A method and system for calculating critical pile length of wharf rock-socketed pile

Abstract

The application provides a wharf rock-embedded pile critical pile length calculation method and system, relates to the critical pile length calculation technical field, through the deep integration and data calibration of numerical simulation and physical test, a high-fidelity comprehensive parameter database is constructed, and a continuous mapping relationship of the critical length-diameter ratio about the base rock strength and the inclination is established. First, numerical analysis is carried out under multiple working conditions, then physical model test is carried out under representative working conditions, the test data are used to construct a correction model to calibrate all simulation results, so that the accuracy of the end resistance ratio prediction is significantly improved. The application effectively solves the dual limitations that the pure numerical method lacks entity verification and the pure theoretical method is difficult to simulate the complex pile-rock contact behavior, through systematically diffusing the discrete test information into the comprehensive simulation data, the stress mechanism of the inclined rock-embedded pile is accurately described, and it is ensured that the mapping relationship established subsequently can truly reflect the physical law under the multi-factor coupling.

Description

Technical Field

[0001] This invention relates to the field of critical pile length calculation technology, specifically to a method and system for calculating the critical pile length of rock-socketed piles for wharves. Background Technology

[0002] Rock-embedded piles, as an important deep-water foundation structure, are widely used in port engineering, cross-sea bridges, and near-shore structures. These pile foundations fully utilize the bearing capacity of the rock mass by embedding the pile into the underlying bedrock, thereby improving the overall stability and resistance to lateral loads. In practical engineering, the design of rock-embedded piles requires comprehensive consideration of multiple factors, including pile inclination angle, bedrock strength, and embedment depth. Determining the critical embedment length is particularly crucial, as it directly affects the bearing capacity of the pile foundation, settlement control, and engineering economics. However, due to the strong nonlinearity of pile-rock contact behavior, the discreteness of rock mass strength, and the complexity of the inclined pile-rock interaction mechanism, traditional calculation methods based on empirical formulas or simplified theories often fail to accurately reflect the actual stress state, easily leading to conservative or insufficient design, affecting project safety and cost.

[0003] Currently, the determination of the critical pile length of rock-socketed piles largely relies on static equilibrium theory, elastic theory solutions, or finite element numerical simulations. While these methods can reflect the stress characteristics of the pile-rock system to some extent, they still have significant limitations. For example, theoretical methods are usually based on homogeneous, isotropic rock masses and ideal pile-rock contact assumptions, making it difficult to realistically simulate interface roughness, nonlinear rock mass failure, and the collaborative working mechanism of inclined piles and rocks after drilling. Pure numerical methods, while considering material nonlinearity and contact behavior, are highly dependent on constitutive models and parameter selection, lacking verification through physical experiments, and their reliability is insufficient, especially under the coupled effects of multiple factors (such as inclination angle, embedment depth, and bedrock strength grade). Furthermore, existing methods mostly focus on vertical piles, with limited research on the end resistance sharing mechanism and critical length variation law of inclined rock-socketed piles, and a systematic parametric design and verification system has not yet been formed. Therefore, engineering practice urgently needs a comprehensive method that integrates numerical simulation, physical experiments, and data-driven correction to more accurately and efficiently determine the critical pile length of wharf rock-socketed piles under different inclination angles and lithological conditions, achieving a balance between safety and economy in the design.

[0004] The information disclosed in the background section is only intended to enhance the understanding of the background of this disclosure, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0005] The purpose of this invention is to provide a method and system for calculating the critical pile length of rock-socketed piles in wharves, so as to solve the problems mentioned in the background art.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] A method for calculating the critical pile length of rock-socketed piles in wharfs, comprising the following steps:

[0008] Step 1: Preset multiple numerical calculation conditions and input them into the analysis model simulating pile-rock contact behavior to obtain the pile top load, pile end resistance and simulated end resistance ratio under each numerical calculation condition. The working parameters of the numerical calculation conditions include inclination angle, rock embedment length and bedrock strength.

[0009] Step 2: Select multiple representative working conditions from the numerical calculation working conditions, prepare model piles and simulate bedrock based on each representative working condition, and conduct physical tests to obtain the pile top load, pile end resistance and measured end resistance ratio under each representative working condition.

[0010] Step 3: Determine the correction coefficient for the representative working condition based on the simulated terminal resistance ratio and the measured terminal resistance ratio, establish a correction model to characterize the mapping relationship between the correction coefficient and the working condition parameters, and use the correction model to correct the simulated terminal resistance ratio to obtain the calibration terminal resistance ratio. Summarize the parameters of each working condition and the corresponding calibration terminal resistance ratio to build a comprehensive parameter database.

[0011] Step 4: Perform fitting analysis on the comprehensive parameter database, establish the attenuation function relationship of the calibration end resistance ratio with the change of working condition parameters, and then determine the critical length-to-diameter ratio under different bedrock strengths and dip angles, and establish a continuous mapping relationship of the critical length-to-diameter ratio with respect to bedrock strength and dip angle;

[0012] Step 5: Determine the critical rock embedment depth of the target project based on the continuous mapping relationship; Analyze the design inclination angle and design pile diameter of the target project by combining the analysis model and the correction model to obtain the calibration end resistance ratio of the target project; Determine whether the calibration end resistance ratio meets the preset requirements to determine the output critical rock embedment length.

[0013] Furthermore, by employing fully factorial or partially factorial experimental design methods, the working parameters are combined to form multiple numerical calculation working conditions for the target project; in the numerical calculation working conditions, each working condition is uniquely determined by a specific set of dip angle, rock embedment length, and bedrock strength values.

[0014] The analysis model is established using the three-dimensional finite element method or the three-dimensional discrete element method. In the analysis model, the pile body adopts an elastic or elastoplastic constitutive model, and the bedrock adopts the Mohr-Coulomb or Hawke-Brown criterion to simulate its elastoplastic failure behavior. The pile-rock contact interface is finely modeled, which is reflected in setting the normal of the contact surface as hard contact and the tangential direction to adopt the Coulomb friction model. The friction coefficient is selected within the preset friction coefficient range according to the surface roughness of the bedrock and the type of pile body material, so as to simulate the actual interface conditions after drilling.

[0015] Four typical inclination angles were set between the pile axis and the vertical direction: 0°, 15°, 30°, and 45°. For each data pair consisting of a typical inclination angle and a bedrock strength, a set of embedment length sequences was set. The length value started from 1 times the pile diameter and increased in increments of 1 times the pile diameter until it reached a length value that made the calculated result of the pile end resistance sharing ratio change by less than 5% for three consecutive times. This ensured that the embedment length sequence completely covered the entire process of pile end resistance from initial exertion to stabilization. The embedment length corresponding to the above-mentioned termination condition was the critical embedment length for the data pair.

[0016] Each numerical calculation condition is input into the analysis model in sequence. The vertical reaction force at the top of the pile under the numerical calculation condition is extracted as the pile top load, the total vertical reaction force at the contact surface at the bottom of the pile is extracted as the pile end resistance, and the ratio of the pile end resistance to the pile top load is calculated as the simulated end resistance ratio.

[0017] For inclined pile conditions, the extracted load and resistance data are decomposed and recorded along the pile axis to ensure consistency with the loading direction of the physical test.

[0018] Furthermore, at least two bedrock strengths are selected from the bedrock strengths covered by the numerical calculation conditions to simulate soft rock and hard rock, respectively; at the same time, four typical dip angles are selected as representative dip angles from the dip angles covered by the numerical calculation conditions.

[0019] The two selected bedrock strengths are cross-combined with four representative dip angles to form a set of main representative working conditions; each main representative working condition is determined by a unique set of bedrock strength and dip angle parameters.

[0020] For each main representative working condition, determine its rock-embedded length sequence and extract at least three key length points from it: the starting length point of the rock-embedded length sequence, an intermediate length point in the middle region of the rock-embedded length sequence, and the critical length point that makes the pile end resistance sharing ratio tend to stabilize.

[0021] Each extracted key length point is combined with the bedrock strength and dip angle parameters in the corresponding main representative working condition to form multiple representative working conditions for physical testing; thus, each main representative working condition generates a set of representative working condition sequences containing different rock embedding lengths.

[0022] Furthermore, the preparation of the model pile and simulated bedrock specifically includes:

[0023] The preparation process of the model pile is as follows: a rigid model pile is prepared using steel, aluminum or engineering plastics, and its elastic modulus is at least 100 times that of the selected simulated bedrock material; the surface of the model pile is sandblasted or treated with sandpaper of a specific particle size to simulate the roughness of the actual pile body, and the friction coefficient between the treated surface and the simulated bedrock material is determined by direct shear test and controlled within the preset friction coefficient range.

[0024] The simulated bedrock preparation process is as follows: using cement mortar or gypsum, by adjusting the mix ratio and curing conditions, homogeneous blocks with different uniaxial compressive strengths are cast to simulate the strength grades of soft and hard rock; during preparation, a micro earth pressure cell is pre-embedded in the mold to ensure that its sensing surface is flush with the preset pile bottom bearing surface.

[0025] Furthermore, on the consolidated bedrock simulation body, prefabricated holes were drilled at four typical inclination angles using a directional drilling tool; model piles were inserted into the holes at typical inclination angles, and grouting material was injected into the pile-rock gap to form a physical interface consistent with the contact conditions set in the analysis model.

[0026] A servo loading system is used, and its loading direction is consistent with the axial direction of the model pile to ensure that the applied load is a pure axial load.

[0027] During the loading process, the pile top load obtained by the force sensor of the loading system and the pile end contact pressure obtained by the micro earth pressure cell are collected and recorded simultaneously.

