High-pile wharf structure safety assessment method based on response surface method

Abstract

The invention discloses a high-pile wharf safety assessment method based on a response surface method. The high-pile wharf safety assessment method comprises the following steps that S1, a finite element model is established; s2, response surface parameters are determined; s3, selecting a polynomial order; s4, carrying out sample experiment design; s5, selecting significant parameters; s6, regression fitting of a response surface; s7, optimizing parameters; and S8, on the basis of taking the corrected three-dimensional finite element model as an evaluation reference, carrying out calculation by utilizing the corrected three-dimensional finite element model which is determined as the reference, and judging whether the high-pile wharf structure is safe or not by comparing a calculated value of the three-dimensional finite element model with a safety threshold value. According to the method, the structural safety of the high-pile wharf can be evaluated more efficiently and accurately.

Description

Technical Field

[0001] The present invention relates to an evaluation method for the structural safety of high-piled wharves based on the response surface method. Background Art

[0002] As a key facility in port and coastal engineering, high-piled wharves carry a huge traffic volume and cargo throughput, and are of great significance for promoting economic development and ensuring maritime traffic safety. However, with the extension of port operation time and the continuous change of the marine environment, high-piled wharves are facing increasingly severe safety challenges.

[0003] Traditional safety evaluation methods for high-piled wharves, such as empirical judgment, on-site inspection, and simple mechanical analysis, although can reflect the safety status of the wharf to a certain extent, still have many deficiencies. Empirical judgment often relies on past cases and expert experience, and it is difficult to accurately predict potential hazards that may occur in the future; on-site inspection can directly obtain the actual state of the wharf, but the inspection process is cumbersome, costly, and cannot achieve real-time monitoring; simple mechanical analysis ignores the complexity and non-linear characteristics of the wharf structure, resulting in inaccurate evaluation results.

[0004] With the continuous progress of computer technology and numerical analysis methods, finite element analysis has gradually become an effective means for predicting structural responses. However, directly applying finite element analysis to evaluate the safety of high-piled wharves still has problems such as large computational amount and long time consumption, and it is difficult to meet the real-time and economic requirements in actual engineering. Summary of the Invention

[0005] The purpose of the present invention is to overcome the defects of the prior art and provide an evaluation method for the structural safety of high-piled wharves based on the response surface method, which can more efficiently and accurately evaluate the safety of high-piled wharves.

[0006] The purpose of the present invention is achieved as follows: An evaluation method for the structural safety of high-piled wharves based on the response surface method, comprising the following steps:

[0007] S1. According to the actual structural dimensions and material parameters of the high-piled wharf, establish a three-dimensional finite element model of the high-piled wharf in three-dimensional finite element analysis software;

[0008] S2. Determine the response surface parameters through theoretical analysis and on-site measurement;

[0009] S3. Select the polynomial order;

[0010] S4. Sample experimental design;

[0011] S5. Selection of significant parameters;

[0012] S6. Regression fitting of the response surface;

[0013] S7. Parameter optimization, and use the optimized parameters as the parameter values for correcting the three-dimensional finite element model.

[0014] S8. Safety assessment, based on the corrected three-dimensional finite element model as the evaluation benchmark, calculate using the corrected and determined three-dimensional finite element model as the benchmark, and then judge whether the high-pile wharf structure is safe by comparing the calculated value of the three-dimensional finite element model with the safety threshold.

[0015] For the above-mentioned method for assessing the safety of high-pile wharf structures based on the response surface method, when performing step S1, the three-dimensional finite element model includes the main structure, pile foundation structure, and soil structure of the high-pile wharf.

[0016] For the above-mentioned method for assessing the safety of high-pile wharf structures based on the response surface method, when performing step S2, the response surface parameters are the main parameter variables of the response surface equation, and the output value of the main measured data of the high-pile wharf is the target variable of the response surface equation.

[0017] For the above-mentioned method for assessing the safety of high-pile wharf structures based on the response surface method, when performing step S3, select the polynomial order according to the complexity of the target parameter variables output by the response surface method and the characteristics of the data.

[0018] For the above-mentioned method for assessing the safety of high-pile wharf structures based on the response surface method, when performing step S4, use the response surface method matrix sampling for response surface experimental design. This sampling method requires at least 3 parameter variables; when sampling, the center point of the value range of one parameter variable is combined with the upper and lower limits of the value ranges of the other parameter variables.

