A method for correcting the vertical bearing capacity of pile foundations for liquefiable silty soil considering vibration time effects

Abstract

This invention provides a method for correcting the vertical bearing capacity of pile foundations in liquefiable silty soil considering the vibration time effect, relating to the field of geotechnical engineering. This method includes S1: based on vibration time history data from the engineering site, baseline correction, bandpass filtering, and normalization are performed on the original vibration acceleration time history to obtain a standardized vibration acceleration time sequence; S2: based on the standardized vibration acceleration time sequence, a one-dimensional equivalent shear beam model is used for seismic response analysis to calculate the cyclic shear stress time history distribution of soil layers at different depths, obtaining the cyclic shear stress time history distribution field of the soil layers. By performing baseline correction, frequency band filtering, and amplitude unification processing on the vibration acceleration time history, the input data possesses stable spectral characteristics and a consistent scale foundation, and combined with a shear propagation model, a continuous distribution of stress response at different depths over time is obtained.

Description

Technical Field

[0001] This invention relates to the field of geotechnical engineering technology, specifically to a method for correcting the vertical bearing capacity of pile foundations for liquefied silty soil considering the vibration time effect. Background Technology

[0002] Geotechnical engineering, a crucial branch of civil engineering, primarily studies the physical and mechanical properties of soil and rock masses under natural conditions and engineering actions, as well as their engineering response laws. It encompasses multiple areas including foundation engineering, slope stability, underground engineering, soil dynamics, and environmental geotechnical engineering. Soil dynamics, as a vital component of geotechnical engineering, focuses on the deformation, strength degradation, and failure mechanisms of soil under dynamic loads such as earthquakes, blasting, and mechanical vibrations. In particular, it addresses the liquefaction phenomenon that can occur in saturated sand or silt under cyclic loading, which significantly alters the soil's bearing capacity and deformation characteristics. A method for correcting the vertical bearing capacity of pile foundations in liquefied silt, considering the vibration time effect, is a method for calculating and correcting the vertical bearing capacity under earthquake or other dynamic load conditions. This method considers the characteristics of liquefaction in saturated silt and its evolution over vibration time, and can reflect the strength degradation of the pile-soil interface, cumulative soil damage, and the interaction between piles. Its purpose is to improve the accuracy of vertical bearing capacity assessment for pile foundations in liquefied sites, providing a more reliable theoretical basis and calculation tools for engineering design and safety evaluation.

[0003] Existing technologies in engineering applications often rely on simplified dynamic indicators or empirical reduction coefficients to handle the effects of liquefaction. Vibration input is often expressed as representative peak values ​​or equivalent cycle counts, lacking a continuous description of the entire actual vibration process. This results in the failure to effectively reflect the differences in frequency components and durations, leading to deviations in stress response results. Soil liquefaction states are often judged using a single threshold, ignoring the gradual accumulation of pore water pressure over the loading process. This leads to a coarse division of liquefaction development stages and is prone to misjudgment under complex seismic records. For example, long-duration weak earthquakes and short-duration strong earthquakes may produce similar judgment results, but the actual effects may differ significantly. Pile-soil interaction analysis often uses fixed resistance parameters or simple reduction methods, failing to consider the continuous attenuation of interface strength over time and with changes in soil state, making it difficult for the calculation results to reflect the true stress path. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a method for correcting the vertical bearing capacity of pile foundations for liquefiable silty soil that considers the vibration time effect. This method solves the problem that existing technologies often rely on simplified dynamic indicators or empirical reduction coefficients to handle the liquefaction effect in engineering applications. Vibration input is often expressed as a representative peak value or equivalent number of cycles, lacking a continuous description of the entire actual vibration process. This results in the failure to effectively reflect the differences in frequency components and durations, leading to deviations in stress response results.

[0005] To achieve the above objectives, the present invention provides the following technical solution: a method for correcting the vertical bearing capacity of pile foundations for liquefiable silty soil considering the vibration time effect, comprising the following steps:

[0006] S1: Based on the vibration time history data of the engineering site, the original vibration acceleration time history is subjected to baseline correction, bandpass filtering and normalization to obtain a standardized vibration acceleration time sequence.

[0007] S2: Based on the standardized vibration acceleration time sequence, a one-dimensional equivalent shear beam model is used to perform seismic response analysis, calculate the time history distribution of cyclic shear stress in soil layers at different depths, and obtain the time history distribution field of cyclic shear stress in soil layers.

[0008] S3: Based on the time history distribution field of the cyclic shear stress in the soil layer, the pore water pressure growth model is used to perform cyclic loading analysis, calculate the evolution process of the pore water pressure ratio at each depth over time, and obtain the time history evolution field of the pore water pressure ratio.

[0009] S4: Based on the pore water pressure ratio time history evolution field, the liquefaction discrimination threshold method is used to determine the time nodes and duration intervals of liquefaction in each soil layer, and the stratified liquefaction time sequence triggering matrix is ​​obtained.

[0010] S5: Based on the layered liquefaction timing triggering matrix, a pile-soil interface strength degradation model is constructed, and the pile side friction and pile end resistance parameters are time-varyingly corrected to obtain the time-varying degradation distribution of pile-soil interface strength.

[0011] S6: Based on the time history distribution field of the cyclic shear stress of the soil layer and the time-varying degradation distribution of the pile-soil interface strength, the degree of damage to the soil during vibration is calculated using the cyclic cumulative damage model, and the vibration cumulative damage factor of the soil is obtained.

[0012] S7: Based on the time-varying degradation distribution of the pile-soil interface strength and the cumulative damage factor of soil vibration, establish a pile group interaction model, calculate the reduction effect of the single pile bearing capacity in the pile group system, and obtain the pile group interaction reduction coefficient.

[0013] S8: Based on the time-varying degradation distribution of the pile-soil interface strength, the cumulative damage factor of soil vibration, and the reduction coefficient of pile group interaction, calculate the change in vertical bearing capacity of the pile group foundation during the entire vibration process, and obtain the time history curve of the vertical bearing capacity of the pile group.

[0014] S9: Based on the time history curve of the vertical bearing capacity of the pile group, extract the bearing capacity at key moments and compare it with the initial bearing capacity to determine the bearing capacity correction coefficient, and obtain the vertical bearing capacity correction coefficient of the pile group considering the vibration time effect.

[0015] Preferably, step S1 includes the following steps:

[0016] S101: Based on the original vibration acceleration time history data, the baseline correction method is used to eliminate low-frequency drift and obtain the preliminary correction vibration time program sequence;

[0017] S102: Based on the preliminary correction vibration time program sequence, a bandpass filtering method is used to remove noise interference to obtain a filtered vibration time program sequence;

[0018] S103: Based on the filtered vibration time program sequence, interpolation discretization is performed using a time step uniform processing method to obtain a vibration time program sequence with equal step size.

[0019] S104: Based on the constant step vibration time program sequence, the amplitude normalization method is used for standardization processing to obtain the standardized vibration acceleration time program sequence.

[0020] Preferably, step S2 includes the following steps:

[0021] S201: Based on the standardized vibration acceleration time sequence, establish a layered soil parameter model;

[0022] S202: Based on the layered soil parameter model, construct a dynamic response calculation model;

[0023] S203: Based on the dynamic response calculation model and the standardized vibration acceleration time sequence, perform seismic response analysis to obtain shear stress time history dataset;

[0024] S204: Based on the shear stress time history dataset, spatial distribution reconstruction is performed to obtain the soil cyclic shear stress time history distribution field.