[0028] For each representative working condition, the total integral value of the pile end contact pressure when it reaches the preset working load or ultimate load is taken as the pile end resistance of that representative working condition; the ratio of the pile end resistance to the synchronously recorded pile top load is recorded as the measured end resistance ratio of that representative working condition.

[0029] Furthermore, the logic for constructing the comprehensive parameter database is as follows:

[0030] The ratio of the measured end resistance ratio to the simulated end resistance ratio for each representative working condition is defined as the correction coefficient for that set of working condition parameter combinations. An initial database is constructed based on all working condition parameter combinations from the numerical calculations, where each record includes dip angle, rock embedment length, bedrock strength, and simulated end resistance ratio. Based on all representative working conditions, a parameterized correction model is constructed using multiple linear regression or machine learning methods, with the simulated end resistance ratio and working condition parameters as input features and the correction coefficient as the output target. The correction coefficient for each numerical calculation working condition in the initial database is obtained based on this correction model, thus yielding the calibrated end resistance ratio. The calibrated end resistance ratio is the product of the simulated end resistance ratio and the corresponding numerical calculation working condition correction coefficient.

[0031] The simulated end resistance ratio in the initial database is updated with the calibration end resistance ratio, ultimately forming a comprehensive parameter database that includes dip angle, rock embedment length, bedrock strength, and calibration end resistance ratio.

[0032] Furthermore, the logic for obtaining the continuous mapping relation is as follows:

[0033] Extract the bedrock strength, dip angle, rock embedment length and their corresponding calibration end resistance ratios for all numerical calculation conditions from the comprehensive parameter database;

[0034] Keeping the bedrock strength and dip angle constant, with the embedment length as the independent variable and the calibration end resistance ratio as the dependent variable, a nonlinear decay function is used to fit the data to establish a decay function relationship between the calibration end resistance ratio and the embedment length; the decay function relationship is in the form of a negative exponential function or a negative power function, and its decay coefficient is expressed as a function of the bedrock strength and dip angle.

[0035] Based on the attenuation function relationship, the rock embedment length corresponding to the decrease of the calibration end resistance ratio to the preset threshold is calculated. The rock embedment length is divided by the pile diameter to obtain the critical length-to-diameter ratio under each group of bedrock strength and dip angle.

[0036] A bivariate nonlinear function incorporating bedrock strength and dip angle is used to perform regression fitting on the obtained critical aspect ratio, establishing a continuous mapping relationship between the critical aspect ratio and bedrock strength and dip angle; the form of the bivariate nonlinear function includes bivariate polynomials and bivariate functions containing trigonometric function terms;

[0037] A set of independent verification conditions is selected to verify the mapping relationship set; the dip angle, bedrock strength, and embedment length parameters of the verification conditions are not included in the comprehensive parameter database; the bedrock strength and dip angle of the verification conditions are substituted into the continuous mapping relationship to calculate the predicted critical aspect ratio, which is then converted into the predicted critical embedment length; the predicted critical embedment length is compared with the actual critical embedment length of the verification condition obtained through physical tests; if the error between the predicted result and the actual measurement is within a preset range, the continuous mapping relationship is confirmed to be valid; the actual critical embedment length is obtained through graded loading physical tests.

[0038] Furthermore, the logic for determining the critical rock-embedded length of the target project is as follows: based on the geological survey report and structural design drawings of the target project, determine its design parameters, including the design pile diameter, design inclination angle, and target bedrock strength;

[0039] Substituting the target bedrock strength and design dip angle into the continuous mapping relationship, the corresponding critical aspect ratio is directly calculated and then converted into the design critical rock embedment depth.

[0040] A calculation model for the target project is created, in which the mechanical parameters of the pile-rock contact interface are set synchronously according to the value range determined by the analysis model to ensure the consistency between the model boundary conditions and the design and construction conditions. The design inclination angle, target bedrock strength, and design critical embedment depth are input into the new calculation model to extract the pile top load and pile end resistance of the target project, and to calculate the simulated end resistance ratio of the target project. This simulated end resistance ratio, together with the design inclination angle, design critical embedment length-to-diameter ratio, and target bedrock strength, is input into the parameterized correction model to obtain the predicted end resistance ratio of the target project.

[0041] Determine whether the predicted end resistance ratio is not greater than the preset threshold. If it is satisfied, output the design critical rock embedment depth as the final recommended value of the critical rock embedment length. If it is not satisfied, generate a design warning, indicating that under the current pile design parameters, the pile end resistance sharing is higher than the safety threshold when the critical state is reached, and give modification suggestions, including increasing the pile diameter and optimizing the pile inclination angle.

[0042] The present invention also provides a calculation system for the critical pile length of rock-socketed piles at wharves. This system is used to implement the aforementioned method for calculating the critical pile length of rock-socketed piles at wharves, and includes:

[0043] The multi-condition numerical simulation analysis module is used to preset various numerical calculation conditions and input them into the analysis model that simulates pile-rock contact behavior to obtain the pile top load, pile end resistance and simulated end resistance ratio under each numerical calculation condition. The working condition parameters of the numerical calculation conditions include inclination angle, rock embedment length and bedrock strength.

[0044] The representative working condition test calibration module is used to extract multiple representative working conditions from the numerical calculation working conditions, prepare model piles and simulate bedrock based on each representative working condition, and conduct physical tests to obtain the pile top load, pile end resistance and measured end resistance ratio under each representative working condition.

[0045] The comprehensive parameter database construction module is used to determine the correction coefficient of the representative working condition based on the simulated end resistance ratio and the measured end resistance ratio, establish a correction model that characterizes the mapping relationship between the correction coefficient and the working condition parameters, and use the correction model to correct the simulated end resistance ratio to obtain the calibration end resistance ratio. It also summarizes the parameters of each working condition and the corresponding calibration end resistance ratio to construct the comprehensive parameter database.

[0046] The mapping relationship establishment module is used to perform fitting analysis on the comprehensive parameter database, establish the attenuation function relationship of the calibration end resistance ratio as a function of the working condition parameters, and then determine the critical aspect ratio under different bedrock strengths and dip angles, and establish a continuous mapping relationship of the critical aspect ratio with respect to bedrock strength and dip angle.

[0047] The critical embedding length determination module is used to determine the design critical embedding depth of the target project based on a continuous mapping relationship; it obtains the calibration end resistance ratio of the target project by jointly analyzing the design inclination angle and design pile diameter of the target project according to the analysis model and the correction model; it determines whether the calibration end resistance ratio meets the preset requirements to determine the output critical embedding length.

[0048] The technical effects and advantages provided by the present invention in the above technical solution are as follows:

[0049] This invention effectively addresses the shortcomings of traditional methods, such as insufficient nonlinear simulation of pile-rock contact, unclear stress mechanism of inclined piles, and lack of verification due to reliance on experience, by combining numerical analysis, physical experiments, and data calibration. Furthermore, by establishing a parametric correction model, this invention deeply integrates numerical calculation results with physical model test data, significantly improving the prediction accuracy of the end resistance sharing ratio under different inclination angles, embedment lengths, and bedrock strength conditions. This allows for a more scientific determination of the critical embedment length. In addition, the systematic verification process ensures the reliability of the design results under actual engineering parameters, avoiding material waste caused by overly conservative designs and preventing engineering risks due to insufficient bearing capacity estimation. This provides accurate, practical, and economical technical support for the design of inclined rock-embedded piles for wharves. Attached Figure Description

[0050] Figure 1 This is a schematic diagram of the overall method flow of the present invention;

[0051] Figure 2 This is a schematic diagram of the contour lines of the simulated critical aspect ratio data of the present invention;

[0052] Figure 3 This is a schematic diagram of the system structure of the present invention. Detailed Implementation

[0053] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments.

[0054] It should be noted that, unless otherwise defined, the technical or scientific terms used in this invention should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0055] Example:

[0056] Please see Figures 1 to 2 The present invention provides a technical solution:

[0057] A method for calculating the critical pile length of rock-socketed piles in wharfs, comprising the following steps:

[0058] Step 1: Preset multiple numerical calculation conditions and input them into the analysis model simulating pile-rock contact behavior to obtain the pile top load, pile end resistance and simulated end resistance ratio under each numerical calculation condition. The working parameters of the numerical calculation conditions include inclination angle, rock embedment length and bedrock strength.

[0059] In this embodiment, a fully factorial experimental design method is preferably used. This method can consider all factors (operating parameters) and all combinations of their levels, thereby comprehensively revealing the influence of each factor and its interactions on the response variable (terminal resistance ratio). If the large number of operating parameters and their levels leads to excessive computation, a partial factorial experimental design, such as an orthogonal design, can also be used to reduce the number of calculated operating conditions without significantly losing information.

[0060] Assuming we consider three factors: dip angle (A), embedment length (B), and bedrock strength (C), if the dip angle has four levels (0°, 15°, 30°, 45°), the bedrock strength has two levels (soft rock and hard rock), and the embedment length has ten levels (1D, 2D, ..., 10D, where D is the pile diameter), then the total number of working cases involved in a fully factorial analysis is 80. If a partial factorial analysis is used, for example, focusing only on the main interactions, the number of working cases may be reduced; the specific combination method needs to be arranged according to an orthogonal array.

[0061] The working parameters are combined to form multiple numerical calculation working conditions for the target project; in the numerical calculation working conditions, each working condition is uniquely determined by a specific set of dip angle, rock embedment length and bedrock strength values.

[0062] Inclination angle: Four typical inclination angles are set between the pile axis and the vertical direction: 0°, 15°, 30°, and 45°. This covers the range from vertical piles to common large-angle inclined piles, and can reflect the influence of inclination angle changes on the pile-rock interaction mechanism.

