.

[0201] In suction conditions, the end of the cylinder, as the outlet of the seepage flow, experiences the largest hydraulic gradient, which weakens the effective stress of the soil in that area and may even lead to a quicksand state. Ignoring this effect will result in an overestimation of the end resistance.

[0202] The determination of the local hydraulic gradient at the cylinder end is based on the real-time negative pressure value, the specific weight of water, and the seepage concentration factor.

[0203] Correspondingly, the method for calculating the local hydraulic gradient i at the end of the cylinder can be:

[0204] i=k _f ×p _s / (γ _w ×h _plug );

[0205] In the formula, i represents the local hydraulic gradient at the end of the cylinder; k _f K is the seepage concentration factor, an empirical coefficient used to account for the non-uniform distribution effect of the seepage field near the cylinder end. Due to the geometric discontinuity at the cylinder end edge, seepage concentration usually occurs, therefore k _f The value of p is usually greater than 1; for example, its range can be 1.2-1.5. _s The real-time negative pressure value applied to the top of the cylinder; γ _w The specific gravity of water; h _plug This represents the current height of the soil plug inside the cylinder.

[0206] After determining the local hydraulic gradient, the initial expansion stress f can be calculated. _0 A correction is made. Since the upward seepage force will offset some of the effective vertical stress generated by the soil's own weight, the corrected initial expansion stress f... _0_modified The calculation formula is:

[0207] f _0_modified =K _p ×(γ×hi×γ_w ×h _tip );

[0208] In the formula, f _0_modified K represents the corrected initial expansion stress. _p γ is the passive earth pressure coefficient; h is the effective unit weight of the foundation soil; i is the penetration depth of the cylindrical foundation; γ is the local hydraulic gradient; _w The specific gravity of water; h _tip The equivalent height of the seepage influence zone near the cylinder end can be approximated as the cylinder wall thickness t in simplified calculations.

[0209] In some alternative implementations, h may not be introduced. _tip Instead, the stress generated by seepage force is directly subtracted from the initial expansion stress, that is:

[0210] f _0_modified =f _0 -i×γ _w ;

[0211] In the formula, f _0 This represents the initial expansion stress, which is uncorrected.

[0212] The corrected initial expansion stress f _0_modified Then, substitute it into the formula to calculate the corrected expansion stress f. _modified The end resistance of the cylinder, which takes into account the effect of seepage, was obtained through calculation.

[0213] The above not only provides a basic calculation framework for cylinder end resistance based on the pore expansion theory, but also proposes a correction method for the quantitative seepage weakening effect for the actual working condition of suction penetration, so that the prediction of cylinder end resistance can maintain high accuracy under different construction conditions.

[0214] According to one aspect of this application, a numerical calculation example is provided to demonstrate the calculation process of the settlement resistance of a cylindrical foundation considering state-dependent factors. The data background of this embodiment comes from centrifugal model tests of the settlement resistance of cylindrical foundations. The calculation results of this invention are compared with experimentally measured data to verify the accuracy, reliability, and engineering practical value of the method provided by this invention.

[0215] Suppose a cylindrical foundation for an offshore wind farm has an inner diameter d of its prototype dimensions. _1 The wall is 6 meters high and the wall thickness t is 10 centimeters, or 0.1 meters. The foundation soil is medium-dense sand, and its basic physical and mechanical parameters, as determined by geotechnical tests, are shown below.

[0216] {Parameters, numerical values, physical meaning; d} _1 6 meters, inner diameter of the cylindrical foundation; t, 0.1 meters, wall thickness of the cylindrical foundation; φ, 36.2 degrees, internal friction angle of the foundation soil; D_r_initial γ', 0.65, initial relative density of foundation soil; γ', 9.71 kN / m³, effective unit weight of foundation soil; a _1 0.18, the basic value of the friction coefficient; a _2 0.20, the rate of increase of the coefficient of friction; A _2 -0.75, equivalent coefficient of cylindrical foundation shape; λ, 0.05, slope of critical state line; Γ, 0.95, critical state porosity under reference pressure; n, 1.5, sensitivity coefficient of state parameter; e _max , 0.90, maximum void ratio; e_min , 0.55, minimum void ratio}.