[0025] Preferably, step S3 includes the following steps:

[0026] S301: The program sequence for calculating the cyclic stress ratio based on the time history distribution field of the cyclic shear stress in the soil layer;

[0027] S302: Based on the program sequence of the cyclic stress ratio, construct a calculation model for pore pressure growth;

[0028] S303: Based on the pore pressure growth calculation model, perform cumulative calculations to obtain the pore water pressure growth sequence;

[0029] S304: Normalize the pore water pressure growth sequence to obtain the pore water pressure ratio time history evolution field.

[0030] Preferably, step S4 includes the following steps:

[0031] S401: Determine the liquefaction discrimination threshold parameter based on the pore water pressure ratio time history evolution field;

[0032] S402: Perform time step comparison based on the liquefaction discrimination threshold parameter to obtain the liquefaction trigger time sequence;

[0033] S403: Determine the liquefaction duration interval based on the liquefaction trigger time series, and obtain liquefaction duration interval data;

[0034] S404: Construct a matrix representation based on the liquefaction duration interval data to obtain a hierarchical liquefaction timing trigger matrix.

[0035] Preferably, step S5 includes the following steps:

[0036] S501: Based on the layered liquefaction timing triggering matrix, identify the soil layers affected by liquefaction and obtain the set of soil layers affected by liquefaction;

[0037] S502: Based on the liquefaction-affected soil layer set, establish an initial pile-soil interface strength model;

[0038] S503: Based on the initial pile-soil interface strength model and liquefaction time information, update the parameters to obtain a time-varying interface strength parameter set;

[0039] S504: Based on the time-varying interface strength parameter set, spatial mapping is performed to obtain the time-varying degradation distribution of pile-soil interface strength.

[0040] Preferably, step S6 includes the following steps:

[0041] S601: Based on the time history distribution field of the cyclic shear stress in the soil layer, the program sequence for calculating shear strain is obtained;

[0042] S602: Extract strain amplitude based on the shear strain time sequence to obtain strain amplitude dataset;

[0043] S603: Based on the strain amplitude dataset and the time-varying degradation distribution of the pile-soil interface strength, damage accumulation calculation is performed to obtain a damage accumulation calculation sequence;

[0044] S604: Based on the damage accumulation calculation sequence, normalization processing is performed to obtain the soil vibration cumulative damage factor.

[0045] Preferably, step S7 includes the following steps:

[0046] S701: Extract the geometric parameters of the pile group based on the time-varying degradation distribution of the pile-soil interface strength to obtain the pile group geometric parameter set;

[0047] S702: Calculate the pile spacing influence based on the geometric parameter set of the pile group to obtain the pile spacing influence coefficient;

[0048] S703: Based on the pile spacing influence coefficient and the soil vibration cumulative damage factor, a coupled calculation is performed to obtain the intermediate coefficient of pile group interaction;

[0049] S704: Based on the intermediate coefficient of the pile group interaction, a reduction process is performed to obtain the pile group interaction reduction coefficient.

[0050] Preferably, step S8 includes the following steps:

[0051] S801: Calculate the pile side friction based on the time-varying degradation distribution of the pile-soil interface strength, and obtain the pile side friction time program sequence;

[0052] S802: Based on the pile side friction time sequence and the soil vibration cumulative damage factor, a modified pile side friction sequence is obtained;

[0053] S803: Calculate the pile end resistance based on the modified pile side friction sequence and the pile group interaction reduction coefficient to obtain the pile end resistance sequence;

[0054] S804: Based on the superposition of the modified pile side friction sequence and the pile end resistance sequence, the time history curve of the vertical bearing capacity of the pile group is obtained.

[0055] Preferably, step S9 includes the following steps:

[0056] S901: Extract feature values ​​based on the time history curve of the vertical bearing capacity of the pile group to obtain a set of key bearing capacity feature values;

[0057] S902: Based on the set of key bearing capacity characteristic values, a comparative calculation is performed to obtain a bearing capacity ratio sequence;

[0058] S903: Based on the bearing capacity ratio sequence, perform statistical analysis to obtain the calculated value of the bearing capacity correction coefficient;

[0059] S904: Based on the calculated value of the bearing capacity correction coefficient, encapsulate and output to obtain the vertical bearing capacity correction coefficient of the pile group considering the vibration time effect.

[0060] This invention provides a method for correcting the vertical bearing capacity of pile foundations for liquefiable silty soil that considers the vibration time effect. It has the following beneficial effects:

[0061] This invention employs baseline correction, frequency band filtering, and amplitude unification processing on vibration acceleration time histories to ensure input data possesses stable spectral characteristics and a consistent scale foundation. Combined with a shear propagation model, it obtains the continuous distribution of stress response at different depths over time, transforming soil dynamic response from a single index to a full-process characterization. Furthermore, it introduces a time-path description of pore water pressure evolution with cyclic loading, shifting liquefaction development from being limited to critical threshold judgment to a dynamic evolutionary process. A time-series structure for liquefaction occurrence is established through layered triggering relationships, providing clear temporal boundaries for soil state changes. Finally, it integrates interfacial resistance parameters with liquefaction development... The phase correlation makes the side resistance and end resistance continuously decrease over time. At the same time, the impact of stress cycle accumulation during vibration on structural damage is combined to form a quantitative index of damage degree, so that the bearing capacity assessment shifts from static reduction to historical path correlation expression. Then, through the coupling analysis of the mutual influence between multiple piles in space, the bearing capacity change of a single pile can reflect the overall group effect. Finally, the bearing capacity evolution curve throughout the entire vibration process is obtained. By comparing key stages, correction coefficients are extracted, so that the bearing capacity evaluation has time resolution and state response consistency, thereby improving the accuracy and reliability of bearing capacity prediction in complex dynamic environments. Attached Figure Description

[0062] Figure 1 This is a schematic diagram of the main steps of the present invention;

[0063] Figure 2 This is a detailed schematic diagram of S1 of the present invention;

[0064] Figure 3 This is a detailed schematic diagram of S2 of the present invention;

[0065] Figure 4 This is a detailed schematic diagram of S3 of the present invention;

[0066] Figure 5 This is a detailed schematic diagram of S4 of the present invention;

[0067] Figure 6 This is a detailed schematic diagram of S5 of the present invention;

[0068] Figure 7 This is a detailed schematic diagram of S6 of the present invention;

[0069] Figure 8 This is a detailed schematic diagram of S7 of the present invention;

[0070] Figure 9 This is a detailed schematic diagram of S8 of the present invention;

[0071] Figure 10 This is a detailed schematic diagram of S9 of the present invention. Detailed Implementation

[0072] 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. 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.

[0073] Example:

[0074] like Figure 1-10 As shown, this embodiment of the invention provides a method for correcting the vertical bearing capacity of pile foundations for liquefiable silty soil considering the vibration time effect, including the following steps:

[0075] S1: Based on the vibration time history data of the engineering site, the original vibration acceleration time history is subjected to baseline correction, bandpass filtering and normalization to obtain a standardized vibration acceleration time sequence.

[0076] S2: Based on the standardized vibration acceleration time sequence, a one-dimensional equivalent shear beam model is used to perform seismic response analysis, calculate the time history distribution of cyclic shear stress in soil layers at different depths, and obtain the time history distribution field of cyclic shear stress in soil layers.