[0063] Rock embedment length: To fully capture the entire process of pile end resistance from its initial development to gradual stabilization and then to a constant value, an incremental sequence of rock embedment lengths is defined for each typical dip angle and bedrock strength combination. The length value starts at 1 times the pile diameter (1D) and increases in increments of 1 times the pile diameter (1D). The termination condition for this increase is: when the calculated pile end resistance sharing ratio (i.e., the ratio of pile end resistance to pile top load) changes by less than 5% for three consecutive times, the rock embedment length is stopped. This last length value is the numerical simulation estimate of the critical rock embedment length corresponding to that specific bedrock strength and dip angle. This process ensures that the rock embedment length sequence fully covers the entire physical process from short piles (where end resistance dominates) to long piles (where side resistance dominates and end resistance tends to stabilize).

[0064] Bedrock Strength: Based on common rock masses encountered in engineering projects, at least two representative bedrock strength grades should be defined. For example, the uniaxial compressive strength (UCS) value can be used to differentiate between soft rock (UCS ≤ 5 MPa) and hard rock (UCS > 30 MPa). Specific UCS values ​​are input into the model; for example, 2 MPa can be used for soft rock and 50 MPa for hard rock.

[0065] The analysis model employs either the three-dimensional finite element method (e.g., using software such as ABAQUS or ANSYS) or the three-dimensional discrete element method (e.g., using...). A refined analysis model is established using software such as [software name missing]. The finite element method is suitable for simulating the deformation and failure of continuous media, while the discrete element method has advantages in dealing with rock mass joints, cracks, and fractures. In this embodiment, the three-dimensional finite element method is preferred.

[0066] In the analysis model, considering that the rock-socketed piles of the wharf are usually reinforced concrete structures with stiffness much greater than that of the rock mass and relatively small nonlinear deformation, a linear elastic constitutive model can be used to simulate the piles. The required input parameters are the elastic modulus (e.g., 30 GPa) and Poisson's ratio (e.g., 0.2). If it is necessary to analyze the strength failure of the pile body, an elastoplastic constitutive model, such as the Mohr-Coulomb model, can be used.

[0067] The mechanical behavior of bedrock is complex, requiring models that can describe its plastic yielding and failure. This embodiment adopts the Mohr-Coulomb criterion because its parameters have clear physical meanings and are easy to obtain. The required input parameters include: elastic modulus (e.g., 0.5 GPa for soft rock, 10 GPa for hard rock), Poisson's ratio (e.g., 0.25), cohesion (e.g., 0.5 MPa for soft rock, 2 MPa for hard rock), internal friction angle (e.g., 25° for soft rock, 40° for hard rock), and dilatation angle (approximately 0° or 1 / 3 of the internal friction angle). For rock masses with well-developed joints and fractures, the Hoek-Brown criterion can also be used, as it better reflects the influence of rock mass structural planes.

[0068] Detailed modeling of the pile-rock contact interface is crucial to the success of the simulation, as the pile-rock contact behavior directly determines the load transfer mechanism. Detailed modeling specifically involves:

[0069] The normal direction of the contact surface is set to hard contact, which means that the contact surface is allowed to transmit pressure when under compression and separate without transmitting tension when under tension. This simulates the actual physical state of the pile-rock interface.

[0070] The tangential behavior is simulated using the Coulomb friction model to represent the interfacial shear stress transfer. The friction coefficient is the core parameter of the Coulomb friction model, and its value should be determined comprehensively based on the surface roughness of the bedrock and the type of pile material. It is not a fixed value, but rather a value within a preset range. In this embodiment, this range is preset to 0.3 to 0.8, which is based on statistical analysis of a large amount of direct shear test data at the rock-concrete (or steel) interface. When the bedrock surface is rough (e.g., using artificial roughening) or the pile body has a rough surface (e.g., a precast pile surface with scoring), the interfacial interlocking is strong, and the friction coefficient can be high (0.6-0.8); when the bedrock surface is smooth (e.g., a naturally smooth mudstone surface) or the pile body is made of smooth steel, the friction coefficient should be low (0.3-0.5).

[0071] For example, for simulating the interface between soft rock with moderate roughness and sandblasted steel piles, the friction coefficient can be taken as 0.5. In practical applications, to determine this value more accurately, it can be determined through a specially designed direct shear test of the rock-concrete (or steel) section. Following ASTM D3080 or similar standards, prepare rock specimens and pile material specimens identical or similar to those used in the actual project, conduct direct shear tests under different normal stresses, and determine the interface friction angle using the Coulomb strength envelope. The friction coefficient is then tan(angle of friction). If testing is not possible, Barton's model can be used for estimation.

[0072] All preset numerical calculation conditions (such as the 80 combinations mentioned above) are sequentially input into the established three-dimensional finite element analysis model for solution calculation. During the calculation, a vertical concentrated force or displacement load is applied to the pile top. After the calculation is completed, key data are extracted from the post-processing results, including:

[0073] Pile top load: Extract the vertical reaction force at the pile top reference point (RP point);

[0074] Pile end resistance: Extract the nodal forces at the contact surfaces between all elements at the pile bottom and the bedrock, and sum them to obtain the total vertical reaction force. For inclined piles, the nodal force vectors need to be projected onto the pile axis before summing.

[0075] Simulated end resistance ratio: This is the ratio of pile end resistance to pile top load. This ratio is a key indicator for measuring the degree to which the pile end bearing capacity is utilized. The smaller the value, the more the load is borne by the pile side skin friction, and the smaller the pile end effect. When the rock embedment length reaches a critical value, this ratio will tend to a very small stable value. For inclined pile conditions, to ensure consistency with the loading direction of subsequent physical tests, all extracted load and resistance data are decomposed and recorded along the pile axis.

[0076] Step 2: Select multiple representative working conditions from the numerical calculation working conditions, prepare model piles and simulate bedrock based on each representative working condition, and conduct physical tests to obtain the pile top load, pile end resistance and measured end resistance ratio under each representative working condition.

[0077] In this embodiment, at least two bedrock strengths are selected from the bedrock strengths covered by the numerical calculation conditions, respectively, to simulate soft rock and hard rock.

[0078] Meanwhile, from the inclination angles covered by the numerical calculation conditions, four typical inclination angles (0°, 15°, 30°, and 45°) were selected as representative inclination angles. All were selected because the change in inclination angle has a significant impact on the force mechanism of the pile-rock contact surface, and all must be covered to establish a complete correction model.

[0079] The two selected bedrock strengths are cross-combined with four representative dip angles to form a set of main representative working conditions. For example, when soft rock and hard rock strengths are selected, the number of main representative working conditions is: Each primary representative working condition is determined by a unique set of bedrock strength and dip angle parameters;

[0080] For each representative working condition, determine its rock-socketed length sequence and extract at least three key length points: the starting length point of the rock-socketed length sequence; and the minimum value in the rock-socketed length sequence, i.e., 1 times the pile diameter. This working condition represents a short pile state where pile end resistance is dominant.

[0081] An intermediate length point in the middle region of the rock-socketed length sequence: for example, taking 1 / 2 of the critical length point or an integer multiple of the pile diameter (such as 3D or 5D) that is not equal to 1D or the critical length point. This condition represents the state in which the pile side friction and pile end resistance act together.

[0082] The critical length point at which the pile end resistance sharing ratio tends to stabilize represents the critical state where the pile side friction has been fully utilized and the pile end resistance tends to be constant.

[0083] Assuming that for the representative working condition of soft rock and 0° dip, the rock embedment length sequence is 1D, 2D, 3D, 4D, 5D, 6D, where 6D is the critical length, then the extracted representative working conditions include (soft rock, 0°, 1D), (soft rock, 0°, 3D), and (soft rock, 0°, 6D).

[0084] Each extracted key length point is combined with the bedrock strength and dip angle parameters of the corresponding master representative working condition to form multiple representative working conditions for the final physical tests. Thus, each master representative working condition generates a sequence of representative working conditions containing three different embedment lengths. The eight master representative working conditions form a total of 24 representative working conditions. If parallel testing is considered to eliminate random errors, the number of tests should be doubled accordingly.

[0085] In this embodiment, the preparation of the model pile and simulated bedrock specifically includes:

[0086] The fabrication process of the model pile is as follows: a rigid model pile is fabricated using steel (45# steel), aluminum (such as LY12 aluminum alloy), or high-strength engineering plastics. The elastic modulus is at least 100 times that of the selected simulated bedrock material to ensure that the pile body exhibits rigidity relative to the bedrock, thereby concentrating deformation at the pile-rock interface and the bedrock itself. For example, if the simulated bedrock elastic modulus is 1 GPa, then the elastic modulus of the model pile material should not be less than 100 GPa; steel (approximately 210 GPa) can meet this requirement.

[0087] To simulate the roughness of piles in actual engineering projects, the model surface needs to be artificially treated. Specifically, this involves sandblasting or applying sandpaper of a specific grit size. Sandblasting involves using quartz sand of a certain mesh size (e.g., 20-60 mesh) to blast the pile surface, resulting in a uniformly rough surface. Applying sandpaper involves selecting sandpaper of a specific grit size (e.g., 40 mesh, 80 mesh) corresponding to the target coefficient of friction and uniformly applying it to the pile surface with high-strength epoxy resin.

[0088] The friction coefficient between the treated model pile surface and the simulated bedrock material needs to be determined through a direct shear test. The treated pile material specimen and the cast-in-place bedrock simulation material specimen (with the same mix proportion) are placed in a direct shear apparatus and sheared under different normal stresses. The friction coefficient is calculated according to Coulomb's law. By adjusting the sandpaper grit size or sandblasting process, the measured friction coefficient is ensured to fall within the preset range (e.g., 0.3-0.8) in step 1 to guarantee the comparability of the interface conditions between the physical test and the numerical simulation.