[0019] For the above-mentioned method for assessing the safety of high-pile wharf structures based on the response surface method, when performing step S5, after the response surface experimental design is completed, according to the designed experimental plan, obtain the corresponding target variable through finite element calculation, and select the parameter variables that significantly affect the target variable in the entire sample space based on variance analysis.

[0020] For the above-mentioned method for assessing the safety of high-pile wharf structures based on the response surface method, when performing step S6, use the quadratic polynomial response surface model. First, establish the quadratic polynomial response surface model, and then use equation (1) to test the goodness-of-fit coefficient R of the response surface equation 2 :

[0021]

[0022] In the above equation (1), N is the number of sample points; y rs is the calculated value of the response surface equation; y is the finite element calculated value of the experimental sample; is the average value of the finite element calculation values of all experimental samples;

[0023] Goodness-of-fit coefficient R 2 The result interval of is [0, 1]. When the calculated goodness-of-fit coefficient is close to 1, the regression accuracy of the response surface equation is relatively high.

[0024] In the above method for evaluating the structural safety of high-piled wharves based on the response surface method, when performing step S7, by setting the target variable as the relative error between the finite element calculation result and the on-site monitoring result, and through the component response surface equation, find the experimental combination with the error closest to 0 within a fixed interval, and the parameter values of this experimental combination are used as the parameter values for modifying the three-dimensional finite element model.

[0025] In the above method for evaluating the structural safety of high-piled wharves based on the response surface method, when performing step S8, based on the modified three-dimensional finite element model as the evaluation benchmark, set the forces at the actual measuring point positions as input parameter variables, use the three-dimensional finite element model that has been modified and determined as the benchmark to perform calculations, obtain the maximum force values of the piles and beams of the high-piled wharf as output parameters, and then based on the design values of the piles and beams of the high-piled wharf under the ultimate limit state of bearing capacity in the relevant specifications as safety thresholds, and then by comparing each output parameter with its corresponding safety threshold one by one, judge whether there is a safety risk in the high-piled wharf structure under specific load conditions; if and only if all the calculated maximum force values do not exceed the corresponding safety thresholds, it is determined that the high-piled wharf structure is safe; otherwise, it is judged that the high-piled wharf structure has a safety risk, and further analysis and corresponding reinforcement measures should be taken.

[0026] In the above method for evaluating the structural safety of high-piled wharves based on the response surface method, when performing step S8, summarize the calculation results and measured results of the three-dimensional finite element model, and then establish the following safety evaluation function equation by the response surface method as formula (2):

[0027]

[0028] In the above formula (2), F1, F2, F3,... are the measured values of the actual measuring points; σ1, σ2, σ3,... are the calculated values of the three-dimensional finite element model at the key positions of the high-piled wharf;

[0029] Judge whether the high-piled wharf structure is safe by comparing the calculated values σ1, σ2, σ3,... of the three-dimensional finite element model with the safety thresholds [σ1], [σ2], [σ3],....

[0030] The evaluation method for the structural safety of high-piled wharves based on the response surface method of the present invention has the following characteristics: Based on the finite element model and measured data of high-piled wharves, first, by constructing a response surface equation between input parameters and structural responses, the three-dimensional finite element of the high-piled wharf structure is corrected. Then, based on the corrected benchmark model, a safety evaluation function equation for high-piled wharves is established by combining the response surface method with measured data. This method not only considers the complexity and nonlinear characteristics of the wharf structure but also combines the accuracy of finite element analysis and the efficiency of the response surface method, and can evaluate the safety of high-piled wharves more efficiently and accurately. Specific implementation mode

[0031] The evaluation method for the structural safety of high-piled wharves based on the response surface method of the present invention includes the following steps:

[0032] S1. Establish a finite element model. According to the actual structural dimensions and material parameters of the high-piled wharf, establish a three-dimensional finite element model of the high-piled wharf in a three-dimensional finite element analysis software. This finite element model includes the main structure, pile foundation structure, and soil structure of the high-piled wharf. When constructing the three-dimensional finite element model of the high-piled wharf, ensure that the parameters input into the finite element model are accurate. If there are errors in the input parameters, it will affect the accuracy and reliability of the calculated values of the finite element model.