[0077] S3: Based on the time history distribution field of the cyclic shear stress in the soil layer, the pore water pressure growth model is used to perform cyclic loading analysis, calculate the evolution process of the pore water pressure ratio at each depth over time, and obtain the time history evolution field of the pore water pressure ratio.

[0078] S4: Based on the pore water pressure ratio time history evolution field, the liquefaction discrimination threshold method is used to determine the time nodes and duration intervals of liquefaction in each soil layer, and the stratified liquefaction time sequence triggering matrix is ​​obtained.

[0079] S5: Based on the layered liquefaction timing triggering matrix, a pile-soil interface strength degradation model is constructed, and the pile side friction and pile end resistance parameters are time-varyingly corrected to obtain the time-varying degradation distribution of pile-soil interface strength.

[0080] S6: Based on the time history distribution field of the cyclic shear stress of the soil layer and the time-varying degradation distribution of the pile-soil interface strength, the degree of damage to the soil during vibration is calculated using the cyclic cumulative damage model, and the vibration cumulative damage factor of the soil is obtained.

[0081] S7: Based on the time-varying degradation distribution of the pile-soil interface strength and the cumulative damage factor of soil vibration, establish a pile group interaction model, calculate the reduction effect of the single pile bearing capacity in the pile group system, and obtain the pile group interaction reduction coefficient.

[0082] S8: Based on the time-varying degradation distribution of the pile-soil interface strength, the cumulative damage factor of soil vibration, and the reduction coefficient of pile group interaction, calculate the change in vertical bearing capacity of the pile group foundation during the entire vibration process, and obtain the time history curve of the vertical bearing capacity of the pile group.

[0083] S9: Based on the time history curve of the vertical bearing capacity of the pile group, extract the bearing capacity at key moments and compare it with the initial bearing capacity to determine the bearing capacity correction coefficient, and obtain the vertical bearing capacity correction coefficient of the pile group considering the vibration time effect.

[0084] S1 includes the following steps:

[0085] S101: Based on the original vibration acceleration time history data, the baseline correction method is used to eliminate low-frequency drift and obtain the preliminary correction vibration time program sequence;

[0086] First, the continuous time series output by the acquisition device is read and divided into multiple sets of sampling points. For example, a structural vibration record is divided into several time slices and the corresponding amplitudes are marked. Then, baseline offset identification is performed on each sampling point, and the average value of the stable intervals before and after the time series is selected as the reference benchmark value. ,in Through formula The calculation yields the following result: This represents the amplitude of the i-th sampling point, where n represents the number of sampling points. Then, a correction is performed on each sampling value. To complete the initial translation correction, in practice, data processing software can be used to import the sequence and calculate the local mean using a sliding window method. For example, the window length can be set to several sampling intervals, and the differences in their means can be compared. When the difference is within a preset interval (e.g., the relative deviation is in a lower interval, i.e., less than a certain proportion), it is considered a stable interval. Then, low-frequency drift is judged by calculating the rate of change of the mean between adjacent intervals. and drift threshold In comparison, when k is greater than the upper limit of the set interval, trendline fitting is performed and the fitted value is subtracted, for example, using a first-order linear function. The sequence is fitted and subtracted point by point to obtain the sequence after removing low-frequency components, which ultimately forms the preliminary correction sequence for vibration.

[0087] S102: Based on the preliminary correction vibration time program sequence, a bandpass filtering method is used to remove noise interference to obtain a filtered vibration time program sequence;

[0088] After initial correction, when filtering the sequence, the frequency composition range is first broken down according to the characteristics of the equipment from which the vibration signal originates. The frequency amplitude distribution is then obtained by performing rapid spectrum analysis on the sequence. For example, the time-domain data is converted to frequency-domain data to obtain the correspondence between frequency f and amplitude A. Finally, upper and lower limits for the bandpass filter are set. ,in Based on the inherent frequency range of the equipment, and through empirical division into effective signal and noise regions, when the frequency is lower than... or higher When a frequency component is identified as an interference component, a filtering function H(f) can be applied to each frequency component in the actual implementation. For example, when... ,otherwise Thus, the filtered spectrum is obtained. The time-domain signal is then recovered through inverse transform. In software operation, the filter parameters are set, and the change in the root mean square (RMS) value before and after filtering is observed. The RMS value can be calculated using the formula... The calculation shows that the filtering parameters are considered effective when the RMS rate of change is within a reasonable range (e.g., not exceeding a set proportion range). Simultaneously, the energy proportions of high-frequency components before and after filtering are compared. Make a judgment when When the temperature drops to the target range, the filtering process is confirmed to be complete, thus obtaining the filtering vibration time program sequence.

[0089] S103: Based on the filtered vibration time program sequence, interpolation discretization is performed using a time step uniform processing method to obtain a vibration time program sequence with equal step size.

[0090] First, extract the timestamp set from the original sequence and calculate the adjacent sampling interval. By statistical analysis of all The distribution range is used to determine whether it falls within a uniform interval. When the difference between the maximum and minimum intervals exceeds a set threshold interval, interpolation is performed, followed by setting a uniform time step. ,Should The average value method can be used Determine where m is the number of intervals, and then construct a new time series. For each new time point, the corresponding amplitude is calculated using linear interpolation. For example, using formulas ,in Enclosing in the original sequence At the two time points, the results are calculated and recorded point by point using programming tools in the specific implementation. At the same time, the interpolation error is evaluated and the error is calculated. and with error threshold The interpolation result is retained if e is within the allowable range; otherwise, it is adjusted. Alternatively, a higher-order interpolation method can be used to repeatedly calculate and obtain the program sequence for constant-step vibration.

[0091] S104: Based on the constant step vibration time program sequence, the amplitude normalization method is used for standardization processing to obtain the standardized vibration acceleration time program sequence.

[0092] First, find the maximum value in the sequence. and minimum value The range of each sampled value is obtained by iterating through all sampled points. Then, a standardized range parameter is set, such as a target range of [0,1] or [-1,1]. Subsequently, a normalization calculation is performed on each sampled value. If a symmetrical interval is used, it is further transformed into During the execution process, it is necessary to determine the difference in the denominator. Whether it is within the valid range, if Δa is lower than the set lower threshold, it indicates insufficient data fluctuation and the input sequence needs to be re-examined. In software operation, batch calculations are used to achieve numerical mapping and statistical analysis of the normalized results, such as calculating the normalized mean. and standard deviation And determine whether σ is within a reasonable range to verify the data distribution status, while filtering out outliers, when certain When the value exceeds the preset range, adjustments are made by truncation or recalculation to obtain a standardized vibration acceleration time sequence.

[0093] S2 includes the following steps:

[0094] S201: Based on the standardized vibration acceleration time sequence, establish a layered soil parameter model;

[0095] First, the collected raw acceleration data is normalized, and the acceleration amplitudes at different measuring points are converted into a dimensionless sequence using ratios. For example, a reference acceleration amplitude can be selected as the baseline value. Acceleration at any given moment Transform into The soil was then divided into several layers according to the stratigraphic information, and the density ρ and shear wave velocity of each layer were extracted based on the engineering survey report. and damping ratio Parameters, through relational formulas Calculate the shear modulus of each layer, where G represents the shear modulus and ρ represents the soil density. The shear wave velocity is represented, and then a layered parameter set is constructed. In the actual example, the density of a certain shallow soil layer can be set to the median value within the normal range, and the shear wave velocity can be taken as the value of common soft soil. The calculated shear modulus is in the middle of the empirical range. By repeating the above process layer by layer, the multi-layer soil parameter matrix is ​​established. Combined with the engineering site, such as a building foundation scenario, the soil parameters of different depths are arranged in the order of depth, and finally a layered soil parameter model is formed.