[0089] The simulated bedrock preparation process involves using cement mortar or gypsum-based materials, and adjusting the water-cement ratio, mortar-bond ratio, and curing conditions to simulate rock masses of different strengths. Cement mortar is suitable for simulating hard rock, while gypsum is more suitable for simulating soft rock.

[0090] By adapting the materials in advance, a curve relating the material mix ratio to the uniaxial compressive strength is established to accurately obtain the target strength. For example, to simulate soft rock with a strength of 2 MPa, a gypsum:water ratio of 1:1.2 (by weight) can be used, and the mixture can be cured for 7 days under standard conditions. To simulate hard rock with a strength of 50 MPa, a cement:sand:water ratio of 1:1.5:0.4 (by weight) can be used, with the addition of an appropriate amount of water-reducing agent, and the mixture can be cured for 28 days.

[0091] To accurately measure pile end resistance, miniature earth pressure cells need to be pre-embedded in the mold during the pouring of simulated bedrock. The earth pressure cells are fixed at the pre-set pile bottom bearing surface position at the bottom of the mold, ensuring that their sensing surface is flush with the pre-set pile bottom plane and facing the pile bottom to receive the pressure transmitted from the pile end. Careful vibration is required during pouring to avoid damaging the sensor or changing its position. The earth pressure cell's lead wires are led out from a pre-drilled hole in the side wall of the mold and connected to the data acquisition system.

[0092] In this embodiment, prefabricated holes are drilled at four typical inclination angles (0°, 15°, 30°, and 45°) on a solidified simulated bedrock test block that has reached the design strength. The hole diameter should be slightly larger than the diameter of the model pile to ensure smooth pile implantation and to leave a uniform gap for subsequent grouting. The prepared model pile is then implanted into the hole at the corresponding typical inclination angle.

[0093] A servo loading system (such as an electro-hydraulic servo universal testing machine) is used for loading. During loading, the actuator angle is adjusted or a special loading fixture is used to ensure that the loading direction is consistent with the axial direction of the model pile, thereby ensuring that the applied load is a pure axial load.

[0094] During the loading process, a graded loading method can be used. The increment of each load level is 1 / 10 to 1 / 15 of the estimated ultimate load. Each load level is maintained for 5-10 minutes or until the deformation stabilizes. Then the data is recorded, and the next load level is applied until the model fails and reaches the predetermined maximum load.

[0095] During the loading process, two types of data are collected simultaneously using a dynamic data acquisition device:

[0096] Pile top load: recorded in real time by a high-precision force sensor integrated into the loading system;

[0097] Pile tip contact pressure: The pressure value is recorded in real time by a miniature earth pressure cell embedded at the bottom of the pile.

[0098] For each representative working condition, when the preset working load (e.g., design load) or ultimate load is reached, the collected pile tip contact pressure is integrated over the pile bottom area to obtain the total pile tip resistance under that working condition. If the pile bottom pressure is uniformly distributed, the pile tip resistance is the product of the pile tip contact pressure and the pile bottom area. If multiple earth pressure cells are used, the average value or a weighted integration can be taken. The calculated pile tip resistance is then... Simultaneously recorded pile top load The ratio of the two values ​​is denoted as the measured terminal resistance ratio for the representative operating condition, i.e. .

[0099] For example, when loading is applied to the (soft rock, 0°, 1D) working condition, the load on the pile top... When the pressure reaches 10 kN, the micro earth pressure cell reading is recorded as 0.5 MPa. The pile bottom area is 0.005 m². Therefore, the pile end resistance... The measured terminal resistance ratio was calculated. .

[0100] Step 3: Determine the correction coefficient for the representative operating condition based on the simulated terminal resistance ratio and the measured terminal resistance ratio, establish a correction model to characterize the mapping relationship between the correction coefficient and the operating condition parameters, and use the correction model to correct the simulated terminal resistance ratio to obtain the calibration terminal resistance ratio. Summarize the parameters of each operating condition and the corresponding calibration terminal resistance ratio to construct a comprehensive parameter database.

[0101] In this embodiment, due to the inherent limitations of numerical simulation in terms of material constitutive properties, boundary conditions, and simplified contact behavior, there will inevitably be a deviation between the calculated results (simulated end resistance ratio) and the physical test results (measured end resistance ratio). The core of this step is to use limited physical test data to establish a correction model, systematically mapping this deviation back to all numerical calculation conditions, thereby obtaining a calibration dataset that is closer to the true physical laws.

[0102] The correction factor serves as a bridge between numerical simulation and physical experimentation. It quantifies the degree of deviation between the numerical simulation results and the actual physical response under specific operating conditions.

[0103] For each representative operating condition obtained through physical testing, the ratio of its measured terminal resistance ratio to the simulated terminal resistance ratio under the corresponding operating condition parameters is defined as the correction coefficient for that set of operating condition parameters. Its mathematical expression is: Where k represents the correction factor. The value represents the simulated end resistance ratio. When k > 1, it indicates that the numerical simulation underestimates the pile end resistance sharing ratio, meaning that the pile end bears more load in the physical test; when k < 1, it indicates that the numerical simulation overestimates the pile end resistance sharing ratio; when k ≈ 1, it indicates that the numerical simulation and physical test are in good agreement.

[0104] For example, for the (soft rock, 0°, 1D) working condition, assuming the numerical simulation of the (soft rock, 0°, 1D) working condition with the same parameters in step 1, the calculated simulated end resistance ratio... (This value is for illustrative purposes only). The measured terminal resistance ratio obtained through physical testing in step 2. Therefore, the correction factor for this working condition is k = 0.25 / 0.3 ≈ 0.833. This figure indicates that, for this working condition, the numerical simulation overestimated the pile end resistance sharing ratio by approximately 16.7%.

[0105] Repeat the above calculation for all representative working conditions selected in step 2 (e.g., 24 working conditions) to obtain a set of discrete correction coefficients. Each correction factor corresponds to a specific combination of working condition parameters (dip angle, rock embedment length, bedrock strength), which constitutes the basic data for the subsequent establishment of a parameterized correction model.

[0106] Before making corrections, all numerical calculation cases and their results obtained in Step 1 need to be systematically organized. Based on all preset numerical calculation cases, an initial database is constructed. The initial database is stored in tabular form, with each record (row) corresponding to an independent numerical calculation case. Each record includes at least the following fields: Case ID (unique identifier), dip angle (e.g., 0°, 15°, 30°, 45°), rock embedment length (e.g., 1D, 2D, 3D, etc., expressed in meters or dimensionless diameter ratios), bedrock strength (e.g., expressed as uniaxial compressive strength UCS values ​​of 2MPa, 50MPa, or classification grades of soft rock and hard rock), and simulated end resistance ratio (the end resistance ratio extracted and calculated from the numerical simulation results).

[0107] For example, a record in the initial database might be [Working Condition 001, Dip Angle = 0°, Rock Embedding Length = 1D, Bedrock Strength = 2MPa, Another record is: [Working condition 002, dip angle = 15°, rock embedment length = 5D, bedrock strength = 50MPa,] ].

[0108] Discrete correction coefficients alone are insufficient to correct for all numerical calculation conditions because these discrete points cannot cover the entire parameter space. Therefore, it is necessary to establish a continuous function or model that can predict the corresponding correction coefficients based on arbitrary input condition parameters, i.e., a parameterized correction model.

[0109] This invention can employ various methods to construct this corrected model, with the specific choice depending on the complexity of the data and the required accuracy.

[0110] Method 1: Multiple Linear Regression

[0111] This approach is suitable for situations where there is an approximately linear relationship between the correction factor and the operating parameters, or where the relationship can be linearized through variable transformation. It can be assumed that the correction factor is a linear function of the dip angle, the embedded length, the bedrock strength, and their interaction terms, for example:

[0112]

[0113] in, Indicates the angle of inclination. Indicates the length of the embedded rock. Indicates bedrock strength. to For the undetermined regression coefficients, This is the error term.

[0114] Using the 24 representative working conditions obtained in step 2 The data can be solved using the least squares method in statistical software (such as SPSS or R language) to obtain the estimated values ​​of each regression coefficient, thereby determining the specific linear regression equation.

[0115] Method 2: Machine Learning Method

[0116] This method is suitable when there is a complex nonlinear relationship between the correction coefficient and the operating parameters, and when the amount of data is relatively large. It can automatically capture high-order interactions and nonlinear patterns in the data. Artificial neural networks, support vector regression, or random forests can be used as methods.

[0117] Preferably, random forest regression is used. The dip angle, embedded length, and bedrock strength, representing the working condition, are used as input features (independent variables), and the correction coefficient is used as the output target (dependent variable). The dataset is divided into training and validation sets using random partitioning or K-fold cross-validation. Specifically, a hold-out method is used, randomly selecting 70% of the total dataset (approximately 17 samples) as the training set to train the random forest model; the remaining 30% (approximately 7 samples) is used as the validation set to evaluate the model's generalization ability and prediction accuracy. To eliminate the randomness introduced by random partitioning, 5-fold cross-validation can be used: the dataset is randomly divided into 5 equal parts, with 4 parts used as the training set and 1 part as the validation set alternately, repeated 5 times, and the average performance index is taken.