[0033] S2. Determine the response surface parameters. Through theoretical analysis and on-site measurement, determine the key factors affecting the structural response of the high-piled wharf, that is, the main parameter variables of the response surface equation, and use the output values of the main measured data of the high-piled wharf as the target variables of the response surface equation. When determining the key factors affecting the structural response of the high-piled wharf, various possible influencing factors should be fully considered and accurately identified and quantified. This requires an in-depth understanding of the working principle and force conditions of the high-piled wharf to ensure the comprehensiveness and accuracy of the evaluation.

[0034] S3. Select the polynomial order. According to the complexity of the target parameter variables output by the response surface method and the characteristics of the data, select the polynomial order. Too low an order may cause the three-dimensional finite element model to fail to accurately capture the nonlinear relationship of the data, while too high an order may lead to overfitting, that is, the three-dimensional finite element model performs well on the training data but has poor generalization ability on new data.

[0035] S4. Sample experimental design. Use the Box-Behnken matrix sampling of the response surface method for the response surface experimental design. This sampling method requires at least 3 parameter variables. When sampling, the center point of the value range of one parameter variable is combined with the upper and lower limits of the value ranges of the other parameter variables.

[0036] S5. Selection of significant parameters. After the response surface experimental design is completed, according to the designed experimental scheme, the corresponding target variables are obtained through finite element calculation. Based on the analysis of variance, the parameter variables that significantly affect the target variables are selected within the entire sample space.

[0037] S6. Regression fitting of the response surface. A quadratic polynomial response surface model is adopted. After establishing the quadratic polynomial response surface model, the goodness-of-fit coefficient R of the response surface equation is tested using Equation (1). 2 :

[0038]

[0039] In the above Equation (1), N is the number of sample points; y rs is the calculated value of the response surface equation; y is the finite element calculated value of the experimental sample; is the average value of the finite element calculated values of all experimental samples;

[0040] The goodness-of-fit coefficient R 2 has a result interval of [0, 1]. When the calculated goodness-of-fit coefficient is close to 1, the regression accuracy of the response surface equation is relatively high.

[0041] When testing the goodness-of-fit coefficient R 2 of the response surface equation, the response surface equation also needs to be verified and optimized through actual engineering cases or on-site test data. If the goodness-of-fit coefficient R 2 is small, it may be that the parameter variables that have a significant impact on the target variable are ignored. It is necessary to re-analyze the sensitivity of the parameter variables, screen out all significantly influential parameter variables, and re-conduct the response surface experimental design.

[0042] S7. Parameter optimization. By setting the target variable as the relative error between the finite element calculation result and the on-site monitoring result, and through the component response surface equation, the experimental combination with the error closest to 0 within the fixed interval is found. The parameter values of this experimental combination are used as the parameter values for modifying the finite element model.

[0043] S8. Based on the modified three-dimensional finite element model as the evaluation benchmark, first set the forces at the actual measurement point positions as input parameter variables, calculate through the three-dimensional finite element model, and obtain the maximum force values of the pile and beam components of the high-piled wharf as output parameters. Then, based on the design values of the pile and beam components of the high-piled wharf under the ultimate limit state of bearing capacity in the relevant specifications as the safety thresholds. By comparing each output parameter with its corresponding safety threshold one by one, it is judged whether there is a safety risk in the high-piled wharf structure under specific load conditions. When and only when all the calculated maximum force values do not exceed the corresponding safety thresholds, it is determined that the high-piled wharf structure is safe; otherwise, it is judged that the high-piled wharf structure has a safety risk, and further analysis and corresponding reinforcement measures need to be taken.

[0044] The calculation results of the three-dimensional finite element model and the measured results are summarized, and then a safety evaluation function equation as shown in Equation (2) below is established by the response surface method:

[0045]

[0046] In the above formula (2), F1, F2, F3,... are the measured values of the actual measurement points; σ1, σ2, σ3,... are the calculated values of the three-dimensional finite element model at the key positions of the high-piled wharf;

[0047] By comparing the calculated values σ1, σ2, σ3,... of the three-dimensional finite element model with the safety thresholds [σ1], [σ2], [σ3],... to judge whether the high-piled wharf structure is safe.

