A pile foundation damage indirect identification and evaluation method based on high pier vibration test
By establishing a finite element model through vibration testing of high piers and calculating the rate of change of the compliance matrix, the problems of high cost and difficulty in damage assessment of traditional methods are solved, and non-destructive testing and efficient assessment are realized.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- SHANDONG JIANZHU UNIV
- Filing Date
- 2024-12-16
- Publication Date
- 2026-04-24
AI Technical Summary
Traditional pile foundation damage identification methods are costly and can potentially damage the structure, making it difficult to comprehensively and accurately assess the damage status of high pier structures.
An indirect identification method based on high pier vibration testing is adopted. Data is obtained through environmental excitation, a finite element model is established, the change rate of the flexibility matrix is calculated, and pile foundation damage is identified.
It eliminates the need for expensive vibration equipment, avoids structural damage, enables comprehensive and accurate assessment of pile foundation damage, reduces testing costs, and improves safety and efficiency.
Smart Images
Figure CN119622888B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of bridge pile foundation damage detection, specifically relating to an indirect identification and assessment method for pile foundation damage based on high pier vibration testing. Background Technology
[0002] In the field of building construction, pile foundations, as a crucial component of the supporting structure, directly affect the overall safety and durability of the project. As bridges, high-rise buildings, and other structures become taller and more complex, the application of high-pier structures is becoming increasingly widespread. However, due to their inherent high flexibility, high slenderness ratio, and complex structural dynamic characteristics, high-pier structures are susceptible to various factors during operation, leading to pile foundation damage and consequently affecting the stability and safety of the overall structure.
[0003] Traditional methods for identifying pile foundation damage often rely on direct observation, static load tests, or localized inspections. While these methods can assess pile foundation damage to some extent, they typically require artificial excitation, necessitating expensive vibration equipment and potentially causing localized damage to the bridge pier structure. This results in limitations such as high inspection costs and potential structural damage. Particularly for high-pier structures, due to their increased height and complexity, traditional methods often struggle to comprehensively and accurately assess pile foundation damage. Therefore, to save costs and ensure the safety of bridge pier structures, a method for indirect identification and assessment of pile foundation damage is needed. This invention addresses this technical problem. Summary of the Invention
[0004] This invention provides an indirect identification and assessment method for pile foundation damage based on high pier vibration testing. It can test the modal vibration characteristics of bridge piers through environmental excitation, saving the cost of excitation equipment, ensuring the safety of bridge pier structures, and enabling comprehensive and accurate identification and assessment of pile foundation damage.
[0005] A method for indirect identification and assessment of pile foundation damage based on high pier vibration testing includes the following steps:
[0006] S1. Conduct preliminary preparations and planning, clarify test objectives and collect relevant materials, and design a plan based on the actual situation;
[0007] S2. Set up measuring points on the high pier, and use environmental excitation to make the high pier vibrate, and collect relevant data during the vibration process;
[0008] S3. Process and analyze the collected data;
[0009] S4. Based on relevant materials and collected data, establish a finite element model of a high pier damaged pile foundation that is intact, and calculate the corresponding theoretical flexibility matrix.
[0010] S5. Calculate the change rate of the measured structural flexibility matrix of the high pier relative to the flexibility matrix of the finite element model of the pier with damaged pile foundation.
[0011] S6. Analyze the obtained change rate to identify whether the pile foundation is damaged and assess the integrity of the pile body.
[0012] Furthermore, step S4 includes the following steps:
[0013] S41. Establish the initial finite element model of the pier and pile foundation based on relevant materials;
[0014] S42. Based on the collected high pier data, the elastic modulus of the bridge pier in the initial pier-pile finite element model is corrected to obtain a pier-pile finite element model with intact high pier and damaged pile foundation.
[0015] S43. Calculate the theoretical flexibility matrix of the finite element model of the damaged pile foundation of the high pier.
[0016] Furthermore, in step S42, the process of correcting the elastic modulus of the bridge pier in the initial finite element model is as follows:
[0017] S421. Based on the vibration frequency of the high pier, the sum of squares of the relative errors between the first two calculated frequencies and the measured frequencies of the initial pier pile finite element model is used as the objective function, the relative errors between the first two calculated frequencies and the measured frequencies are used as the state variables, and the design variable is the elastic modulus of the high pier.
[0018] S422. Design variables are represented in the following ways:
[0019]
[0020] in, Let T represent the nth design variable, T represent the transpose of the vector, and n represent the number of design variables.