[0118] The performance of a random forest model is highly dependent on the settings of its core parameters. The preferred parameter design in this invention is as follows, along with the basis and range for parameter adjustment: Initially, the total number of regression decision trees in the random forest is set to 100. Too few trees may lead to underfitting and insufficient prediction accuracy; too many trees will increase computational overhead, and once the number reaches a certain value, the model's performance improvement will tend to plateau or even saturate. Typically, the number of trees is set between 100 and 500. For regression problems, the default value for the maximum number of features is usually 1 / 3 of the total number of features. In this example, the total number of features is 3, so the maximum number of features is initially set to 1. The maximum number of features controls the randomness of the trees. The smaller the value, the lower the correlation between trees, and the stronger the model's resistance to overfitting, but the predictive ability of a single tree may decrease; the larger the value, the higher the correlation between trees, and the more the model emphasizes overall fitting ability. Typically, cross-validation is used to search between 1 and the total number of features to select the value that minimizes the error on the validation set. The maximum depth of the decision tree limits the maximum number of layers each tree can grow; initially, it is set to unlimited (or a large value, such as 10) to allow the trees to grow fully. Limiting tree depth prevents a single tree from overfitting to noise in the training data. Excessive depth may cause the tree to learn detailed noise from the training data, leading to overfitting; insufficient depth may result in underfitting. A suitable depth can be chosen through cross-validation, or the tree's complexity can be controlled by other parameters (such as the minimum number of samples per leaf node). The minimum number of samples per leaf node is initially set to 5; this parameter also controls tree growth and prevents overfitting. A larger value makes the tree less likely to grow too deep and the model smoother, but may lose local details; a smaller value makes the tree more complex and may lead to overfitting. It is typically set to a value between 1 and 10 and optimized through cross-validation.

[0119] In a Python environment (such as Jupyter Notebook), import the `RandomForestRegressor` class from the scikit-learn library and create a random forest regressor object according to the parameters set above. Call the object's `fit()` method, inputting the feature matrix and target vector of the training set, and training will begin. The training process will automatically build 100 decision trees, each on its corresponding Bootstrap sample set, recursively growing according to the principle of feature randomness. Regardless of the method used, the established modified model needs to be validated. Input the working condition parameters of the validation set that were not involved in model training into the model to obtain the predicted correction coefficients, and compare them with the actual correction coefficients calculated based on physical experiments. If the prediction error is within an acceptable range (e.g., the average relative error is less than 10%), the modified model is confirmed to be effective and can be used for subsequent modifications to all working conditions.

[0120] After training, the feature matrix of the validation set is input into the trained model, and the `predict()` method is called to obtain the predicted values ​​of the correction coefficients for the validation set samples. The predicted values ​​are compared with the true target values ​​of the validation set, and evaluation metrics are calculated, including the coefficient of determination, root mean square error, and mean absolute error.

[0121] If the performance of the initial model's validation set does not meet the requirements, parameter tuning is necessary, for example, by using a grid search combined with cross-validation.

[0122] The final training and validation yields a random forest regression model with the optimal parameter combination, which is the final parameterized correction model. Using this established and validated parameterized correction model, all numerical computational scenarios in the initial database can be corrected, resulting in a physically calibrated dataset covering the entire parameter space.

[0123] The working parameters (dip angle, rock embedment length, bedrock strength) of each record (i.e., each numerical calculation case) in the initial database are used as inputs and substituted into the established parameterized correction model (such as a trained random forest model or a determined regression equation) to calculate the correction coefficient corresponding to the working condition.

[0124] The simulated end resistance ratio for each numerical calculation condition is multiplied by its corresponding correction factor to obtain the calibrated end resistance ratio for that condition. This calibrated end resistance ratio is a comprehensive estimate that combines the efficiency of numerical simulation with the accuracy of physical experiments. It represents the pile end resistance sharing ratio that is closer to the actual physical situation under that specific condition.

[0125] Using the initial database as a template, the simulated end resistance ratio field in each record is replaced or a calibration end resistance ratio field is added. The resulting comprehensive parameter database contains the dip angle, rock embedment length, bedrock strength and their corresponding calibration end resistance ratios for all numerical calculation conditions.

[0126] Through the above steps, this invention successfully disseminates and integrates discrete and costly physical experiment information into a comprehensive numerical simulation dataset, constructing a high-fidelity, high-coverage integrated parameter database.

[0127] Step 4: Perform fitting analysis on the comprehensive parameter database to establish the attenuation function relationship between the calibration end resistance ratio and the working condition parameters, thereby determining the critical aspect ratio under different bedrock strengths and dip angles, and establishing a continuous mapping relationship between the critical aspect ratio and bedrock strength and dip angle. In this embodiment, all data used for modeling are extracted from the comprehensive parameter database constructed in Step 3. Records under all numerical calculation working conditions are extracted from the database, and each record contains four core fields: bedrock strength... (For example, expressed as uniaxial compressive strength UCS value, in MPa), inclination angle (Units are degrees or radians), rock embedment length (usually in terms of aspect ratio) This indicates (dimensionless) and its corresponding calibration terminal resistance ratio. For ease of subsequent fitting, we first consider the bedrock strength. and tilt angle Group the data. For example, if the database contains two bedrock strengths (2MPa, 50MPa) and four dip angles (0°, 15°, 30°, 45°), the data is grouped. There are several data sets. Each data set describes the data in a fixed... and Under the condition, the resistance ratio at the calibration terminal With rock embedment length The changing pattern.

[0128] For each fixed combination, The ratio decreases as L / D increases, and the rate of decrease gradually changes until it eventually tends to a stable value (i.e., the pile side friction has been fully utilized, and the pile end resistance sharing ratio no longer decreases significantly). This law is very suitable for being described by a nonlinear decay function.

[0129] The present invention preferably uses the following two forms of nonlinear decay functions for fitting, and the specific choice depends on the best fitting effect of the data.

[0130] Form 1: Negative exponential function:

[0131]

[0132] in, is the aspect ratio; a, b, and c are the parameters to be fitted. Parameter a controls the initial descent of the curve, parameter b controls the rate of decay (i.e., the steepness of the curve), and parameter c represents the value when the embedded length approaches infinity. The approximate residual value (i.e., the lower limit of the terminal resistance ratio).

[0133] Form 2: Negative power function:

[0134]

[0135] in, , , The parameters to be fitted are: For proportionality coefficients, parameters The power exponent (controls the rate of decay), parameter This also represents the residual value of the terminal resistance ratio.

[0136] The nonlinear least squares method was used to fit each data set separately using mathematical software (such as MATLAB, OriginPro, or Python's SciPy library).

[0137] With bedrock strength S=50MPa and dip angle Taking the data set as an example, this data set includes the calibration terminal resistance ratio at different aspect ratios, i.e. ,Right now ,Right now ,Right now ,Right now ,Right now ,Right now ,Right now In Python, the `scipy.optimize.curve_fit` function is used to call the negative exponential function model. Fit the above data. The fitting result may be: , , Thus, we obtained this specific and The specific attenuation function relationship under the combination is as follows:

[0138]

[0139] Goodness of fit A value greater than 0.99 indicates a very good fit.

[0140] Observing the above fitting process, it can be found that for different S and The parameters a, b, c obtained from the fitting or , , These parameters are variable. Therefore, they can be further expressed as bedrock strength S and dip angle. The function.

[0141] The critical length-to-diameter ratio is the core engineering indicator to be output in this embodiment. It is defined as follows: when the rock embedment length reaches a certain value, the pile end resistance sharing ratio decreases to a negligible level. At this point, further increasing the rock embedment length will have little contribution to improving the bearing capacity. This rock embedment length is the critical rock embedment length, and its ratio to the pile diameter is the critical length-to-diameter ratio.

[0142] The key to this embodiment is defining how to reduce the load to a negligible level. This embodiment introduces a preset threshold to quantify this level. The preset threshold refers to the maximum ratio of pile end resistance to pile top load that we allow under critical conditions. When the calibrated end resistance ratio is less than or equal to this preset threshold, we consider the pile end effect to be negligible, and the corresponding rock embedment length is the critical rock embedment length.

[0143] Based on the different requirements of settlement control and load-bearing safety for the target project, the preset threshold is selected within the range of 5% to 15%. Extensive engineering practice and research show that when the pile end resistance sharing ratio is below approximately 10%, the load borne by the pile end is very limited, and the pile foundation bearing characteristics are mainly controlled by the pile side skin friction. At this point, further increasing the embedment depth significantly reduces the effect on improving bearing capacity. For structures with extremely strict settlement requirements (such as high-pile wharves and precision equipment foundations), a smaller threshold (e.g., 5%) can be selected to ensure that the vast majority of the load is borne by the side skin friction, thereby effectively controlling pile end settlement. This corresponds to a more conservative design. For structures with general settlement control requirements, a larger threshold (e.g., 15%) can be selected, allowing the pile end to bear a portion of the load, thereby appropriately reducing the embedment depth while ensuring safety and improving economy. The technical solution of this invention allows designers to flexibly select this threshold between 5% and 15% according to specific project needs, reflecting the adaptability and flexibility of the method.

[0144] For each fixed S and By combining the fitted attenuation function relationship with the preset threshold, the corresponding critical aspect ratio can be obtained.

[0145] By performing the above calculations on each of the eight data sets (two intensities × four tilt angles), a set of discrete critical aspect ratio data points can be obtained.

[0146] The discrete data points mentioned above can only provide the critical aspect ratio for specific strengths and dip angles, and cannot cover all possible engineering situations. Therefore, it is necessary to establish a continuous function, i.e., a continuous mapping relationship, with bedrock strength and dip angle as independent variables and critical aspect ratio as the dependent variable.

[0147] Selection of the form of the bivariate nonlinear function: Based on the distribution trend of the data points and the qualitative understanding of the mechanical mechanism, the present invention can use the following two forms of bivariate nonlinear functions for regression fitting.