[0096] S202: Based on the layered soil parameter model, construct a dynamic response calculation model;

[0097] Based on the established layered soil parameter model, the shear modulus G and damping ratio of each soil layer are first read. And parameters such as layer thickness H, and establish a single-degree-of-freedom or multi-degree-of-freedom system according to the basic equations of dynamics, treating each layer as a mass-spring-damped unit, and through mass... Calculate the equivalent mass of each layer, where ρ represents density and H represents layer thickness. Then, calculate the interlayer stiffness coefficient using the stiffness k = G / H. Finally, apply the damping coefficient c according to... An estimation is performed, where ξ is the damping ratio, k is the stiffness, and m is the mass. The dynamic response matrix is ​​constructed using these parameters. In practical applications, general-purpose numerical calculation software can be used to establish the matrix equations. In this model, [M] is the mass matrix, [C] is the damping matrix, [K] is the stiffness matrix, and {F(t)} is the input seismic action. The standardized vibration acceleration time history is used as the input load and converted into an equivalent force F(t) = m·a(t), where a(t) is the time history acceleration. The displacement and velocity responses are solved by a step-by-step integration method. For example, a small interval within the allowable range of the project is selected for the time step. The response results are obtained by iterative calculation step by step. Combined with a specific site such as a slope or foundation soil layer, the response of each node is solved to form a complete dynamic response calculation model.

[0098] S203: Based on the dynamic response calculation model and the standardized vibration acceleration time sequence, perform seismic response analysis to obtain shear stress time history dataset;

[0099] First, the input acceleration sequence is divided into continuous discrete points according to time steps. For each time step, the dynamic equation is called to calculate the response and obtain the shear strain γ of each layer. The shear stress is then calculated using the relationship τ=G·γ, where τ is the shear stress, G is the shear modulus, and γ is the shear strain. The shear strain can be obtained by dividing the displacement difference Δu between adjacent nodes by the layer thickness H, i.e., γ=Δu / H. In a specific example, it can be assumed that the displacement difference between the upper and lower nodes is within the range of common small deformations within a certain time step. The shear strain value is obtained by substituting these values ​​into the calculation, and then multiplied by the shear modulus of that layer to obtain the corresponding shear stress value. The results of each time step are recorded sequentially to form a shear stress time history dataset. During the "calculation" process, the above formula can be called step by step through a loop. For the "judgment" step, a shear strain threshold can be set. The threshold is the median value within the empirically permissible range. When γ exceeds this threshold, it is marked as a nonlinear stage; otherwise, it is a linear stage. The setting can be based on the recommended interval in the specification, taking the middle value. After setting through examples, the values ​​are compared and judged in the calculation, and finally a complete shear stress time history dataset is obtained over the entire time series.

[0100] S204: Based on the shear stress time history dataset, spatial distribution reconstruction is performed to obtain the soil cyclic shear stress time history distribution field.

[0101] First, extract the shear stress values ​​of each soil layer at different time steps, and then perform interpolation according to spatial location. Linear interpolation methods can be used to estimate the values ​​at unmeasured nodes, for example, for adjacent layers with known shear stress. Through formula Calculate the shear stress at any depth, where x represents the target depth. Given the known layer locations, in practical examples, the layer spacing can be set to the thickness range of conventional engineering projects. Continuous distribution values ​​are obtained through interpolation calculations. During the "reconstruction" process, the above interpolation calculations need to be repeated for different time steps to form a three-dimensional data structure. For the "filtering" process, a stress change rate threshold can be set. When η exceeds the upper limit of the set interval, data smoothing is performed, and the threshold is used. Based on the median value of the interval selected according to engineering experience, and after setting through examples, it is applied to the screening process. Finally, the shear stress data of each time step and each spatial location are integrated into a continuous distribution field to form the time history distribution field of soil cyclic shear stress.

[0102] S3 includes the following steps:

[0103] S301: The program sequence for calculating the cyclic stress ratio based on the time history distribution field of the cyclic shear stress in the soil layer;

[0104] Based on the shear stress time history distribution information obtained from the dynamic response of the soil layer, the distribution information is discretized along the depth direction. For each discrete unit, the peak shear stress and effective overburden stress are extracted. Further normalization is then performed to form a cyclic stress ratio sequence. In practice, a representative soil layer unit can be selected, and its shear stress values ​​at multiple time steps can be recorded. For example, the corresponding shear stress amplitude can be extracted at several time nodes, and combined with the effective stress at that depth using a formula... The calculation is performed, where τ represents the shear stress amplitude. The effective overburden stress (CSR) is represented by a discrete CSR value sequence calculated time-by-time. The CSR sequence is then made continuous using time interpolation. For the "calculation" process, array operations can be performed using conventional numerical software such as MATLAB to perform item-by-item ratio calculations between the shear stress matrix and the effective stress vector. For the "judgment" process, reasonable ranges for CSR can be set. For example, CSR can be divided into a low range where the value is below a certain empirical lower limit, a high range where the value is above a certain empirical upper limit, and a transition range in between. The ranges are classified by comparing the calculation results item by item, and finally, a time-continuous cyclic stress ratio time sequence is formed.

[0105] S302: Based on the program sequence of the cyclic stress ratio, construct a calculation model for pore pressure growth;

[0106] A pore water pressure growth model is constructed based on the obtained cyclic stress ratio (CSR) sequence. The CSR sequence is used as the input variable for function fitting and parameter setting. During the execution process, the CSR sequence is first segmented into several intervals, and a corresponding growth function relationship is established for each interval. For example, the pore pressure growth relationship ru=f(CSR,t) can be expressed in exponential or power function form, where ru represents the pore pressure ratio, CSR is the cyclic stress ratio, and t represents the number of cycles or time steps. The function coefficients are determined using existing experimental data. For the "analysis" process, curve fitting software such as Origin can be used to select the function form with a high goodness of fit as the model expression. For the "calculation" process, the corresponding ru increment is calculated by substituting the CSR values ​​at different time steps. For the "weight" setting, correction coefficients can be set according to different soil layer conditions. For example, dense soil layers are given a lower weight coefficient, and loose soil layers are given a higher weight coefficient. The weight coefficients can be obtained by averaging historical experimental data and normalizing them to ensure that their values ​​are within a reasonable range. By calculating step by step for each time step, a complete pore pressure growth calculation model is constructed.

[0107] S303: Based on the pore pressure growth calculation model, perform cumulative calculations to obtain the pore water pressure growth sequence;

[0108] Based on the established pore pressure growth model, a stepwise cumulative calculation is performed, superimposing the pore pressure increments at each time step to form a complete pore water pressure growth sequence. During the execution process, the initial value of the pore pressure ratio is first initialized to a certain baseline state value, and then the growth amount at each time step is gradually accumulated according to the time step sequence. Δru is calculated by the aforementioned model, and the overall process can be expressed as follows: Where n represents the time step number, the entire sequence calculation is completed through iterative loops. For the "cumulative calculation" process, a loop structure can be used in the programming environment, such as using a for loop in Python to accumulate the array item by item. For the "judgment" process, when the ru value is close to the preset upper limit threshold, a stopping condition can be set. This threshold can be set based on the statistical range of the pore pressure ratio approaching the limit state in the experimental data, and an interval range can be determined by averaging multiple sets of data as a reference standard. By updating and storing the results of each step, the complete pore water pressure growth sequence is obtained.