[0021] S423, The objective function is expressed as:
[0022]
[0023]
[0024]
[0025] in, Let n be the objective function, and n be the modal order. To calculate the frequency, For the measured frequency, m and n have the same range of values, and the constraints are: Indicates the i-th error. This represents the i-th parameter to be corrected. and Let represent the upper and lower limits of the i-th parameter to be corrected. The objective function continuously decreases under the constraints and eventually converges. The parameter values at the convergence point of the objective function are the optimal solutions.
[0026] Furthermore, in step S421, the state variables are calculated as follows:
[0027] S4211. Represent the state variables as follows:
[0028]
[0029] in, Calculate the frequency values for the first two vertical bends. These are the measured frequency values for the first two vertical bends.
[0030] The constraint condition is set to ±10%, that is, the range of E is [-0.1, 0.1], so there are two state variables in total;
[0031] S4212. The objective function J is defined as follows:
[0032]
[0033] In the formula Corresponding to two state variables, The weighting factors for each corresponding state variable are:
[0034]
[0035] because With corresponding frequency errors The value is proportional to the square of the objective function, which ensures that each optimization iteration proceeds in the direction of a rapid decrease in the objective function value, thereby improving optimization efficiency.
[0036] Furthermore, in step S42, the matching between the corrected finite element model of the pier and the actual tested mode shapes of the pier is calculated and analyzed. This can be characterized by the modal correlation criterion (MAC), and the calculation expression for MAC is as follows:
[0037]
[0038] In the formula, This represents the calculated mode shape vector. These represent the measured mode shape vectors. The higher the MAC value, the better the correlation between the mode shapes.
[0039] Furthermore, in step S43, the modal compliance of the high pier structure can be expressed as:
[0040]
[0041] In the formula, For structural modal compliance, To identify structural vibration modes, For normalized mode shapes, n represents the total number of identified modes. Let r be the natural frequency of the structure.
[0042] As can be seen from the above equation, due to higher frequency...
[0043] Since the values are relatively small, the compliance matrix is mainly determined by the low-order modal parameters. Therefore, as long as the low-order modes of the pier are identified, a compliance matrix with high accuracy can be obtained.
[0044] Furthermore, step S5 includes:
[0045] S51. Calculate the difference in the diagonal elements of the measured structural flexibility matrix of the high pier relative to the theoretical flexibility matrix of the finite element model of the pier with damaged pile foundation.
[0046] S52. Calculate the change rate of the diagonal elements of the measured structural flexibility matrix of the high pier relative to the theoretical flexibility matrix of the finite element model of the pier with damaged pile foundation.
[0047] Furthermore, step S3 includes:
[0048] S31. Perform preprocessing operations, including noise reduction and filtering, on the collected vibration signals to improve signal quality;
[0049] S32. Use modal analysis techniques to extract modal parameters of the high pier, including natural frequency, damping ratio, and mode shape.
[0050] Furthermore, step S2 includes:
[0051] S21. Select representative measuring points on the high pier;
[0052] S22. Install vibration sensors at the selected measuring points, ensuring that the sensors are securely fixed and can accurately capture vibration signals.
[0053] S23. According to the test plan, environmental excitation is used to induce vibration in the high pier;
[0054] S24. Start the data acquisition system and record the acceleration response data of the high pier during the vibration process.
[0055] Furthermore, step S1 includes:
[0056] S11. Clearly define the specific objectives of the test, including identifying the specific location of damage to the pile foundation and assessing the degree of damage;
[0057] S12. Collect relevant data, including design drawings, geological survey reports, and historical maintenance records, for the high piers and their pile foundations.
[0058] S13. Based on the actual conditions of the target and the high pier, design a reasonable vibration test plan, including the layout of measuring points, selection of test equipment, and test time.
[0059] The technical effects of this invention are as follows:
[0060] (1) The pile foundation damage indirect identification and assessment method based on high pier vibration test provided by the present invention only requires the installation of an acceleration sensor on the high pier, then obtaining the frequency mode shape and measured flexibility matrix of the high pier under environmental excitation, and establishing an initial finite element model of the high pier and the pile foundation. Then, the elastic modulus of the bridge pier in the initial pier-pile finite element model is corrected according to the measured frequency of the high pier, and the pier-pile finite element model with the high pier damaged and the pile foundation intact is obtained. The theoretical flexibility matrix of the finite element model with the high pier damaged and the pile foundation intact is calculated. Finally, the change rate of the measured flexibility matrix relative to the theoretical flexibility matrix of the high pier damaged and the pile foundation intact model is calculated, so that the pile foundation condition can be comprehensively and quantitatively evaluated. Therefore, it is not necessary to conduct tests by interrupting bridge traffic, knocking on the bridge pier and the pile foundation, etc., which will not cause any damage to the pile foundation. Moreover, no excitation equipment is required, which saves costs and improves the safety of the structure.