[0217] The following example demonstrates the calculation process of this invention by taking the calculation of the sinking resistance when the penetration depth h is 5 meters.

[0218] Accordingly, a dynamic iterative method is applied. At a penetration depth of 5 meters, with an initial relative density D... _r_0 The iteration begins with an initial value of 0.65. After several iterations, the final convergent dynamic relative compactness D is assumed to be... _r_final The value is 0.68. This result indicates that at this depth, the soil undergoes slight compaction due to penetration shear.

[0219] The optional calculation method of Example 4 is applied. Accordingly, based on the converged relative density D... _r_final =0.68, calculate the current void ratio e=0.90-0.68×(0.90-0.55)=0.662.

[0220] Furthermore, the average effective stress p' at the current depth is calculated, and the critical state porosity e at this stress level is further calculated. _c =0.650.

[0221] Next, calculate the state parameter ψ=ee. _c =0.662-0.650=0.012. Since ψ>0, it indicates that the soil at this depth is still in a slightly loose, critical state.

[0222] Based on this, the earth pressure coefficient ξ on the outer wall is calculated. _1 Assume the reference earth pressure coefficient K _base If ξ is 0.6, then ξ _1 =0.6×exp(-1.5×0.012)≈0.589.

[0223] Simultaneously, the interfacial friction coefficient μ=a is calculated. _1 +a _2 ×D _r_final =0.18+0.20×0.68=0.316.

[0224] Based on this, calculate the outer wall friction F. _2 =(1 / 2)×0.316×0.589×9.71×5 2 ×π×(6+2×0.1)≈446.7 kN.

[0225] Optionally, a multi-mechanism coupling calculation method can be applied. The basic rotation angle is calculated, taking into account the coupling between the inner and outer walls and dynamic evolution.

[0226] Accordingly, based on the coupling mechanism between the inner and outer walls, the outer wall constraint ratio η is calculated. _out =0.55.

[0227] Calculate the basic rotation angle θ _base Assuming that the interface conditions, depth of development, and state parameter ψ are comprehensively considered, θ is calculated. _base =15.2 degrees.

[0228] Next, the inner and outer wall coupling correction is applied to obtain the corrected rotation angle θ. _coupled =θ _base ×f(η _out f(η) _out ) is (1+η _out ), then θ _coupled =15.2×(1+0.55)=23.56 degrees.

[0229] Next, a dynamic evolution model is applied for correction. θ _coupled Considered as the limiting rotation angle θ _lim At a penetration depth of h = 5 meters, and at the midpoint of the cylinder wall z' = 2.5 meters, θ(z') = 20.5 degrees is calculated.

[0230] Based on the averaged principal stress rotation angle, K is calculated. _1 =2.85.

[0231] Based on this, calculate the inner wall friction F. _1 =(1 / 2)×0.316×2.85×9.71×5 2 ×π×6≈2055.8 kN.

[0232] Accordingly, the initial expansion stress f is calculated. _0 =tan 2 (45°+36.2° / 2)×9.71×5≈189.7 kPa.

[0233] The final expansion stress is calculated to be f = 250.0 kPa.

[0234] Based on this, calculate the cylinder end resistance F. _3=250.0×(π / 4)×(6 2 -(6-2×0.1) 2 F ≈ 463.4 kN. _z =F _1 +F _2 +F _3 =2055.8+446.7+463.4=2965.9 kN.

[0235] By comparing the subsidence resistance, frictional resistance, and end resistance calculated using the above process for different penetration depths with the measured data from centrifugal model tests, comparison curves can be obtained. The resistance curves calculated by the method of this invention show a high degree of agreement with the experimental data points, proving the effectiveness and accuracy of the method provided by this invention. Furthermore, in another set of tests with a changed cylinder wall thickness of 7.5 cm, the method of this invention also exhibited good predictive performance, indicating that this method has good engineering extrapolation properties.