[0109] S304: Normalize the pore water pressure growth sequence to obtain the pore water pressure ratio time history evolution field.

[0110] The obtained pore water pressure growth sequence is normalized and converted into a standardized pore pressure ratio time history evolution field. During the execution process, the maximum and minimum values ​​in the sequence are first obtained, and a normalization formula is constructed. ,in This represents the normalized pore pressure ratio, where ru is the original pore pressure ratio. and These are the minimum and maximum values ​​in the sequence. The sequence is normalized by substituting each value into the calculation. For the "calculation" process, the array can be linearly transformed using data processing software. For the "comparison" process, the normalized result is compared with a preset interval. For example, the normalized value is divided into three intervals: low, medium, and high. The classification is completed by setting the interval boundary values. For the "threshold" setting, the interval boundary position can be determined based on engineering experience or historical data statistics. A stable reference value is obtained by averaging multiple sets of sample data. By spatially mapping the normalized data, the pore pressure ratio corresponding to different depths and times is reconstructed in two or three dimensions, ultimately forming the time history evolution field of pore water pressure ratio.

[0111] S4 includes the following steps:

[0112] S401: Determine the liquefaction discrimination threshold parameter based on the pore water pressure ratio time history evolution field;

[0113] First, the pore water pressure ratio sequence corresponding to different time steps is exported from numerical simulation software or field monitoring system. The pore water pressure ratio corresponding to each depth layer is expressed as a function r(t) that varies with time, where r represents the pore water pressure ratio and t represents the time step number. The sequence is read point by point, and the increment between adjacent time steps is calculated by simple difference. When Δr shows an increasing trend over multiple consecutive time steps, this stage is recorded as a candidate change segment. Combined with a preset liquefaction threshold range, the pore water pressure ratio is divided into a low range (e.g., a segment close to the initial state), a medium range (significantly rising but not reaching the critical state), and a high range (close to or reaching saturation). The threshold parameters are obtained through statistical analysis of historical experimental data. For example, the frequency of liquefaction occurring when the pore water pressure ratio reaches a certain range under multiple operating conditions is selected, and the frequency is calculated using a frequency statistical formula. ,in The threshold range is determined by the frequency of occurrence within a certain range and N represents the total number of samples. The interval with the most concentrated occurrence frequency is selected as the threshold range. In the example, it is assumed that the r(t) of a certain soil layer gradually increases from the initial lower interval to the upper limit interval during the vibration loading process. By comparing the rate of change and the cumulative value in this process, a set of threshold parameters for subsequent discrimination is finally determined, and the liquefaction discrimination threshold parameters are obtained.

[0114] S402: Perform time step comparison based on the liquefaction discrimination threshold parameter to obtain the liquefaction trigger time sequence;

[0115] First, the time series is discretized into multiple equally spaced time steps. Then, the pore water pressure ratio r(t) at each time step is compared point-by-point with a threshold parameter. This comparison process is achieved by constructing a discriminant function. ,in The threshold for liquefaction is defined as follows: when f(t) is greater than zero, it is marked as a triggered state; when it is less than zero, it is marked as a non-triggered state. The occurrence positions of the triggered state are counted in continuous time steps, and the time point when the state first changes from non-triggered to triggered is selected as the initial trigger time through logical judgment. At the same time, it is compared whether f(t) > 0 is continuously satisfied in subsequent time steps. If there is a brief period of time when the value is lower than the threshold, an allowable fluctuation range is set. For example, within a certain proportion range, it is still considered as a continuous state. In the example, after vibration loading, the pore water pressure ratio of a certain soil layer gradually approaches the threshold in multiple time steps and exceeds the threshold at a certain moment. Multiple trigger times are obtained by step-by-step comparison. These times are arranged in chronological order to form a sequence structure, which yields the liquefaction trigger time series.

[0116] S403: Determine the liquefaction duration interval based on the liquefaction trigger time series, and obtain liquefaction duration interval data;

[0117] First, sort the time series and calculate the time interval between adjacent trigger times. By setting a time continuity discrimination coefficient k, Δt is compared with k. When Δt is less than a certain continuity judgment range, the corresponding time point is assigned to the same continuous interval. When Δt exceeds the range, it is divided into a new interval. The continuity judgment range is obtained through statistical analysis of historical loading cycle data. For example, a time scale is set based on the distribution range of vibration cycles. In the example, assuming that multiple consecutive time steps within a certain period meet the liquefaction triggering condition, this period is marked as a continuous interval, and the interval start time is used as the basis for the classification. With end time Describe the interval and calculate its length. As a persistent feature parameter, this process is repeated for all intervals to gradually form a set of multiple liquefaction persistence intervals. The start and end information of each interval is stored through a data structure to obtain liquefaction persistence interval data.

[0118] S404: Construct a matrix representation based on the liquefaction duration interval data to obtain a hierarchical liquefaction timing trigger matrix.

[0119] First, spatial stratification information is mapped to time intervals. Different depth layers are numbered i, and different time intervals are numbered j, constructing a two-dimensional matrix M(i,j), where the matrix elements represent the liquefaction state of the i-th layer in the j-th time interval. The assignment rule is determined by whether there is a trigger record for the layer in the corresponding time interval. If there is, it is assigned a state value of one; otherwise, it is assigned a state value of zero. In the specific implementation, the interval range is mapped to a unified time axis by traversing the continuous interval data of each layer, and the matrix elements are filled by discrete time index. At the same time, the matrix is ​​standardized, and the time axis is uniformly divided into time units of fixed length to avoid inconsistencies caused by different interval lengths. In the example, it is assumed that there are multiple soil layers that liquefy in different time intervals. Through the above mapping and filling process, a matrix structure is formed with rows representing layers and columns representing time intervals. Furthermore, the state distribution of each column or each row is calculated by simple statistical calculation, and finally, the stratified liquefaction timing trigger matrix is ​​obtained.

[0120] S5 includes the following steps:

[0121] S501: Based on the layered liquefaction timing triggering matrix, identify the soil layers affected by liquefaction and obtain the set of soil layers affected by liquefaction;

[0122] Based on the stratified liquefaction timing triggering matrix, soil layers affected by liquefaction are identified, resulting in a set of liquefaction-affected soil layers. First, the soil layer data collected in the field are classified according to layer thickness and soil properties to form a stratified data table. Each layer is labeled with soil property number, void ratio, water content, relative density, and other parameters. Simultaneously, based on the liquefaction triggering matrix, different soil layers are initially ranked according to their liquefaction susceptibility. This ranking is then determined using a formula. Calculate the liquefaction index for each layer, where For effective stress, The critical stress, The loosening coefficient of the soil layer is used, and the calculation results are compared with the preset liquefaction threshold. The threshold range is set to 0.8-1.2. When the liquefaction index is greater than 1.0, it is judged as a high liquefaction risk layer; 0.9-1.0 is a medium liquefaction risk layer; and less than 0.9 is a low liquefaction risk layer. After each layer is calculated, the set of soil layers affected by liquefaction is listed in a table, indicating the layer number, liquefaction index, soil type and thickness. A visual matrix diagram is generated in the software to assist in the verification. Finally, the set of soil layers affected by liquefaction is formed, which is convenient for subsequent pile-soil interface strength analysis.