[0061] (2) This scheme uses environmental excitation to excite the high pier structure and analyzes the collected data. There is no need to use excitation equipment for manual excitation, which makes up for the shortcomings of the existing pile foundation damage detection technology, improves the detection efficiency and convenience of non-destructive testing of pile foundation integrity, and provides a new method and basis for judging the specific type of pile foundation disease in non-destructive testing.
[0062] (3) This scheme adopts environmental excitation. It only needs to measure the pier response caused by environmental excitations such as traffic load, wind, and water flow to identify the modal parameters of the high pier. There is no need to use artificial excitation, which ensures the structural safety and also eliminates the need to close traffic for testing, thereby improving the practicality of this method. Attached Figure Description
[0063] Figure 1 This is a flowchart of the modification process of the present invention.
[0064] Figure 2 This is a diagram of the high pier at the test site.
[0065] Figure 3 A finite element model diagram of the pier and pile is provided.
[0066] Figure 4 This is a diagram showing the layout of the testing points on the high pier in the test plan.
[0067] Figure 5 This is a finite element model diagram of pier and pile damage.
[0068] Figure 6 This is a time history graph of acceleration.
[0069] Figure 7 The measured vibration mode diagram of the high pier.
[0070] Figure 8 A schematic diagram showing the theoretical frequencies of the finite element model for pier and pile damage versus the measured frequencies of the finite element model for pier and pile damage.
[0071] Figure 9 This is a schematic diagram showing the parameter correction values and rate of change.
[0072] Figure 10 This is a comparison chart of the frequency correction values of the finite element model of pier damage and pile damage and the measured values of the finite element model of pier damage and pile damage.
[0073] Figure 11 This is a schematic diagram of the theoretical flexibility matrix of the corrected finite element model for pile damage.
[0074] Figure 12 A schematic diagram of the measured flexibility matrix of the pier pile.
[0075] Figure 13 This is a schematic diagram of the difference between the diagonal elements and the rate of change of the diagonal elements in the compliance matrix. Detailed Implementation
[0076] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The following description of at least one exemplary embodiment is merely illustrative and is in no way intended to limit the present invention or its application or use. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. Unless otherwise specifically stated, the relative arrangement, expressions, and values of the components and steps described in these embodiments do not limit the scope of the present invention.
[0077] It should also be understood that, for ease of description, the dimensions of the various parts shown in the accompanying drawings are not drawn to actual scale. Techniques, methods, and devices known to those skilled in the art may not be discussed in detail, but where appropriate, such techniques, methods, and devices should be considered part of the specification. In all examples shown and discussed herein, any specific values should be interpreted as merely exemplary and not as limitations. Therefore, other examples of exemplary embodiments may have different values.
[0078] A method for indirect identification and assessment of pile foundation damage based on high pier vibration testing includes the following steps:
[0079] S1. Conduct preliminary preparations and planning, clarify test objectives and collect relevant materials, and design a plan based on the actual situation;
[0080] S2. Set up measuring points on the high pier, and use environmental excitation to make the high pier vibrate, and collect relevant data during the vibration process;
[0081] S3. Process and analyze the collected data;
[0082] S4. Based on relevant materials and collected data, establish a finite element model of a high pier damaged pile foundation that is intact, and calculate the corresponding theoretical flexibility matrix.
[0083] S5. Calculate the change rate of the measured structural flexibility matrix of the high pier relative to the flexibility matrix of the finite element model of the pier with damaged pile foundation.
[0084] S6. Analyze the obtained change rate to identify whether the pile foundation is damaged and assess the integrity of the pile body.
[0085] A positive change in flexibility rate indicates damage to the pile foundation and that the lateral stiffness of the pile foundation does not meet the design requirements. The larger the positive value of the change in flexibility rate, the greater the degree of damage to the pile foundation. A negative change in flexibility rate indicates that the lateral stiffness of the pile foundation meets the design requirements. Thus, a comprehensive evaluation is made to determine whether the actual pile foundation meets the design requirements, and an inspection report is generated.