[0236] According to another aspect of this application, a system for calculating the settlement resistance of cylindrical foundations is provided. This system provides a hardware and software implementation platform that can process the physical model and calculation process proposed in this invention, providing technical tools for engineering design and analysis.

[0237] One of them, a system for calculating the settlement resistance of a cylindrical foundation, is characterized by comprising:

[0238] processor;

[0239] Memory, which stores computer programs;

[0240] When the computer program is executed by the processor, it implements the method described in any one of the present invention.

[0241] Accordingly, the system for calculating the settlement resistance of cylindrical foundations can be a general-purpose computer device, such as a personal computer, workstation, or server, or a dedicated embedded computing unit. In terms of hardware structure, this system specifically includes, but is not limited to, a processor, memory, and optionally, input / output interfaces and communication interfaces.

[0242] A processor can be a central processing unit (CPU), a graphics processing unit (GPU), an application-specific integrated circuit (ASIC), or a field-programmable gate array (FPGA), or any other logic circuit capable of executing computational instructions. The processor is used to read and execute computer programs stored in memory to implement the computational tasks defined in this invention.

[0243] Memory can be volatile memory, such as random access memory (RAM), used to store temporary data and intermediate calculation results required during program execution; or it can be non-volatile memory, such as read-only memory (ROM), flash memory, hard disk drive (HDD), or solid-state drive (SSD), used to store computer programs and raw input data for long periods of time, such as the geometric parameters of cylindrical foundations and various physical and mechanical parameters of the foundation soil.

[0244] Input / output interfaces are used to enable data interaction between the system and external devices or users. For example, input interfaces can connect to a keyboard, mouse, or data file reading device to receive calculation parameters input by the user; output interfaces can connect to a monitor or printer to display the final calculated total sinking resistance and detailed results of each component resistance in numerical, tabular, or graphical form.

[0245] In this embodiment, a computer program is stored in the memory. When the processor executes the computer program, it is configured to implement the method as described in any one of the present invention. Specifically, the computer program can be logically divided into multiple functional modules, each module being responsible for executing one or more specific steps in the method of the present invention.

[0246] For example, the input parameter module is used to receive and manage various geometric, physical, and empirical parameters.

[0247] The state evolution module is configured to perform a dynamic iterative calculation process to determine the dynamic state parameters of the foundation soil by iteratively calculating the shear mobilization ratio and updating the relative density at a given penetration depth until the convergence condition is met.

[0248] The outer wall resistance module is configured to provide at least two calculation modes. One mode implements a calculation method based on empirical formulas; the other, optional mode implements a mechanistic calculation method based on critical state theory. Users can choose according to their required calculation accuracy and parameter completeness.

[0249] The inner wall resistance module is configured to implement a comprehensive calculation process integrating multiple physical mechanisms. Specifically, this module can handle the coupling relationship between the inner and outer walls, such as correcting the principal stress rotation angle by calculating the outer wall constraint ratio; the module integrates three selectable principal stress rotation angle calculation algorithms; this module is also configured to execute a dynamic evolution model to reflect the gradual development process of the soil arching effect; in addition, this module also includes the function of handling the influence of negative pressure seepage under suction conditions, and can calculate and apply seepage weakening factors to correct the calculation results.

[0250] The cylinder end resistance module is configured to perform calculations to determine cylinder end resistance. It can calculate the foundation end resistance based on the cavitation expansion theory, and can also correct the initial expansion stress by calculating the local hydraulic gradient under suction conditions.

[0251] The results summary and output module is responsible for summing the calculation results of the outer wall resistance module, the inner wall resistance module, and the cylinder end resistance module to obtain the final total sinking resistance, which is then presented to the user through the output interface.

[0252] It should be understood that the division of functional modules is merely illustrative; in actual software development, functions can be integrated or organized in different ways. The above embodiment provides a computing system, offering a material basis for the engineering application of the technical solution of this invention.