[0123] S502: Based on the liquefaction-affected soil layer set, establish an initial pile-soil interface strength model;

[0124] Based on the liquefaction-affected soil layer set, an initial pile-soil interface strength model is established. First, the liquefaction-affected soil layer set is input into the pile-soil interface strength calculation module. For each liquefied soil layer, the interface friction coefficient is calculated using the friction coefficient method. The formula is as follows: ,in For soil cohesion, This refers to the earth pressure on the pile side. The pile-soil friction angle is used to calculate the cohesion by taking the void ratio and relative density of each soil layer. The cohesion benchmark value is set to 20~60kPa, and the friction angle is taken from the 30°~35° range in the soil property table. The pile-soil friction resistance is calculated for different layers, and an initial pile-soil interface strength distribution table is generated, listing the friction resistance corresponding to each pile segment. During the calculation, the earth pressure value can be adjusted using a simple iterative method to make the interface strength model cover the entire pile length, and finally obtain the initial interface strength parameter set when each pile segment is in contact with the liquefiable soil layer.

[0125] S503: Based on the initial pile-soil interface strength model and liquefaction time information, update the parameters to obtain a time-varying interface strength parameter set;

[0126] Based on the initial pile-soil interface strength model and liquefaction time information, parameters are updated to obtain a time-varying interface strength parameter set. First, the liquefaction time series information is matched with the initial interface strength model, and a time decay coefficient is defined for each soil layer. ,in The time of liquefaction. The attenuation coefficient, with a baseline value of 0.05~0.1, represents the percentage decrease in interface strength per hour, calculated using the formula... Calculate the interface strength at each time step, where To determine the initial interface strength, each pile segment is calculated segment by segment. The attenuation coefficient is weighted according to the thickness of the liquefaction layer, with weights ranging from 0.3 to 0.7 to reflect the more significant attenuation effect of thick soil layers. A time-varying interface strength table is obtained through hourly calculations, listing the interface strength values ​​for each hour or stage. Finally, a complete set of time-varying interface strength parameters is formed, covering the strength change trend throughout the entire liquefaction process.

[0127] S504: Based on the time-varying interface strength parameter set, spatial mapping is performed to obtain the time-varying degradation distribution of pile-soil interface strength.

[0128] Based on the time-varying interface strength parameter set, spatial mapping is performed to obtain the time-varying degradation distribution of pile-soil interface strength. First, the time-varying interface strength parameter set is input into a spatial grid model, and the soil layer around the pile is divided into three-dimensional units. Each unit is associated with corresponding time strength data. The interface strength of adjacent units is smoothed using interpolation, as shown in the formula: ,in This is the distance weight, with a value ranging from 0.5 to 1.0. To determine the interface strength of adjacent units, the interface strength values ​​of each unit at different time steps are obtained through mesh mapping. The results are represented in the form of a matrix or color map, so that the spatial distribution shows the strength degradation trend over time, and finally the complete time-varying degradation distribution of pile-soil interface strength is obtained.

[0129] S6 includes the following steps:

[0130] S601: Based on the time history distribution field of the cyclic shear stress in the soil layer, the program sequence for calculating shear strain is obtained;

[0131] First, the shear stress versus time curve from the numerical calculation software is discretized. The continuous curve is divided into several intervals according to the time step. For example, the time interval is selected as a small-scale interval, and the shear stress value corresponding to each moment is denoted as . Subsequently, based on the dynamic constitutive relation of the soil, the relationship between shear modulus G and shear stress was adopted. Calculate the corresponding shear strain, where the shear modulus G is taken from a reasonable range based on the site soil sample test results. For example, a representative value can be selected within a certain range for medium-dense sand. The shear strain is obtained by substituting the τ values ​​at different time points into the formula. In practical engineering, a sequence can be exemplified by the soil layer surrounding a pile foundation at a certain moment under seismic loading, where the shear stress is at a moderate level. The corresponding shear modulus is taken as the median value of the empirical range for that soil layer. The shear strain at that moment is calculated, and this process is repeated for all time history points to form a complete sequence. If stress abrupt changes occur during the calculation, they are smoothed using interpolation methods to make the sequence continuous, ultimately obtaining the shear strain sequence result that varies with time.

[0132] S602: Extract strain amplitude based on the shear strain time sequence to obtain strain amplitude dataset;

[0133] First, the shear strain sequence Extreme value identification is performed by using a peak-valley extraction method to identify the maximum and minimum values ​​in each loading cycle, and half of the difference between adjacent peaks and valleys is defined as the strain amplitude. ,in ,parameter This represents the maximum shear strain within a given cycle. This represents the corresponding minimum value. In practice, data processing tools can be used to traverse and judge the sequence. When adjacent points meet the conditions of changing from increasing to decreasing or from decreasing to increasing, they are marked as extreme points. Then, the corresponding amplitude is calculated. In the example, if the shear strain fluctuates in a certain range within a certain cycle, its maximum and minimum values ​​are extracted and substituted into the formula to obtain the amplitude data. Then, the amplitudes of all cycles are summarized to form a dataset. For "higher amplitudes", they can be divided into the part that exceeds the upper limit of the overall mean, for example, the mean plus a certain percentage range is used as the judgment boundary. "Lower amplitudes" are located below the mean minus a certain percentage range. The strain amplitude dataset is constructed in this way.

[0134] S603: Based on the strain amplitude dataset and the time-varying degradation distribution of the pile-soil interface strength, damage accumulation calculation is performed to obtain a damage accumulation calculation sequence;

[0135] Based on the strain amplitude dataset and the time-varying degradation distribution of pile-soil interface strength, the initial interface strength is first determined. And construct a degenerate function based on the number of iterations n, for example, using The form is given by α, where α is the degradation coefficient, whose value is selected within an empirical range based on the results of indoor cyclic shear tests. This is achieved by considering the strain amplitude corresponding to each cycle. With current cycle strength Compare and calculate the amount of damage per incident. ,in As a reference strain threshold, which is determined according to standards or tests as the median of a reasonable range, the cumulative damage is obtained by successively accumulating the strain values. In practical examples, several cyclic amplitude data and corresponding degradation intensity values ​​can be substituted into the above formula for step-by-step calculation. For example, the initial intensity is taken in the first cycle, and subsequent cycles are calculated by decreasing according to the degradation function. The damage sequence is obtained by cyclic accumulation. At the same time, "significant damage" is defined as the proportion of the cumulative value exceeding a certain upper limit range, and "minor damage" is defined as the range below the lower limit range, and finally the sequence result of damage development with cycles is formed.

[0136] S604: Based on the damage accumulation calculation sequence, normalization processing is performed to obtain the soil vibration cumulative damage factor.

[0137] First, obtain the maximum value in the damage sequence. and minimum value Construct a normalized expression Where D represents the cumulative damage value of the current cycle, the normalized result is obtained by substituting the D value at each time step into this formula. During implementation, if... and If the difference is in a small range, a small correction needs to be introduced to prevent the denominator from approaching zero. This is done by setting a correction coefficient. Adjust by taking a very small interval value, that is, replacing the denominator with In the example, several damage values ​​can be selected for normalization calculation. For example, if a certain cycle damage value is in the middle range, the normalization result will fall between zero and one. By traversing the entire sequence, a unified scale conversion is completed. At the same time, the normalized values ​​can be divided into intervals. For example, the interval close to one is defined as a high damage level, and the interval close to zero is defined as a low damage level. Finally, the cumulative damage factor of soil vibration is obtained.