[0086] Furthermore, step S4 includes the following steps:
[0087] S41. Establish the initial finite element model of the pier and pile foundation based on relevant materials;
[0088] S42. Based on the collected high pier data, the elastic modulus of the bridge pier in the initial pier-pile finite element model is corrected to obtain a pier-pile finite element model with intact high pier and damaged pile foundation.
[0089] S43. Calculate the theoretical flexibility matrix of the finite element model of the damaged pile foundation of the high pier.
[0090] In practical engineering, the theoretical calculation values of bridge finite element models established based on drawings, specifications, and other standards often differ significantly from the measured values obtained through experiments, sometimes even failing to meet the accuracy requirements of actual engineering projects. In other words, the established finite element model cannot reflect the true working state of the structure. Therefore, it is essential to correct the established structural finite element model to ensure that the calculated values of the structural finite element model parameters match the measured values.
[0091] This scheme applies a dynamic finite element model correction method, specifically a parametric correction method. The parametric correction method involves modifying some parameters in the model to make the calculated values of the corrected model closer to the measured values. The correction parameters are typically chosen from elastic modulus, density, and boundary conditions. Similar to structural optimization theory, the parametric correction method constructs the error of the dynamic information under the same excitation as the objective function, and then modifies some physical parameters in the finite element model to minimize the objective function, thereby achieving correction. Since the objective function is generally nonlinear, iterative optimization algorithms are often chosen during the optimization calculation.
[0092] Since the order of the measured modal parameters of bridge piers is limited, and the higher the order, the greater the modal error in the identification, the target value for correction should be a modal parameter with a smaller error to avoid ill-conditioned problems caused by the error in the correction solution process. In the modal parameter identification process, the accuracy of frequency is higher than that of mode shape and damping ratio. Therefore, this paper selects the elastic modulus of the concrete of the high pier as the parameter to be corrected.
[0093] Furthermore, in step S42, the process of correcting the elastic modulus of the bridge pier in the initial finite element model is as follows:
[0094] S421. Based on the vibration frequency of the high pier, the sum of squares of the relative errors between the first two calculated frequencies and the measured frequencies of the initial pier pile finite element model is used as the objective function, the relative errors between the first two calculated frequencies and the measured frequencies are used as the state variables, and the design variable is the elastic modulus of the high pier.
[0095] S422. Design variables are represented in the following ways:
[0096]
[0097] in, Let represent the nth design variable, T represent the transpose of the vector, and n represent the number of design variables; design variables The constraints are ,in, and These represent design variables. Upper and lower limit constraints;
[0098] S423, The objective function is expressed as:
[0099]
[0100]
[0101]
[0102] in, Let n be the objective function, and n be the modal order. To calculate the frequency, For the measured frequency, m and n have the same range of values, and the constraints are: Indicates the i-th error. This represents the i-th parameter to be corrected. and Let represent the upper and lower limits of the i-th parameter to be corrected. The objective function continuously decreases under the constraints and eventually converges. The parameter values at the convergence point of the objective function are the optimal solutions.
[0103] In engineering and physics, calculating the first two natural frequencies of a system usually refers to performing modal analysis, which is particularly common in mechanical, civil and aerospace engineering. This is typically performed using specialized finite element analysis software such as ANSYS, ABAQUS or NASTRAN. These software programs offer powerful computational capabilities and user-friendly interfaces, and can effectively handle complex engineering problems. This part is prior art known to those skilled in the art and will not be described in detail here.
[0104] Furthermore, in step S421, the state variables are calculated as follows:
[0105] S4211. Represent the state variables as follows:
[0106]
[0107] in, Calculate the frequency values for the first two vertical bends. The measured frequency values of the first two vertical bends are given, and their constraint is set to ±10%, meaning that the range of E is [-0.1, 0.1]. Therefore, there are two state variables.
[0108] S4212. The objective function J is defined as follows:
[0109]
[0110] In the formula Corresponding to two state variables, The weighting factors for each corresponding state variable are:
[0111]
[0112] because With corresponding frequency errors The square of the value is proportional to the objective function value, which ensures that each optimization iteration proceeds in the direction of rapidly decreasing objective function value, thereby improving optimization efficiency. The coefficient 10000 is used to increase the objective function value.