[0253] On the other hand, some methods of the present invention may also include the following steps:

[0254] Optionally, the wall friction F can be calculated based on the relative density of the foundation soil, the friction parameters of the cylinder-foundation interface, the cylinder diameter, and the cylinder wall thickness. 摩 The calculation process shown is as follows:

[0255] F 摩 =F1+F2;

[0256] In the formula, F1 is the frictional resistance of the inner wall of the cylinder; F2 is the frictional resistance of the outer wall of the cylinder.

[0257] Furthermore, the calculation method for the frictional resistance F1 of the inner wall of the cylinder is as follows:

[0258] ;

[0259] In the formula, h represents the penetration depth of the cylinder. c The height of the cylinder end or related features is indicated by γ, the weight of the foundation soil is indicated by μ, the friction coefficient of the cylinder-foundation interface is indicated by d1, and K is the cylinder diameter. p Let K1 represent the passive earth pressure coefficient, K1 represent the inner wall lateral pressure coefficient considering the soil arching effect, m1 be the evolution equation of vertical stress along the arch line, m2 be the calculation equation considering the arch line deflection and soil strength, and h be the passive earth pressure coefficient. cr To determine the critical development depth of the soil arching effect, the influence of both geometric factors and soil compaction must be considered simultaneously.

[0260] Furthermore, the calculation method for the frictional resistance F2 of the outer wall of the cylinder is as follows:

[0261] ;

[0262] In the formula, h is the penetration depth of the cylinder, γ is the weight of the foundation soil, ξ1 is the external earth pressure coefficient considering the cylinder diameter, cylinder wall thickness and foundation soil state parameters, μ is the friction coefficient of the cylinder-foundation interface, d1 is the cylinder diameter, t is the cylinder wall thickness, and ξ1 is the external earth pressure coefficient considering the cylinder diameter, cylinder wall thickness and foundation soil density.

[0263] Optionally, the cylinder end resistance F3 can be calculated based on parameters such as cylinder diameter and cylinder wall thickness. The calculation process is as follows:

[0264] ;

[0265] In the formula, d1 is the cylinder diameter, t is the cylinder wall thickness, and f is the expansion stress.

[0266] Optionally, calculate the sinking resistance F. z The calculation process is as follows:

[0267] F z =F 摩 +F3.

[0268] This invention proposes a bidirectional coupling calculation framework for the frictional resistance between the inner and outer walls. Specifically, when calculating the frictional resistance of the inner wall, an outer wall stress state parameter, such as the outer wall constraint ratio, which characterizes the strength of the external soil constraint, is introduced. This parameter is used to dynamically correct the physical quantity that determines the intensity of the internal soil arching effect, namely the principal stress rotation angle. By establishing a mechanical transmission and influence path from the outer wall to the inner wall, this invention breaks the traditional model of calculating the inner and outer walls independently, making the prediction of the total resistance more consistent with the stress state of the cylinder wall as a mechanical continuum.

[0269] Furthermore, an iterative state evolution mechanism based on shear mobilization was constructed. At each penetration depth increment, this method dynamically solves the problem through a closed-loop iterative process. This process assesses the degree of soil shearing under the current load, i.e., the shear mobilization ratio. Based on this mobilization ratio, the state evolution function is used to update the soil's relative density and other state parameters until convergence. This dynamic approach allows the model to intrinsically simulate the shear contraction or dilatation phenomena that may occur in the soil under penetration shear, ensuring that the soil parameters used in the calculations are consistent with the actual physical processes.

[0270] The optional embodiments of the present invention have been described in detail above. However, the present invention is not limited to the specific details of the above embodiments. Within the scope of the technical concept of the present invention, various equivalent transformations can be made to the technical solution of the present invention, and these equivalent transformations all fall within the protection scope of the present invention.