[0138] S7 includes the following steps:

[0139] S701: Extract the geometric parameters of the pile group based on the time-varying degradation distribution of the pile-soil interface strength to obtain the pile group geometric parameter set;

[0140] The starting point for extracting geometric parameters of pile groups based on the time-varying degradation distribution of pile-soil interface strength can be to first discretize the data on the change of pile-soil interface strength over time, and then arrange the interface shear strength corresponding to different time nodes after construction in a time series. Let the interface strength be... Where t represents the time step, by selecting several typical moments Combined with field test data or numerical simulation results, the strength degradation rate is calculated using a differential method. Then, different pile locations are classified and marked according to the degradation rate distribution. For example, when the degradation rate is within a preset range (such as being divided into three ranges according to experience: slow degradation zone, medium degradation zone, and fast degradation zone), different geometric correction coefficients are assigned accordingly. Subsequently, based on the pile foundation layout diagram, foundation parameters such as single pile diameter d, pile length L, and center-to-center distance s are extracted. Dimensionless parameters η=s / d and λ=L / d are then calculated through geometric normalization, where η reflects the relative spacing between piles and λ describes the slenderness ratio of the pile length. In specific examples, it can be assumed that a certain pile diameter is within the range of common engineering standards, and the pile spacing is several times that pile diameter, thus obtaining η within the range of common engineering standards. Then, the correction coefficients corresponding to different degradation zones are combined with η and λ to form a set of geometric parameters for the pile group. , where i represents different pile number, and a complete set of parameters is formed by organizing them one by one for subsequent calculation and processing.

[0141] S702: Calculate the pile spacing influence based on the geometric parameter set of the pile group to obtain the pile spacing influence coefficient;

[0142] The starting point for calculating the impact of pile spacing based on the geometric parameter set of pile groups is to read the dimensionless pile spacing η in the aforementioned parameter set item by item, and establish the pile spacing influence function in combination with the pile group arrangement (such as rectangular or quincunx arrangement). Let the influence coefficient be α, and its basic expression can be written as: In practice, empirical formulas can be used, such as... Where β is an empirical coefficient, its value is set based on engineering experience or recommended intervals in specifications. A simple example illustrates this: when η takes the midpoint of a certain conventional interval, the calculated α is within a reasonable range. Then, the calculated α values ​​for different pile positions are compared and analyzed. If the α value falls within a preset interval (e.g., divided into weak, medium, and strong influence zones based on engineering experience), the corresponding level is recorded. Simultaneously, different λ values ​​are weighted and corrected. Let the weighting coefficient w = λ / (λ + constant term). The corrected pile spacing influence coefficient is obtained by weighted averaging of α and w. Its calculation process can be expressed as follows: ,in The baseline influence value is determined by selecting empirical values ​​under typical pile spacing conditions. In the example, a reference value under common layout can be taken. By calculating each item, the set of pile spacing influence coefficients corresponding to each group of piles is finally obtained, providing input parameters for subsequent coupling calculations.

[0143] S703: Based on the pile spacing influence coefficient and the soil vibration cumulative damage factor, a coupled calculation is performed to obtain the intermediate coefficient of pile group interaction;

[0144] The starting point for coupled calculation based on the pile spacing influence coefficient and the cumulative damage factor of soil vibration can be to first obtain the cumulative damage factor D of the soil under cyclic loading. This factor can be obtained by considering the number of cycles N and the critical number of cycles. The ratio between them is calculated and expressed as follows: ,in The pile spacing influence coefficient is determined based on soil type and stress level through experiments or empirical formulas. Coupled with the damage factor D, an intermediate coefficient γ is constructed, and expressed as... Where m is the damage sensitivity index, its value is set within a reasonable range based on the soil type. In actual calculations, it can be assumed that the number of cycles reaches a certain proportion under a certain working condition, so that D is in a medium range. Then, the corresponding... Substitute the values ​​into the calculated γ values, divide the γ values ​​into intervals (e.g., low coupling zone, medium coupling zone, high coupling zone) to determine their level, and further perform statistical averaging or weighting on the γ values ​​of different pile locations, setting an average coefficient. ,in As weighting coefficients related to pile length or pile diameter, intermediate coefficients for the overall interaction of pile groups are obtained by substituting each item into the calculation, providing basic data for subsequent reduction processing.

[0145] S704: Based on the intermediate coefficient of the pile group interaction, a reduction process is performed to obtain the pile group interaction reduction coefficient.

[0146] Starting from the reduction process based on the intermediate coefficient of pile group interaction, the aforementioned intermediate coefficient γ can be standardized and mapped to a unified range. Let the standardized coefficient be... ,in and These are the minimum and maximum median coefficient values ​​in the sample, obtained statistically, and then introduced into a reduction function form as follows: Where θ is the reduction adjustment coefficient, the value of which is set within a reasonable range based on engineering experience, and illustrated through example calculations. When the value is in the medium range, the ψ value shows a corresponding trend with the change of θ. Then, by setting a reduction threshold range (e.g., dividing ψ into strong reduction, medium reduction, and weak reduction zones), the calculation results are judged within this range. If ψ is below a certain threshold, it is classified as a strong reduction level. Simultaneously, ψ is corrected based on the overall layout of the pile group, and a corrected coefficient is set. , where μ is the arrangement correction coefficient, the value of which is determined based on the pile group arrangement density. In the example, a reasonable value can be assigned according to common arrangement densities. The final pile group interaction reduction coefficient result is obtained by step-by-step substitution calculation, and then a unified output parameter is formed for subsequent analysis and processing.

[0147] S8 includes the following steps:

[0148] S801: Calculate the pile side friction based on the time-varying degradation distribution of the pile-soil interface strength, and obtain the pile side friction time program sequence;

[0149] First, soil samples were taken around the pile, and interfacial shear strength curves at different time stages were obtained through indoor shear tests. These curves were then discretized into strength value intervals corresponding to several time nodes. For example, the early stage strength was divided into a high interval, the middle stage into a transitional interval, and the later stage into a low interval. Then, the pile was divided into several unit segments according to its length. Each unit segment was then further divided according to… A formal expression for calculating friction is established, where τ represents unit lateral friction, z represents pile depth, and t represents time stage. The original strength is corrected by introducing a reduction function η(t). The range of values ​​is divided into multiple intervals based on the change in the slope of the test curve. For example, the smaller interval value of η corresponds to the stage where the slope drops significantly. Combined with the soil density distribution within a certain pile depth range in actual engineering, the density coefficient is used as a weight in the calculation. The pile side friction value at each time is obtained by segment-by-segment integration. The results of different time nodes are arranged in chronological order to form a sequence. Finally, the discrete results reflecting the change of pile side friction with time are output.

[0150] S802: Based on the pile side friction time sequence and the soil vibration cumulative damage factor, a modified pile side friction sequence is obtained;

[0151] First, vibration acceleration data at different time periods are acquired using on-site vibration monitoring equipment. The acceleration time history is then converted into equivalent cycle counts using the rainflow counting method. Finally, a damage accumulation model is used. Calculate the damage factor, where The actual number of cycles corresponding to a certain vibration amplitude. The allowable number of cycles for the material at this amplitude is determined using an empirical curve. The calculated D value is then divided into low damage, medium damage, and high damage intervals, with different correction coefficients for each interval. , Defined by linear or piecewise functions, for example, when D is in the middle interval. Take the middle range value, and then multiply the friction value at each time node in the original pile side friction sequence by the value at the corresponding time. The correction was made, and the vibration intensity change trend of a certain construction stage in the engineering example was combined with different weights for different time nodes to make the correction results continuous. Finally, a set of pile side friction sequences after damage correction was obtained.