[0148] Form 1: Bivariate polynomial function:

[0149]

[0150] in, This is a constant term, representing the benchmark critical aspect ratio when both the bedrock strength and dip angle are zero (or the benchmark value); and These are bedrock strength and tilt angle The coefficient of the first-order term reflects S and The linear main effect on the critical aspect ratio; and They are and The quadratic coefficients are used to capture the critical aspect ratio as a function of S or Nonlinear bending tendency during change; It is an interactive item The coefficient quantifies the coupling effect between bedrock strength and dip angle, i.e., whether the influence of one factor on the critical aspect ratio changes with the change of another factor. This form is highly versatile and can approximate arbitrarily complex surfaces by adding higher-order terms.

[0151] Form 2: Bivariate functions containing trigonometric terms:

[0152] Considering the periodic effect of the tilt angle (although nonlinearity is dominant in the 0-45° range, trigonometric basis functions may provide a better fit):

[0153]

[0154] in, , , The meaning and polynomial driving , , Similarly, these represent the coefficients of the constant term, the first term, and the quadratic term of the bedrock strength, respectively; yes The coefficient of represents a basis function coefficient representing the influence of the inclination angle on the critical aspect ratio; It is an interactive item The coefficient quantifies the coupling effect between bedrock strength and the sinusoidal value of the dip angle; yes The coefficient is used to capture the nonlinear component of the tilt angle effect. This form better reflects the periodic or nonlinear effects brought about by tilt angle changes.

[0155] Using the 8 discrete data points obtained in the previous step as input, a multivariate nonlinear regression method (such as the fitlm or nlinfit function in MATLAB, or the multivariate regression model in scikit-learn in Python) is used to fit the selected bivariate nonlinear function form and solve for all the undetermined coefficients p.

[0156] Assume we use a bivariate quadratic polynomial function (including interaction terms) for fitting:

[0157]

[0158] After performing regression calculations using 8 data points, the following specific relationship was obtained (the coefficient values ​​are for illustrative purposes only):

[0159]

[0160] By calculating this regression equation The goodness of fit can be evaluated; a value higher than 0.98 indicates a good fit.

[0161] To ensure that the established continuous mapping relationship has reliable predictive power, it must be validated using independent data.

[0162] A new set of working conditions is selected as the validation set. These conditions include combinations of dip angle, bedrock strength, and embedment length parameters not previously included in the working conditions used to construct the comprehensive parameter database. For example, new combinations such as dip angles of 10°, 22.5°, and 37.5°, and bedrock strengths of 5 MPa, 25 MPa, and 40 MPa can be selected. The specific validation process is as follows:

[0163] Substituting the bedrock strength and dip angle of the verification working condition into the continuous mapping relationship obtained by the above fitting, the predicted critical aspect ratio is calculated.

[0164] For this verification condition, following the method described in step 2, the critical embedment length under this condition was measured through a graded loading physical test. The method is as follows: Model piles with different embedment lengths under this condition were loaded, and a curve showing the pile end resistance sharing ratio as a function of embedment length was plotted. The embedment length corresponding to the point where the curve begins to flatten (the rate of change is less than 5%) is the actual critical embedment length. Then, this length was divided by the pile diameter to obtain the measured critical length-to-diameter ratio.

[0165] Calculate the relative error between the predicted value and the measured value. If the relative error of all verification conditions is within the preset range (e.g., less than 15%), then the established continuous mapping relationship is confirmed to be effective and reliable, and can be used for subsequent target engineering design.

[0166] If the relative error of some or all verification conditions exceeds the preset range, it indicates that the accuracy of the currently established continuous mapping relationship is insufficient and cannot reliably predict the critical aspect ratio. In this case, the following measures need to be taken for optimization and improvement:

[0167] First, go back to step 3 and check the accuracy of the parameterized correction model. It's possible that the correction model failed to adequately capture the discrepancies between the physical experiments and numerical simulations, resulting in systematic errors in the integrated parameter database itself. In this case, try using more advanced machine learning algorithms (e.g., upgrading from multiple linear regression to random forest or support vector regression), or increase the number of representative operating conditions (e.g., increasing the number of representative operating conditions in step 2 from 24 to 36 or more), rebuild the correction model, and update the integrated parameter database.

[0168] It's also possible that the chosen negative exponential or negative power function form fails to best describe the decay pattern of the data. Other nonlinear function forms, such as logarithmic or hyperbolic functions, can be tried, and the goodness of fit of different function forms can be compared to select the one with the best fit.

[0169] In addition, the evaluation results may be distorted due to overly extreme or insufficient selection of validation cases. To address this, the number of validation cases should be increased and ensured to be evenly distributed within the parameter space to more comprehensively test the predictive power of the mapping relationship.

[0170] Furthermore, if the order of the bivariate polynomial or trigonometric function terms used is too low, it may be unable to accurately fit complex surfaces where the critical aspect ratio varies with parameters. The order of the polynomial can be appropriately increased (e.g., from quadratic to cubic), or a more complex combination of basis functions can be introduced to re-fit the regression. However, it is important to avoid overfitting; the model complexity and prediction accuracy should be balanced by incorporating the validation set error.

[0171] The preset range (i.e., the upper limit of the allowable relative error) is set at 15%, based on a comprehensive consideration of multiple factors, reflecting a balance between engineering practicality and scientific rigor. For example, geotechnical materials (especially rock masses) have high discreteness and uncertainty. Even carefully controlled physical model tests typically have lower repeatability than tests on metallic materials. Differences in strength and stiffness between different specimens, as well as minor deviations in experimental operation, can lead to inherent fluctuations of ±5% to ±10% in the measured critical length-to-diameter ratio. Therefore, requiring excessively small errors between predicted and measured values ​​(e.g., less than 5%) is not only unrealistic but also an excessive demand on model accuracy. Furthermore, in pile foundation design, the critical rock-socketing length is usually used to initially determine pile length or for scheme comparison. The final designed pile length must also consider various factors such as load combinations, pile group effects, corrosion allowance, and construction errors, and be rounded to a certain modulus (e.g., 0.5m or 1m). Therefore, a ±15% prediction error will not lead to fundamental changes in the design scheme or safety issues in most cases. For example, if the predicted critical embedment length is 10m, an error of ±15% means that the actual critical value is between 8.5m and 11.5m, which is usually within the acceptable safety and economic margin in the design.

[0172] To intuitively reveal the nonlinear coupling law of the critical aspect ratio with dip angle and bedrock strength, this embodiment uses calibration end resistance ratio data from a comprehensive parameter database. It obtains the critical aspect ratio values ​​under different working conditions by simultaneously fitting a nonlinear decay function and solving a preset threshold. Table 1 summarizes 36 representative calculation results, covering a wide range of dip angles from 0° to 25° and bedrock strengths from 2 to 100 MPa. This comprehensively reflects the variation trend of the critical aspect ratio within the key parameter space, as shown in the table below:

[0173] Table 1. Schematic diagram of simulated data for critical aspect ratio:

[0174]

[0175] According to Table 1 and Figure 2 As shown, the nonlinear distribution law of the critical aspect ratio as it changes with both is intuitively demonstrated. Figure 2 The color bar on the right side of the middle transitions gradually from bottom to top, corresponding to the critical length-to-diameter ratio gradually increasing from 2.2 (short pile) to 7.4 (long pile). Figure 2 On the left, the filled colored cloud map is used to grasp the overall distribution trend of the critical aspect ratio, while the contour lines superimposed on it accurately delineate the outlines of areas with equal critical aspect ratio values. The density of these lines clearly reveals the gradient of the critical aspect ratio variation: the denser the lines, the more drastic the changes in critical rock-socketed lengths caused by small changes in parameters (dip angle or lithology), making these areas sensitive in the design; conversely, sparser lines indicate that the critical length changes gradually within the parameter range, resulting in higher design robustness.

[0176] from Figure 2 Two main patterns are clearly visible: First, the critical aspect ratio increases significantly with increasing bedrock strength, reflected in the color change of the contour map on the Y-axis and the steep upward trend of the contour lines. This indicates that high-strength rock can more fully utilize the pile side friction, allowing the pile end load sharing ratio to stabilize more quickly, thus permitting a greater critical embedment depth. Second, the critical aspect ratio decreases with increasing dip angle, reflected in the color change of the contour map from left to right under the same lithology, with the contour lines also curving downwards accordingly. This confirms that inclined piles are more likely to reach the critical state under the same rock mass conditions. This image, through the combination of contour map color and contour line accuracy, effectively verifies the rationality and engineering applicability of the continuous mapping relationship established in this invention, providing an intuitive and quantifiable reference for the critical length design of wharf embedded piles under varying dip angles and lithologies.

[0177] Step 5: Determine the critical rock embedment depth of the target project based on the continuous mapping relationship; Analyze the design inclination angle and design pile diameter of the target project by combining the analysis model and the correction model to obtain the calibration end resistance ratio of the target project; Determine whether the calibration end resistance ratio meets the preset requirements to determine the output critical rock embedment length.

[0178] In this embodiment, the logic for determining the critical rock-embedded length of the target project is as follows:

[0179] Based on the geological survey report and structural design drawings of the target project, the following core design parameters are determined:

[0180] Design pile diameter: determined by the structural stress requirements and the dimensions of the superstructure, and the unit is meters (m). For example, a wharf project may use rock-socketed piles with a diameter of 1.2m.

[0181] Design inclination angle: determined by the wharf's structural form and stress characteristics, measured in degrees (°). For example, to resist ship impacts and horizontal earth pressure, the front piles of the wharf may be designed with an inclination angle. Inclined piles.