Claims

1. A method for calculating the settlement resistance of a cylindrical foundation considering state-dependent factors, characterized in that, include: Obtain the geometric parameters and soil state parameters of the cylindrical foundation, and determine the outer wall friction and associated outer wall stress state parameters of the cylindrical foundation. Based on the stress state parameters of the outer wall, the frictional resistance of the inner wall of the cylindrical foundation is determined considering the soil arching effect, and the coupling calculation relationship between the frictional resistance of the inner and outer walls is established. Determine the end resistance of the cylindrical foundation based on geometric parameters and soil condition parameters; The total sinking resistance is calculated based on the frictional resistance of the inner wall, the frictional resistance of the outer wall, and the resistance at the end of the cylinder. The determination of the inner wall friction of the cylindrical foundation specifically includes: determining the inner wall lateral pressure coefficient based on the principal stress rotation angle reflecting the soil arching effect; calculating the inner wall friction based on the inner wall lateral pressure coefficient; wherein the principal stress rotation angle is determined based on the outer wall stress state parameters; and K... _1 =(σ _1 +σ _3 -(σ _1 -σ _3 )×cos(2θ)) / (σ _1 +σ _3 +(σ _1 -σ _3 )×cos(2θ)); where K _1 σ is the pressure coefficient on the inner wall side; _1 σ is the maximum principal stress; _3 The minimum principal stress is θ, which is the principal stress rotation angle. The determination of the principal stress rotation angle specifically includes: determining the outer wall constraint ratio as the outer wall stress state parameter; and correcting the principal stress rotation angle based on the outer wall constraint ratio. The outer wall constraint ratio is defined as the ratio of the normal stress to the vertical stress at the outer wall of the cylindrical foundation.

2. The method according to claim 1, characterized in that, Determining the outer wall friction of the cylindrical foundation specifically includes: The state equation related to the relative compaction in the foundation soil state parameters is invoked to determine the coefficient of earth pressure on the outer wall; The frictional resistance of the outer wall is calculated based on the earth pressure coefficient of the outer wall.

3. The method according to claim 1, characterized in that, Determining the end resistance of a cylindrical foundation includes: Calculate the initial expansion stress based on the soil state parameters and the penetration depth of the cylindrical foundation; The expansion stress is calculated based on the initial expansion stress and parameters reflecting the elastic-plastic strain characteristics of the foundation soil. The end resistance of the cylinder is calculated based on this.

4. The method according to claim 1, characterized in that, The state parameters of the foundation soil are dynamically determined through iterative calculations. Each iteration includes: Based on the foundation soil state parameters obtained from the previous iteration, the shear mobilization ratio is calculated. Based on the shear mobilization ratio, the foundation soil state parameters for the current iteration are updated.

5. The method according to claim 4, characterized in that, Calculating the shear mobilization ratio specifically includes: Based on the foundation soil state parameters obtained from the previous iteration, the ultimate skin friction and the current mobilization skin friction are determined respectively. Calculate the ratio of the current mobilization frictional resistance to the ultimate frictional resistance to obtain the shear mobilization ratio; The updated foundation soil state parameters for the current iteration are as follows: The shear mobilization ratio is input into the state evolution function to adjust the state parameters of the foundation soil.

6. The method according to claim 1, characterized in that, Determining the outer wall friction of the cylindrical foundation specifically includes: Obtain the current void ratio from the foundation soil state parameters; Calculate the critical state porosity at the current stress level; Determine the state parameters based on the difference between the current porosity and the critical state porosity; Determine the earth pressure coefficient of the outer wall based on the state parameters; The frictional resistance of the outer wall was calculated based on the outer wall earth pressure coefficient.

7. The method according to claim 1, characterized in that, Determining the inner wall lateral pressure coefficient further includes: Based on the real-time negative pressure applied at the top of the cylinder and the state parameters of the foundation soil, the seepage weakening factor is determined. The pressure coefficient of the inner wall side is corrected based on the seepage weakening factor.

8. The method according to claim 3, characterized in that, Calculation of initial expansion stress further includes: The local hydraulic gradient at the top of the cylinder is determined based on the real-time negative pressure applied at the top of the cylinder. The initial expansion stress is corrected based on the local hydraulic gradient at the end of the cylinder.

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