[0113] Furthermore, in step S42, the matching between the corrected finite element model of the pier and the actual tested mode shapes of the pier is calculated and analyzed. This can be characterized by the modal correlation criterion (MAC), and the calculation expression for MAC is as follows:
[0114]
[0115] In the formula, This represents the calculated mode shape vector. These represent the measured mode shape vectors. A higher MAC value indicates a better correlation between mode shapes, meaning smaller differences. A lower MAC value indicates a larger difference. By evaluating the MAC criterion, the difference between the corrected finite element model and the actual test results can be quantified, helping engineers assess the accuracy and reliability of the model.
[0116] Furthermore, in step S43, the modal compliance of the high pier structure can be expressed as:
[0117]
[0118] In the formula, For structural modal compliance, To identify structural vibration modes, For normalized mode shapes, n represents the total number of identified modes. Let r be the natural frequency of the structure.
[0119] As can be seen from the above equation, due to higher frequency... Since the values are relatively small, the compliance matrix is mainly determined by the low-order modal parameters. Therefore, as long as the low-order modes of the bridge pier are identified, a relatively accurate compliance matrix can be obtained. The establishment of the compliance matrix is an existing technique known to those skilled in the art and will not be described in detail here.
[0120] Furthermore, step S5 includes:
[0121] S51. Calculate the difference in the diagonal elements of the measured structural flexibility matrix of the high pier relative to the theoretical flexibility matrix of the finite element model of the pier with damaged pile foundation.
[0122] S52. Calculate the change rate of the diagonal elements of the measured structural flexibility matrix of the high pier relative to the theoretical flexibility matrix of the finite element model of the pier with damaged pile foundation.
[0123] Specifically, the rate of change of the compliance of diagonal elements can be obtained in the following way:
[0124] Diagonal elements are extracted from both the measured compliance matrix and the finite element model compliance matrix. These diagonal elements typically represent the displacement response under a unit load on each degree of freedom.
[0125] For each diagonal element, calculate the rate of change of its measured value relative to the theoretical value of the finite element model. The rate of change can be calculated using the following formula:
[0126]
[0127] in, Represents the diagonal elements of the measured compliance matrix. These are the diagonal elements of the compliance matrix of the finite element model;
[0128] Then, the rate of change of the diagonal elements in each degree of freedom is analyzed to assess the extent to which damage affects the structural flexibility. A higher rate of change may indicate that there is more severe damage to the structure in that degree of freedom.
[0129] Furthermore, step S3 includes:
[0130] S31. Perform preprocessing operations, including noise reduction and filtering, on the collected vibration signals to improve signal quality;
[0131] S32. Use modal analysis techniques to extract modal parameters of the high pier, including natural frequency, damping ratio, and mode shape.
[0132] Furthermore, step S2 includes:
[0133] S21. Select representative measuring points on the high pier, usually including the top of the pier, different heights of the pier body, and key locations that may be affected by pile foundation damage.
[0134] S22. Install sensors for detecting vibration at the selected measuring points, ensuring that the sensors are firmly fixed and can accurately capture vibration signals. Specifically, a horizontal vibration pickup or an accelerometer can be used.
[0135] S23. According to the test plan, environmental excitation methods (such as wind, traffic load, etc.) are used to make the high pier vibrate;
[0136] S24. Start the data acquisition system to record the acceleration response data of the high pier during the vibration process. The data acquisition system (DAS) is existing technology and will not be described in detail here.
[0137] Furthermore, step S1 includes:
[0138] S11. Clearly define the specific objectives of the test, including identifying the specific location of damage to the pile foundation and assessing the degree of damage;
[0139] S12. Collect relevant data, including design drawings, geological survey reports, and historical maintenance records, for the high piers and their pile foundations.
[0140] S13. Based on the actual conditions of the target and the high pier, design a reasonable vibration test plan, including the layout of measuring points, selection of test equipment, and test time.