[0182] The target bedrock strength is determined based on the rock mass characteristics of the bearing stratum at the pile tip in the geological survey report, and is usually expressed as the standard value of the uniaxial compressive strength of the rock, in megapascals (MPa). For example, the geological survey report reveals that the bearing stratum is moderately weathered granite, and its standard value of saturated uniaxial compressive strength is 45 MPa.

[0183] Based on the established and validated continuous mapping relationship, preliminary design values ​​can be quickly obtained. Substituting the target bedrock strength and design dip angle into this continuous mapping relationship, the corresponding critical length-to-diameter ratio can be directly calculated; multiplying the critical length-to-diameter ratio by the design pile diameter yields the preliminary design critical embedment depth.

[0184] The preliminary design values ​​mentioned above are based on statistical regression formulas and have been verified. However, for specific projects, a final, refined verification based on the actual design parameters of this project is still required. This is equivalent to performing another simulation and correction loop before the final decision is made.

[0185] A computational model of the target project is created. The mechanical parameters of the pile-rock interface are set synchronously based on the value range determined by the analysis model to ensure consistency between the model boundary conditions and the design and construction conditions. In particular, the mechanical parameters of the pile-rock interface (such as the friction coefficient) must be set synchronously based on the value range determined in step 1 (e.g., 0.3-0.8) and the recommended values ​​in the geotechnical investigation report for this project. For example, according to the geological investigation report, a friction coefficient of 0.7 is recommended for the interface between moderately weathered granite and concrete piles. This ensures a high degree of consistency between the model boundary conditions and the design and construction conditions.

[0186] The design inclination angle, target bedrock strength, and design critical embedment depth of the target project are input into a new calculation model to extract the pile top load and pile end resistance, and calculate the simulated end resistance ratio of the target project. This simulated end resistance ratio, along with the design inclination angle, design critical embedment aspect ratio, and target bedrock strength, is then input into a parameterized correction model. Based on its internal mapping relationship, the correction model outputs a calibrated predicted end resistance ratio that is closer to reality.

[0187] The predicted end resistance ratio is compared with a preset threshold to determine if it is not greater than the preset threshold. If it is, this means that when the pile length is the design critical rock embedment depth, the predicted end resistance ratio (representing the actual situation) after physical test calibration is still lower than or equal to the set critical state threshold. This indicates that at this pile length, the proportion of load borne by the pile tip is sufficiently small, and the pile's bearing characteristics have reached the expected critical state. The design critical rock embedment depth is then output as the final recommended value for the critical rock embedment length. If it is not, this means that although calculated according to the regression formula, after more refined verification, it is found that at this pile length, the proportion of load actually borne by the pile tip (predicted end resistance ratio) is still higher than our set safety threshold. This may be due to local deviations in the regression formula or the target engineering parameters being in the edge region of the formula's prediction. Directly adopting this design may lead to excessive pile tip settlement or insufficient safety reserve. A design warning is then generated, indicating that under the current pile design parameters, the pile tip resistance sharing is higher than the safety threshold when the critical state is reached, and modification suggestions are given. Common modification suggestions include:

[0188] Increasing the pile diameter: Increasing the pile diameter can reduce the length-to-diameter ratio (with the same rock embedment length) or equivalently increase the side friction, thereby reducing the end resistance ratio.

[0189] Optimize the pile inclination angle: Adjusting the inclination angle within a certain range may change the stress mechanism of the pile-rock contact surface, thereby affecting the critical rock embedment length.

[0190] Increase the rock embedding depth appropriately: increase the design critical rock embedding depth by a compensation, such as by 0.5D or 1D, and then repeat the above judgment until the predicted end resistance ratio is not greater than the preset threshold.

[0191] After completing the above judgments and decisions, the final determined critical embedment length should be used as the formal design parameter and archived. The design critical embedment depth that meets the requirements, or the optimized embedment length, should be used as the design value for the critical embedment length of the target project. A calculation report or design description should be generated containing the following: basic information of the target project (pile diameter, inclination angle, bedrock strength), selected preset thresholds and their selection basis, the calculation process of the preliminary design critical embedment depth (including the mapping formulas used), the establishment of the final verification model and the application process of the correction model, the judgment results and the final determined critical embedment length, and if a design warning is triggered, the warning content and optimization iteration process should be recorded.

[0192] Please see Figure 3 The present invention also provides a calculation system for the critical pile length of a wharf rock-socketed pile. This system is used to implement the aforementioned method for calculating the critical pile length of a wharf rock-socketed pile, and includes:

[0193] The multi-condition numerical simulation analysis module is used to preset various numerical calculation conditions and input them into the analysis model that simulates pile-rock contact behavior to obtain the pile top load, pile end resistance and simulated end resistance ratio under each numerical calculation condition. The working condition parameters of the numerical calculation conditions include inclination angle, rock embedment length and bedrock strength.

[0194] The representative working condition test calibration module is used to extract multiple representative working conditions from the numerical calculation working conditions, prepare model piles and simulate bedrock based on each representative working condition, and conduct physical tests to obtain the pile top load, pile end resistance and measured end resistance ratio under each representative working condition.

[0195] The comprehensive parameter database construction module is used to determine the correction coefficient of the representative working condition based on the simulated end resistance ratio and the measured end resistance ratio, establish a correction model that characterizes the mapping relationship between the correction coefficient and the working condition parameters, and use the correction model to correct the simulated end resistance ratio to obtain the calibration end resistance ratio. It also summarizes the parameters of each working condition and the corresponding calibration end resistance ratio to construct the comprehensive parameter database.

[0196] The mapping relationship establishment module is used to perform fitting analysis on the comprehensive parameter database, establish the attenuation function relationship of the calibration end resistance ratio as a function of the working condition parameters, and then determine the critical aspect ratio under different bedrock strengths and dip angles, and establish a continuous mapping relationship of the critical aspect ratio with respect to bedrock strength and dip angle.

[0197] The critical embedding length determination module is used to determine the design critical embedding depth of the target project based on a continuous mapping relationship; it obtains the calibration end resistance ratio of the target project by jointly analyzing the design inclination angle and design pile diameter of the target project according to the analysis model and the correction model; it determines whether the calibration end resistance ratio meets the preset requirements to determine the output critical embedding length.

[0198] The above formulas are all dimensionless calculations. The formulas are derived from software simulations based on a large amount of collected data to obtain the most recent real-world results. The preset parameters in the formulas are set by those skilled in the art according to the actual situation.

[0199] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented in software, the above embodiments can be implemented, in whole or in part, as a computer program product. Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented by electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution.

[0200] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment, depending on actual needs.

[0201] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application.

Claims

1. A method for calculating the critical pile length of rock-socketed piles in wharfs, characterized in that, The specific steps include: Step 1: Preset multiple numerical calculation conditions and input them into the analysis model simulating pile-rock contact behavior to obtain the pile top load, pile end resistance and simulated end resistance ratio under each numerical calculation condition. The working parameters of the numerical calculation conditions include inclination angle, rock embedment length and bedrock strength. Step 2: Select multiple representative working conditions from the numerical calculation working conditions, prepare model piles and simulate bedrock based on each representative working condition, and conduct physical tests to obtain the pile top load, pile end resistance and measured end resistance ratio under each representative working condition. Step 3: Determine the correction coefficient for the representative working condition based on the simulated terminal resistance ratio and the measured terminal resistance ratio, establish a correction model to characterize the mapping relationship between the correction coefficient and the working condition parameters, and use the correction model to correct the simulated terminal resistance ratio to obtain the calibration terminal resistance ratio. Summarize the parameters of each working condition and the corresponding calibration terminal resistance ratio to build a comprehensive parameter database. Step 4: Perform fitting analysis on the comprehensive parameter database, establish the attenuation function relationship of the calibration end resistance ratio with the change of working condition parameters, and then determine the critical length-to-diameter ratio under different bedrock strengths and dip angles, and establish a continuous mapping relationship of the critical length-to-diameter ratio with respect to bedrock strength and dip angle; Step 5: Determine the critical rock embedment depth of the target project based on the continuous mapping relationship; Analyze the design inclination angle and design pile diameter of the target project by combining the analysis model and the correction model to obtain the calibration end resistance ratio of the target project; Determine whether the calibration end resistance ratio meets the preset requirements to determine the output critical rock embedment length.

2. The method for calculating the critical pile length of a wharf rock-socketed pile according to claim 1, characterized in that, Using fully factorial or partially factorial experimental design methods, the working parameters are combined to form multiple numerical calculation working conditions for the target project; in the numerical calculation working conditions, each working condition is uniquely determined by a specific set of dip angle, rock embedment length and bedrock strength values; The analysis model is established using the three-dimensional finite element method or the three-dimensional discrete element method. In the analysis model, the pile body adopts an elastic or elastoplastic constitutive model, and the bedrock adopts the Mohr-Coulomb or Hawke-Brown criterion to simulate its elastoplastic failure behavior. The pile-rock contact interface is finely modeled, which is reflected in setting the normal of the contact surface as hard contact and the tangential direction to adopt the Coulomb friction model. The friction coefficient is selected within the preset friction coefficient range according to the surface roughness of the bedrock and the type of pile body material, so as to simulate the actual interface conditions after drilling. Four typical inclination angles were set between the pile axis and the vertical direction: 0°, 15°, 30°, and 45°. For each data pair consisting of a typical inclination angle and a bedrock strength, a set of embedment length sequences was set. The length value started from 1 times the pile diameter and increased in increments of 1 times the pile diameter until it reached a length value that made the calculated result of the pile end resistance sharing ratio change by less than 5% for three consecutive times. This ensured that the embedment length sequence completely covered the entire process of pile end resistance from initial exertion to stabilization. The embedment length corresponding to the above-mentioned termination condition was the critical embedment length for the data pair. Each numerical calculation condition is input into the analysis model in sequence. The vertical reaction force at the top of the pile under the numerical calculation condition is extracted as the pile top load, the total vertical reaction force at the contact surface at the bottom of the pile is extracted as the pile end resistance, and the ratio of the pile end resistance to the pile top load is calculated as the simulated end resistance ratio. For inclined pile conditions, the extracted load and resistance data are decomposed and recorded along the pile axis to ensure consistency with the loading direction of the physical test.