[0048] The following takes a specific high-piled wharf as an example to illustrate the evaluation method for the safety of the high-piled wharf structure based on the response surface method of the present invention,

[0049] S1. Establish a three-dimensional finite element model:

[0050] According to the design and construction plan of the high-piled wharf structure, use the Midas / GTS NX (New eXperience of Geo-Technical analysis System) finite element analysis software to establish a complete three-dimensional finite element model of the high-piled wharf structure and the underlying soil foundation. The entire three-dimensional finite element model has a total of 339,841 elements and 2,397,324 nodes. In the three-dimensional finite element model, a three-dimensional coordinate system is established with the transverse direction of the wharf as the X-axis, the longitudinal direction as the Y-axis, and the vertical direction as the Z-axis. The X-axis, Y-axis, and Z-axis conform to the right-hand rule. The length unit is taken as m, and the unit of force is kN; according to the engineering modeling experience, 1.5 times the penetration depth is used as the calculation boundary range to eliminate the boundary effect; the overall size of the three-dimensional finite element model is 200 m in length, 140 m in width, and 87.6 m in height;

[0051] S2. Determine the response surface parameters: According to the structural characteristics of the high-piled wharf and influencing factors such as the working environment, determine to select the uniformly distributed load of the high-piled wharf, the elastic modulus of the pile foundation (PHC pipe pile), and the elastic modulus of the transverse and longitudinal beams as the parameter variables for modifying the three-dimensional finite element model at the initial completion of the wharf; according to the spatial variation of the actual monitoring data of the pile foundation (PHC pipe pile), the maximum value of the axial stress change appears near the mud surface. Therefore, select the average value of the stress change monitored by the sensor on the shore side near the mud surface of the No. 1 pile foundation as the first target variable of the response surface equation. At the same time, according to the structural characteristics of the transverse and longitudinal beams of the high-piled wharf and the finite element calculation results, select the average value of the stress change monitored at the positions where the maximum axial tensile stress of the longitudinal and transverse beams of the high-piled wharf appears as the other two target variables of the response surface equation; calculate the axial stress changes at these three positions between the completed wharf condition and the pile foundation construction condition through the three-dimensional finite element model, and use this as the calculated value of the three-dimensional finite element model; the actual values of the monitoring data and the calculation results of the unmodified three-dimensional finite element model are shown in Table 1:

[0052] Table 1

[0053]

[0054]

[0055] Taking the uniformly distributed load of the high-piled wharf and the elastic moduli of the pile foundation, cross beams, and longitudinal beams as influencing factors, the specific values are shown in Table 2:

[0056] Table 2

[0057] Influencing factors Value range Uniform load of high-piled wharf F / kPa 1～10 <![CDATA[Elastic modulus E1 of PHC pipe piles / GPa]]> 37～39 <![CDATA[Elastic modulus E2 of the horizontal and vertical beams / GPa]]> 31.5～33.5

[0058] S3. Select the polynomial order:

[0059] The response surface equation is generally expressed by a quadratic polynomial (3):

[0060]

[0061] In the above formula (3), a0 is the constant term obtained by fitting, and a i and a ij are the first-order term coefficient and the second-order term coefficient determined by the least squares method respectively; x i and x j are the i-th parameter variable and the j-th parameter variable respectively;

[0062] S4. Sample experimental design: Adopt the response surface method (Box-Behnken) matrix sampling for response surface experimental design;

[0063] S5. Selection of significant parameters: Taking the uniform load F on the high-piled wharf, the elastic modulus E1 of PHC pipe piles, and the elastic modulus E2 of the transverse and longitudinal beams as influencing factors, and taking the errors R1, R2, and R3 between the calculated results of stress changes at three measuring points and the measured data as the dependent variables of the response surface equation, a response surface analysis experiment with 15 experimental combinations was designed. The experimental scheme and experimental results are shown in Table 3:

[0064] Table 3

[0065]

[0066]

[0067] S6. Regression fitting of the response surface equation:

[0068] Using the response surface analysis software (Design Expert), the least squares method was used to fit the error R1 obtained from 15 experimental combinations, and the fitting equation of the error R1 is as follows:

[0069] R1 = 1.03093 - 0.242173A - 0.009333B + 0.008487C + 0.001353AB

[0070] -0.001273AC - 0.000163BC - 8.07327×10 -6 A 2 +0.000200B 2 -0.000038C 2

[0071] Among them, the parameters A, B, and C represent the uniform load F on the upper part of the high-piled wharf, the elastic modulus E1 of PHC pipe piles, and the elastic modulus E2 of the transverse and longitudinal beams, respectively;