[0141] Specifically, the specific testing process in this embodiment is as follows:
[0142] See Figure 1 To establish a reasonable finite element model, the initial pier and pile finite element model needs to be dynamically modified so that the modified model can better and more comprehensively reflect the overall dynamic and static performance of the structure. Depending on the actual situation, an appropriate method can be selected. The process used in this embodiment is as follows: Figure 1 As shown, firstly, parametric modeling and nonlinear dynamic and static analysis of the high pier structure are performed based on the APDL language, and the results are extracted through post-processing. Then, the calculated values are compared with the measured values to determine if correction is needed. When the difference between the calculated and measured values is significant and correction is required, eigenvalue sensitivity analysis is used to select the parameters to be corrected, ignoring parameters with low sensitivity. Next, the optimization module (OPT, or OptiStruct) is entered; this is a finite element software with an optimization module. Then, referring to the nonlinear static analysis results, the upper and lower limits of the parameters to be corrected (design variables) are determined. Finally, state variables are declared: specifying... The calculated natural frequency of the structure is used as a state variable, and reasonable constraints are determined based on the measured values. An objective function is defined: the relative error between the calculated and measured natural frequencies of the structure (high pier) is used as the objective function, and a weighted approach is adopted to consider the required degree of agreement for different orders. A first-order algorithm is specified as the optimization algorithm, and an appropriate optimization iteration process control method is selected. Optimization analysis then begins, and the results of each optimization iteration are saved. The final optimization result is then analyzed, and its reasonableness is determined. If the difference between the optimized calculated value and the measured value is small, the optimization result is considered reasonable. The specific process described above will be mentioned below.
[0143] See Figure 2The bridge in a certain highway project is a high-pier, three-span continuous beam bridge. Its superstructure consists of 6 small box girders, each with a span of 40m and a width of 3.04m. The 11th pier on the right side of the bridge consists of 3 pier columns with a circular cross-section of 2.2m in diameter. The distance between the center points of two adjacent pier columns is 7.448m. From left to right, the heights of these 3 pier columns (excluding the cap beam) are 25.227m, 25.268m, and 25.309m, respectively. The pile foundations are all 48m long and 2.2m in diameter.
[0144] See Figure 3 Based on the bridge design drawings, an initial finite element model of the high pier pile foundation is established, that is, the initial pier pile finite element model after the pier and pile are completed. The current bridge foundation code considers the pile as a beam supported on an elastic foundation and satisfies the Winkler assumption. Therefore, according to the elastic foundation beam theory, the pile foundation can be simulated using beam elements. The interaction between the pile and the soil is simulated by setting up soil springs according to the m method. The transverse horizontal force of the soil on the pile can be simulated by a set of horizontal springs, and the pile bottom support reaction force can be simulated by a set of vertical springs.
[0145] See Figure 4 According to the testing plan, three accelerometers are vertically arranged along the pier, numbered sequentially from left to right and top to bottom. The arrangement of the measuring points is as follows: Figure 4 As shown. The longitudinal horizontal acceleration time history response data of the high pier were collected under environmental excitation. To ensure the accuracy of the collected data, two sets of data were collected, each lasting 30 minutes, and the sampling frequency was set to 500Hz.
[0146] See Figure 5 To fully utilize finite element method (FEM) software to simulate actual bridge damage, the cross-sectional area of the elements within the upper 5-15m range of the pile foundation in the finite element model of the pier and pile foundation is reduced by 30% to simulate pile foundation damage. Similarly, the cross-sectional area of the elements within the upper 15-25m range of the high pier in the finite element model of the pier and pile foundation is reduced by 30% to simulate high pier damage, thus establishing a finite element model of pier and pile damage. Figure 5 As shown, this finite element model can fully simulate the high piers and pile foundations of actual engineering projects, and its vibration response is the vibration response of the actual pier and pile structure.
[0147] See Figure 6 By applying Gaussian white noise with a duration of 150s and a mean of 0 to simulate ground pulsation and other environmental excitations to the finite element model of pier and pile damage, the horizontal acceleration response of each measuring point of the finite element model of pier and pile damage under environmental excitation is extracted.
[0148] See Figure 7The vibration acceleration time history response data of the finite element model of pier and pile damage under white noise excitation were analyzed using modal parameter identification methods such as SSI and EFDD. The frequency, mode shape and other modal characteristics of the finite element model of pier and pile damage were identified, and the first two frequencies of the pier and pile structure were identified as 0.65Hz and 4.517Hz.
[0149] To improve the efficiency of optimization and correction, it is necessary to select reasonable parameters to be corrected. Based on eigenvalue sensitivity analysis, insensitive parameters are removed, and the elastic modulus of the high pier element in the finite element model of the pier and pile is selected as the parameter to be corrected. The finite element model of the pier and pile is then corrected. Here, based mainly on engineering experience, the upper and lower limits of the design parameters are set to ±10%, that is, the design elastic modulus of the high pier E0=35GPa, and its allowable variation range is [0.9E0,1.1E0], which is [31.5,38.5]. Eigenvalue sensitivity analysis is an existing technology known to those skilled in the art and will not be described in detail here.