3. The method for calculating the critical pile length of a wharf rock-socketed pile according to claim 2, characterized in that, From the bedrock strengths covered by the numerical calculation cases, at least two bedrock strengths are selected to simulate soft rock and hard rock, respectively; at the same time, from the dip angles covered by the numerical calculation cases, four typical dip angles are selected as representative dip angles. The two selected bedrock strengths are cross-combined with four representative dip angles to form a set of main representative working conditions; each main representative working condition is determined by a unique set of bedrock strength and dip angle parameters. For each main representative working condition, determine its rock-embedded length sequence and extract at least three key length points from it: the starting length point of the rock-embedded length sequence, an intermediate length point in the middle region of the rock-embedded length sequence, and the critical length point that makes the pile end resistance sharing ratio tend to stabilize. Each extracted key length point is combined with the bedrock strength and dip angle parameters in the corresponding main representative working condition to form multiple representative working conditions for physical testing. Therefore, each main representative working condition generates a set of representative working condition sequences containing different rock embedding lengths.

4. The method for calculating the critical pile length of a wharf rock-socketed pile according to claim 3, characterized in that, The preparation of the model pile and simulated bedrock specifically includes: The preparation process of the model pile is as follows: a rigid model pile is prepared using steel, aluminum or engineering plastics, and its elastic modulus is at least 100 times that of the selected simulated bedrock material; the surface of the model pile is sandblasted or treated with sandpaper of a specific particle size to simulate the roughness of the actual pile body, and the friction coefficient between the treated surface and the simulated bedrock material is determined by direct shear test and controlled within the preset friction coefficient range. The simulated bedrock preparation process is as follows: using cement mortar or gypsum, by adjusting the mix ratio and curing conditions, homogeneous blocks with different uniaxial compressive strengths are cast to simulate the strength grades of soft and hard rock; during preparation, a micro earth pressure cell is pre-embedded in the mold to ensure that its sensing surface is flush with the preset pile bottom bearing surface.

5. The method for calculating the critical pile length of a wharf rock-socketed pile according to claim 4, characterized in that, On the solidified bedrock simulation, prefabricated holes were drilled at four typical inclination angles using a directional drilling tool; model piles were inserted into the holes at typical inclination angles, and grouting material was injected into the pile-rock gap to form a physical interface consistent with the contact conditions set in the analysis model. A servo loading system is used, and its loading direction is consistent with the axial direction of the model pile to ensure that the applied load is a pure axial load. During the loading process, the pile top load obtained by the force sensor of the loading system and the pile end contact pressure obtained by the micro earth pressure cell are collected and recorded simultaneously. For each representative working condition, the total integral value of the pile end contact pressure when it reaches the preset working load or ultimate load is taken as the pile end resistance of that representative working condition; the ratio of the pile end resistance to the synchronously recorded pile top load is recorded as the measured end resistance ratio of that representative working condition.

6. The method for calculating the critical pile length of a wharf rock-socketed pile according to claim 1, characterized in that, The logic for constructing the comprehensive parameter database is as follows: The ratio of the measured end resistance ratio to the simulated end resistance ratio for each representative working condition is defined as the correction coefficient for that set of working condition parameter combinations. An initial database is constructed based on all working condition parameter combinations from the numerical calculations, where each record includes dip angle, rock embedment length, bedrock strength, and simulated end resistance ratio. Based on all representative working conditions, a parameterized correction model is constructed using multiple linear regression or machine learning methods, with the simulated end resistance ratio and working condition parameters as input features and the correction coefficient as the output target. The correction coefficient for each numerical calculation working condition in the initial database is obtained based on this correction model, thus yielding the calibrated end resistance ratio. The calibrated end resistance ratio is the product of the simulated end resistance ratio and the corresponding numerical calculation working condition correction coefficient. The simulated end resistance ratio in the initial database is updated with the calibration end resistance ratio, ultimately forming a comprehensive parameter database that includes dip angle, rock embedment length, bedrock strength, and calibration end resistance ratio.

7. The method for calculating the critical pile length of a wharf rock-socketed pile according to claim 2, characterized in that, The logic for obtaining the continuous mapping relation is as follows: Extract the bedrock strength, dip angle, rock embedment length and their corresponding calibration end resistance ratios for all numerical calculation conditions from the comprehensive parameter database; Keeping the bedrock strength and dip angle constant, with the embedment length as the independent variable and the calibration end resistance ratio as the dependent variable, a nonlinear decay function is used to fit the data to establish a decay function relationship between the calibration end resistance ratio and the embedment length; the decay function relationship is in the form of a negative exponential function or a negative power function, and its decay coefficient is expressed as a function of the bedrock strength and dip angle. Based on the attenuation function relationship, the rock embedment length corresponding to the decrease of the calibration end resistance ratio to the preset threshold is calculated. The rock embedment length is divided by the pile diameter to obtain the critical length-to-diameter ratio under each group of bedrock strength and dip angle. A bivariate nonlinear function incorporating bedrock strength and dip angle is used to perform regression fitting on the obtained critical aspect ratio, establishing a continuous mapping relationship between the critical aspect ratio and bedrock strength and dip angle; the form of the bivariate nonlinear function includes bivariate polynomials and bivariate functions containing trigonometric function terms; A set of independent verification conditions is selected to verify the mapping relationship set; the dip angle, bedrock strength, and embedment length parameters of the verification conditions are not included in the comprehensive parameter database; the bedrock strength and dip angle of the verification conditions are substituted into the continuous mapping relationship to calculate the predicted critical aspect ratio, which is then converted into the predicted critical embedment length; the predicted critical embedment length is compared with the actual critical embedment length of the verification condition obtained through physical tests; if the error between the predicted result and the actual measurement is within a preset range, the continuous mapping relationship is confirmed to be valid; the actual critical embedment length is obtained through graded loading physical tests.

8. The method for calculating the critical pile length of a wharf rock-socketed pile according to claim 6, characterized in that, The logic for determining the critical rock-embedded length of the target project is as follows: Based on the geological survey report and structural design drawings of the target project, determine its design parameters, including the design pile diameter, design inclination angle, and target bedrock strength; Substituting the target bedrock strength and design dip angle into the continuous mapping relationship, the corresponding critical aspect ratio is directly calculated and then converted into the design critical rock embedment depth. A calculation model for the target project is created, in which the mechanical parameters of the pile-rock contact interface are set synchronously according to the value range determined by the analysis model to ensure the consistency between the model boundary conditions and the design and construction conditions. The design inclination angle, target bedrock strength, and design critical embedment depth are input into the new calculation model to extract the pile top load and pile end resistance of the target project, and to calculate the simulated end resistance ratio of the target project. This simulated end resistance ratio, together with the design inclination angle, design critical embedment length-to-diameter ratio, and target bedrock strength, is input into the parameterized correction model to obtain the predicted end resistance ratio of the target project. Determine whether the predicted end resistance ratio is not greater than the preset threshold. If it is satisfied, output the design critical rock embedment depth as the final recommended value of the critical rock embedment length. If it is not satisfied, generate a design warning, indicating that under the current pile design parameters, the pile end resistance sharing is higher than the safety threshold when the critical state is reached, and give modification suggestions, including increasing the pile diameter and optimizing the pile inclination angle.

9. A calculation system for the critical pile length of rock-socketed piles in wharfs, characterized in that, The system for calculating the critical pile length of a wharf rock-socketed pile is used to implement the method for calculating the critical pile length of a wharf rock-socketed pile as described in any one of claims 1-8, including: The multi-condition numerical simulation analysis module is used to preset various numerical calculation conditions and input them into the analysis model that simulates pile-rock contact behavior to obtain the pile top load, pile end resistance and simulated end resistance ratio under each numerical calculation condition. The working condition parameters of the numerical calculation conditions include inclination angle, rock embedment length and bedrock strength. The representative working condition test calibration module is used to extract multiple representative working conditions from the numerical calculation working conditions, prepare model piles and simulate bedrock based on each representative working condition, and conduct physical tests to obtain the pile top load, pile end resistance and measured end resistance ratio under each representative working condition. The comprehensive parameter database construction module is used to determine the correction coefficient of the representative working condition based on the simulated end resistance ratio and the measured end resistance ratio, establish a correction model that characterizes the mapping relationship between the correction coefficient and the working condition parameters, and use the correction model to correct the simulated end resistance ratio to obtain the calibration end resistance ratio. It also summarizes the parameters of each working condition and the corresponding calibration end resistance ratio to construct the comprehensive parameter database. The mapping relationship establishment module is used to perform fitting analysis on the comprehensive parameter database, establish the attenuation function relationship of the calibration end resistance ratio as a function of the working condition parameters, and then determine the critical aspect ratio under different bedrock strengths and dip angles, and establish a continuous mapping relationship of the critical aspect ratio with respect to bedrock strength and dip angle. The critical embedding length determination module is used to determine the design critical embedding depth of the target project based on a continuous mapping relationship; it obtains the calibration end resistance ratio of the target project by jointly analyzing the design inclination angle and design pile diameter of the target project according to the analysis model and the correction model; it determines whether the calibration end resistance ratio meets the preset requirements to determine the output critical embedding length.

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