[0072] The least squares method was used to fit the compressive stress of PHC pipe piles, and the fitting equation of the error R2 is as follows:

[0073] R2 = 0.971119 - 0.226825A + 0.006468B - 0.005595C + 0.001091AB

[0074] -0.002356AC - 0.000196BC - 9.69514×10 -6 A 2 -3.92106×10 -16 B 2 +0.000196C 2

[0075] The horizontal displacement of the structural panel of the high-pile wharf is fitted by the least squares method, and the fitting equation of the error R3 is as follows:

[0076] R3 = -0.043534 - 0.134728A + 0.002991B - 0.018359C + 0.000268AB

[0077] -0.002113AC - 5.88182×10 -5 BC - 0.000206A 2 -5.11297×10 -5 B 2 + 0.000126C 2

[0078] According to the introduction of the response surface method, the main index of the goodness-of-fit test is the coefficient of determination R 2 , which reflects the proportion of the variance that can be explained by the response surface equation. The credibility standard for the goodness-of-fit of the response surface equation to the design experimental data generally takes R 2 > 0.9. The goodness-of-fit test is performed on the obtained response surface equation, and the evaluation results are shown in Table 4:

[0079] Table 4

[0080]

[0081]

[0082] As can be seen from Table 4, the coefficients of determination R 2 of the response surface equations for the three target variables all exceed 0.9. Therefore, the accuracy of the fitting equation of the experimental data by the response surface method within the determined interval is relatively high, and the three-dimensional finite element model can be corrected on this basis;

[0083] S7. Parameter optimization:

[0084] Using the response surface equations of the target variables obtained by regression analysis, through iterative calculation, the values of the design variables that make the three errors closest to 0 are obtained, as shown in Table 5:

[0085] Table 5

[0086] Parameter item Initial value Correction value Deviation (%) F / kPa 5.5 4.329 21.29 <![CDATA[E1 / GPa]]> 38 38.609 1.60 <![CDATA[E2 / GPa]]> 32.5 32.324 0.54

[0087] From the correction results in Table 5, the correction range of the elastic modulus E1 of the PHC piles and the elastic modulus E2 of the transverse and longitudinal beams are not large, but the uniform load F on the upper part of the wharf has a large correction. The reason for the large correction of the uniform load F is that after the completion of the wharf, some upper loads such as material accumulation and crowd load will inevitably appear on the upper part of the wharf. These loads have a great influence on the stress of the wharf components, but it is difficult to measure them accurately in practice. Therefore, the uniform load F of the high-pile wharf in the three-dimensional finite element model has a large correction; for the elastic modulus E1 of the PHC piles and the elastic modulus E2 of the transverse and longitudinal beams, since the elastic modulus of concrete has a certain relationship with the construction conditions, there is a certain deviation between the elastic modulus of the actual high-pile wharf structural components and the standard value of the specification, but generally there will not be a huge difference, so the correction range of the elastic modulus E1 of the PHC piles and the elastic modulus E2 of the transverse and longitudinal beams is small;

[0088] S8. Safety assessment: The modified three-dimensional finite element model is used as the assessment benchmark, and key parameters are output, especially the maximum force values ​​of piles and beam components under various load combinations. By comparing each output parameter with its corresponding safety threshold one by one, it is determined whether there is a safety risk in the high-pile wharf structure under specific load conditions. The calculated results and measured results of the three-dimensional finite element model are summarized, and then the safety assessment function equation is established through the response surface method.

[0089] The above embodiments are only used to illustrate the present invention, rather than to limit the present invention. Those skilled in the relevant technical field may make various changes or modifications without departing from the spirit and scope of the present invention. Therefore, all equivalent technical solutions should also belong to the scope of the present invention and should be defined by the claims.

Claims

1. A method for evaluating the structural safety of a high-pile wharf based on response surface methodology, characterized in that: The evaluation method comprises the following steps: S1. According to the actual structural dimensions and material parameters of the high-pile wharf, a three-dimensional finite element model of the high-pile wharf is established in a three-dimensional finite element analysis software; S2. Determine the response surface parameters through theoretical analysis and field measurements; S3. Select the polynomial order; S4. Sample experimental design; S5. Selection of significant parameters; S6. Regression fitting of response surface; S7. Optimizing parameters and using the optimized parameters as parameter values ​​for modifying the three-dimensional finite element model; S8. Safety assessment is based on the revised three-dimensional finite element model as the assessment benchmark, and the three-dimensional finite element model that has been revised and determined as the benchmark is used for calculation. The safety of the high-pile wharf structure is then determined by comparing the calculated value of the three-dimensional finite element model with the safety threshold.