[0150] See Figure 8 The theoretical frequencies of the first two pier and pile damage finite element models and the measured frequencies of the pier and pile damage finite element models are as follows: Figure 8 As shown, it can be seen that the initial finite element model of the pier and pile differs greatly from the measured frequency of the pier. The initial finite element model of the pier and pile cannot represent the actual pier and pile foundation. Model correction is required to obtain a finite element model of the pier and pile with good pier damage and pile damage. The first-order optimization method of finite element model correction is adopted, and the measured frequency of the pier is used as the state variable based on the finite element model of pier damage and pile damage to construct the optimization objective function.
[0151] See Figure 9 , Figure 10 The correction values and rates of change of the elastic model parameters of the bridge piers are as follows: Figure 9 As shown, the relative errors between the theoretical and measured frequencies of the pier pile structure after the first two corrections are as follows: Figure 10 As shown, the relative error between the measured and corrected frequency values is 5.5% at most and 2.4% at least. The frequency values of the pier-pile finite element model after correction are closer to the measured values. Thus, the pier damage state is considered in the pier-damaged-pile-good finite element model, and the pier-damaged-pile-good finite element model can be used as the original design model of the pile foundation.
[0152] See Figure 11 , Figure 12The first two frequencies and first two modes of vibration of the bridge obtained from the measured data are used to calculate the flexibility matrix of the finite element model of the pier and pile damage. This flexibility matrix is the measured pier and pile flexibility matrix in engineering applications. Then, the theoretical frequency and mode of vibration of the finite element model of the pier and pile damage are obtained by using the finite element model correction method to calculate the theoretical flexibility matrix of the finite element model of the pier and pile damage. The change rate of the measured flexibility matrix of the pier and pile and the theoretical flexibility matrix of the finite element model of the pier and pile damage are compared to analyze and identify whether the pile foundation is damaged and assess the integrity of the pile body. The actual pile length is judged to meet the design requirements.
[0153] See Figure 13 Calculate the difference between the measured flexibility matrix of the pier pile and the theoretical flexibility matrix of the corrected pier damage and pile good finite element model, as well as the rate of change of the diagonal elements of the flexibility matrix. Figure 13 It can be seen that the measured compliance matrix of the pier pile has a significant change rate compared with the theoretical compliance matrix of the optimized finite element model of the pier damaged pile. In particular, the compliance change rate of the 3rd, 6th and 9th measuring points at the pier column connection is relatively large, with a change rate of 34%-36%. This indicates that the tested pile foundation may have defects such as pile breakage, necking, and insufficient pile length. Therefore, the pile foundation damage indirect identification and assessment method based on high pier vibration test can comprehensively evaluate the integrity and pile length of the tested pile foundation, generate a reliable test report, greatly reduce the time spent on batch testing of pile foundations, and has high accuracy, strong reliability, and makes the test more economical, practical and convenient.
[0154] The above description is merely an exemplary embodiment of the present invention and does not limit the patent scope of the present invention. Any equivalent structural transformations made using the contents of the present invention specification and drawings under the technical concept of the present invention, or direct / indirect applications in other related technical fields, are included within the patent protection scope of the present invention.
Claims
1. A method for indirect identification and assessment of pile foundation damage based on high pier vibration testing, characterized in that, Includes the following steps: S1. Conduct preliminary preparations and planning, clarify test objectives and collect relevant materials, and design a plan based on the actual situation; S2. Set up measuring points on the high pier, and use environmental excitation to make the high pier vibrate, and collect relevant data during the vibration process; S3. Process and analyze the collected data; S4. Based on relevant materials and collected data, establish a finite element model of a high pier damaged pile foundation that is intact, and calculate the corresponding theoretical flexibility matrix. S5. Calculate the change rate of the measured structural flexibility matrix of the high pier relative to the flexibility matrix of the finite element model of the pier with damaged pile foundation. S6. Analyze the obtained change rate to identify whether the pile foundation is damaged and assess the integrity of the pile body. Step S4 includes the following steps: S41. Establish the initial finite element model of the pier and pile foundation based on relevant materials; S42. Based on the collected high pier data, the elastic modulus of the bridge pier in the initial pier-pile finite element model is corrected to obtain a pier-pile finite element model with intact high pier and damaged pile foundation. S43. Calculate the theoretical flexibility matrix of the finite element model of the damaged pile foundation of the high pier; In step S42, the process of correcting the elastic modulus of the bridge pier in the initial finite element model is as follows: S421. Based on the vibration frequency of the high pier, the sum of squares of the relative errors between the first two calculated frequencies and the measured frequencies of the initial pier pile finite element model is used as the objective function, the relative errors between the first two calculated frequencies and the measured frequencies are used as the state variables, and the design variable is the elastic modulus of the high pier. S422. Design variables are represented in the following ways: ； in, Let T represent the nth design variable, T represent the transpose of the vector, and n represent the number of design variables. S423, The objective function is expressed as: ； ； ； in, Let n be the objective function, and n be the modal order. To calculate the frequency, For the measured frequency, m and n have the same range of values, and the constraints are: Indicates the i-th error. This represents the i-th parameter to be corrected. and Let represent the upper and lower limits of the i-th parameter to be corrected. The objective function continuously decreases under the constraints and eventually converges. The parameter values at the convergence point of the objective function are the optimal solutions.