2. The safety assessment method for high-pile docks based on response surface methodology according to claim 1 is characterized in that: When performing step S1, the three-dimensional finite element model includes the main structure, pile foundation structure and soil structure of the high-pile wharf.

3. The safety assessment method for high-pile docks based on response surface methodology according to claim 1 is characterized in that: When performing step S2, the response surface parameters are the main parameter variables of the response surface equation, and the output values ​​of the main measured data of the high-pile wharf are the target variables of the response surface equation.

4. The safety assessment method for high-pile docks based on response surface methodology according to claim 1 is characterized in that: When performing step S3, the polynomial order is selected according to the complexity of the target parameter variable output by the response surface method and the characteristics of the data.

5. The safety assessment method for high-pile docks based on response surface methodology according to claim 1 is characterized in that: When performing step S4, response surface method matrix sampling is used to perform response surface experiment design. This sampling method requires at least 3 parameter variables. When sampling, the center point of a parameter variable value interval and the upper and lower limits of the remaining parameter variable value intervals are combined with each other.

6. The safety assessment method of a high-pile wharf based on response surface methodology according to claim 1 is characterized in that: When performing step S5, after the response surface experiment design is completed, the corresponding target variable is obtained through finite element calculation according to the designed experimental plan, and the parameter variables that significantly affect the target variable are selected in the entire sample space based on variance analysis.

7. The safety assessment method for high-pile docks based on response surface methodology according to claim 1 is characterized in that: When performing step S6, a quadratic polynomial response surface model is used. After the quadratic polynomial response surface model is first established, the goodness of fit coefficient R of the response surface equation is tested using formula (1). 2 : In the above formula (1), N is the number of sample points; y rs Calculate values ​​for the response surface equation; y is the finite element calculated value of the experimental sample; is the average value of the finite element calculation values ​​of all experimental samples; Goodness of fit coefficient R 2 The result interval is [0,1]. When the calculated goodness of fit coefficient is close to 1, the regression accuracy of the response surface equation is high.

8. The safety assessment method for high-pile docks based on response surface methodology according to claim 1 is characterized in that: When performing step S7, by setting the target variable to the relative error between the finite element calculation result and the on-site monitoring result, the component response surface equation is used to find the experimental combination with the error closest to 0 within a fixed interval. The parameter values ​​of the experimental combination are used as the parameter values ​​for correcting the three-dimensional finite element model.

9. The method for evaluating the structural safety of a high-pile wharf based on response surface methodology according to claim 1 is characterized in that: When performing step S8, based on the corrected three-dimensional finite element model as the evaluation benchmark, the force at the actual measuring point position is set as the input parameter variable, and the three-dimensional finite element model that has been corrected and determined as the benchmark is used for calculation to obtain the maximum force values ​​of the piles and beam components of the high-pile wharf as output parameters, and then the design values ​​of the piles and beam components of the high-pile wharf under the ultimate bearing capacity state in the relevant specifications are used as the safety threshold, and then by comparing each output parameter with the corresponding safety threshold one by one, it is determined whether the high-pile wharf structure has a safety risk under specific load conditions; if and only if all the calculated maximum force values ​​do not exceed the corresponding safety threshold, the high-pile wharf structure is determined to be safe; Otherwise, it is judged that there is a safety risk in the high-pile wharf structure, and further analysis and corresponding reinforcement measures are required.

10. The method for evaluating the structural safety of a high-pile wharf based on response surface methodology according to claim 9 is characterized in that: When performing step S8, the calculation results and the measured results of the three-dimensional finite element model are summarized, and then the safety assessment function equation of the following formula (2) is established by the response surface method: In the above formula (2), F1, F2, F3, ... are the measured values ​​of the actual measuring points; σ1, σ2, σ3, ... are the calculated values ​​of the three-dimensional finite element model of the key positions of the high-pile wharf; The safety of the high-pile wharf structure is determined by comparing the calculated values ​​σ1, σ2, σ3, ... of the three-dimensional finite element model with the safety thresholds [σ1], [σ2], [σ3], ...

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