2. The method for indirect identification and assessment of pile foundation damage based on high pier vibration testing according to claim 1, characterized in that, In step S421, the state variables are calculated as follows: S4211. Represent the state variables as follows: ； in, Calculate the frequency values for the first two vertical bends. The measured frequency values of the first two vertical bends are given, and their constraint is set to ±10%, meaning that the range of E is [-0.1, 0.1]. Therefore, there are two state variables. S4212. The objective function J is defined as follows: ； In the formula Corresponding to two state variables, The weighting factors for each corresponding state variable are: ； because With corresponding frequency errors The value is proportional to the square of the objective function, which ensures that each optimization iteration proceeds in the direction of a rapid decrease in the objective function value, thereby improving optimization efficiency.
3. The method for indirect identification and assessment of pile foundation damage based on high pier vibration testing according to claim 2, characterized in that, In step S42, the matching between the corrected finite element model of the pier and the actual tested mode shapes of the pier is calculated and analyzed. The modal correlation criterion (MAC) is used to characterize this matching. The calculation expression for MAC is as follows: ； In the formula, This represents the calculated mode shape vector. These represent the measured mode shape vectors. The higher the MAC value, the better the correlation between the mode shapes.
4. The method for indirect identification and assessment of pile foundation damage based on high pier vibration testing according to claim 1, characterized in that, In step S43, the modal compliance of the high pier structure is expressed as follows: ； In the formula, For structural modal compliance, To identify structural vibration modes, For normalized mode shapes, n represents the total number of identified modes. Let r be the natural frequency of the structure. As can be seen from the above equation, due to higher frequency... Since the values are relatively small, the compliance matrix is mainly determined by the low-order modal parameters. Therefore, as long as the low-order modes of the pier are identified, a compliance matrix with high accuracy can be obtained.
5. The method for indirect identification and assessment of pile foundation damage based on high pier vibration testing according to claim 1, characterized in that, Step S5 includes: S51. Calculate the difference in the diagonal elements of the measured structural flexibility matrix of the high pier relative to the theoretical flexibility matrix of the finite element model of the pier with damaged pile foundation. S52. Calculate the change rate of the diagonal elements of the measured structural flexibility matrix of the high pier relative to the theoretical flexibility matrix of the finite element model of the pier with damaged pile foundation.
6. The method for indirect identification and assessment of pile foundation damage based on high pier vibration testing according to claim 1, characterized in that, Step S3 includes: S31. Perform preprocessing operations, including noise reduction and filtering, on the collected vibration signals to improve signal quality; S32. Use modal analysis techniques to extract modal parameters of the high pier, including natural frequency, damping ratio, and mode shape.
7. The method for indirect identification and assessment of pile foundation damage based on high pier vibration testing according to claim 1, characterized in that, Step S2 includes: S21. Select representative measuring points on the high pier; S22. Install vibration sensors at the selected measuring points, ensuring that the sensors are securely fixed and can accurately capture vibration signals. S23. According to the test plan, environmental excitation is used to induce vibration in the high pier; S24. Start the data acquisition system and record the acceleration response data of the high pier during the vibration process.
8. The method for indirect identification and assessment of pile foundation damage based on high pier vibration testing according to claim 1, characterized in that, Step S1 includes: S11. Clearly define the specific objectives of the test, including identifying the specific location of damage to the pile foundation and assessing the degree of damage; S12. Collect relevant data, including design drawings, geological survey reports, and historical maintenance records, for the high piers and their pile foundations. S13. Based on the actual conditions of the target and the high pier, design a reasonable vibration test plan, including the layout of measuring points, selection of test equipment, and test time.