[0152] S803: Calculate the pile end resistance based on the modified pile side friction sequence and the pile group interaction reduction coefficient to obtain the pile end resistance sequence;

[0153] Using the corrected pile side friction sequence as input, and incorporating the interaction effect of pile groups, the pile end resistance is calculated. First, the pile spacing to pile diameter ratio is determined based on the pile group arrangement. This ratio is then divided into densely arranged and sparsely arranged intervals, and a reduction factor ψ is selected accordingly. The value of ψ is set in intervals based on existing experimental or standard curves; for example, a lower value is taken for ψ in intervals with smaller pile spacing. Then, the ultimate bearing capacity of a single pile end is calculated using the end resistance formula. ,in For the effective stress at the pile tip, The bearing capacity coefficient is obtained from geological survey data. The scope, and determined according to soil type. The range value is then multiplied by ψ to obtain the corrected end resistance value under the condition of pile group. At the same time, the end resistance is synchronously adjusted according to the time node by combining the trend of pile side friction change at different time stages, forming a pile end resistance sequence corresponding to time.

[0154] S804: Based on the superposition of the modified pile side friction sequence and the pile end resistance sequence, the time history curve of the vertical bearing capacity of the pile group is obtained.

[0155] After obtaining the corrected pile side friction sequence and pile end resistance sequence, the two parts are combined for calculation. First, the pile side friction is integrated over the pile length to obtain the total side resistance value at each time node. Then, the pile end resistance at the corresponding time node is added to form the expression for the total bearing capacity. ,in This represents the result of the side resistance integral. The end resistance value is represented by discrete processing at different time points in the specific implementation. For example, the construction stage is divided into several time periods, the corresponding Q value is calculated for each time period, and the continuity of the results is checked. The difference between adjacent time points is used to determine whether the change range is within a reasonable range. When the change range exceeds the preset range, it is smoothed by interpolation. Finally, the bearing capacity results of each time point are connected in chronological order to form a bearing capacity curve data set that reflects the overall change trend.

[0156] S9 includes the following steps:

[0157] S901: Extract feature values ​​based on the time history curve of the vertical bearing capacity of the pile group to obtain a set of key bearing capacity feature values;

[0158] First, load-bearing capacity curve data over time is obtained through field loading tests or numerical simulations. This curve is then discretized into a sequence of load-bearing capacity values ​​corresponding to several time points. During execution, peak points, inflection points, and the average value of the stable phase in the curve are selected as candidate features. The data is segmented by setting a time window length (e.g., dividing the loading phase into initial loading segment, transition segment, and stable segment), and a simple mean formula is used for each segment. Extract the average bearing capacity, where This represents the bearing capacity of the i-th sampling point, where n represents the number of sampling points. A maximum value function is used for peak value extraction. Then, by comparing the rate of change of bearing capacity ΔF / Δt in adjacent time periods, nodes with significant changes are selected as key feature points. The threshold of the rate of change can be set as an empirical value within a certain range based on historical test data. For example, in the loading process of a group of pile foundations, the bearing capacity increases slowly in the early stage, a rapid growth phase occurs in the middle stage, and then tends to stabilize in the later stage. The key bearing capacity values ​​representing different stages are extracted by the above method and formed into a feature value set, and finally the key bearing capacity feature value set is obtained.

[0159] S902: Based on the set of key bearing capacity characteristic values, a comparative calculation is performed to obtain a bearing capacity ratio sequence;

[0160] The bearing capacity feature values ​​extracted from different time points are arranged in chronological order to form a sequence, and a ratio calculation rule is established during the execution process, such as using a ratio between adjacent feature values. Perform calculations, where Represents the feature value at the current time. This represents the feature value at the previous moment. For cross-stage comparisons, a benchmark value method can be used, setting the feature value of the initial stage as the benchmark value. And calculate the ratio of each stage. In practice, the characteristic values ​​are entered using a table tool and the ratio sequence is automatically generated. The division of the ratio interval can be set such that the interval close to 1 indicates a gradual change, the interval above a certain empirical upper limit indicates a significant increase, and the interval below a certain empirical lower limit indicates a decay trend. Through an example, the bearing capacity characteristic value of a certain project shows a gradual increasing trend at different stages. A set of increasing ratio sequences is obtained through the above ratio calculation, forming a complete bearing capacity ratio sequence.

[0161] S903: Based on the bearing capacity ratio sequence, perform statistical analysis to obtain the calculated value of the bearing capacity correction coefficient;

[0162] First, perform basic statistics calculations on the comparison value series, including the mean. ,in Let m represent the i-th ratio, m represent the number of ratios, and m represent the standard deviation. To measure the degree of dispersion, weighting coefficients are set during execution to weight the ratios of different stages. For example, higher weights are assigned to stable stages and lower weights to fluctuating stages. These weighting coefficients can be set based on time proportions or engineering experience, and must meet certain requirements. The constraints are defined, and outliers are filtered out. Outlier identification can be done using an interval method, for example, when... When the deviation from the mean exceeds a certain multiple of the standard deviation, the remaining ratios are discarded, and then a weighted average is calculated to obtain the correction factor. In practical cases, the above processing is performed by comparing the value sequence to obtain a stable statistical result, which ultimately forms the calculated value of the bearing capacity correction coefficient.

[0163] S904: Based on the calculated value of the bearing capacity correction coefficient, encapsulate and output to obtain the vertical bearing capacity correction coefficient of the pile group considering the vibration time effect.

[0164] First, the statistically obtained correction coefficients are formatted, including retaining significant digits and standardizing the data structure. Then, during execution, these are encapsulated in conjunction with engineering design parameters; for example, the correction coefficients are correlated with the standard value of the pile foundation design bearing capacity to form the output data structure. Where K represents the correction factor. This represents the design bearing capacity. In practice, the calculation results can be automatically written into a preset template using a simple program or spreadsheet tool. At the same time, verification rules can be set. For example, when the correction coefficient is within a preset reasonable range, it is marked as valid data. If it exceeds the range, a recalculation is prompted. The range can be set as a reasonable fluctuation range based on historical engineering data. As illustrated by the example, the correction coefficient calculated in a pile group project is verified and then encapsulated in the design report data table and used as the input parameter for subsequent calculations. The final output is the correction coefficient of the vertical bearing capacity of the pile group considering the vibration time effect.

[0165] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for correcting the vertical bearing capacity of pile foundations in liquefiable silty soil considering the vibration time effect, characterized in that, Includes the following steps: S1: Based on the vibration time history data of the engineering site, the original vibration acceleration time history is subjected to baseline correction, bandpass filtering and normalization to obtain a standardized vibration acceleration time sequence. S2: Based on the standardized vibration acceleration time sequence, a one-dimensional equivalent shear beam model is used to perform seismic response analysis, calculate the time history distribution of cyclic shear stress in soil layers at different depths, and obtain the time history distribution field of cyclic shear stress in soil layers. S3: Based on the time history distribution field of the cyclic shear stress in the soil layer, the pore water pressure growth model is used to perform cyclic loading analysis, calculate the evolution process of the pore water pressure ratio at each depth over time, and obtain the time history evolution field of the pore water pressure ratio. S4: Based on the pore water pressure ratio time history evolution field, the liquefaction discrimination threshold method is used to determine the time nodes and duration intervals of liquefaction in each soil layer, and the stratified liquefaction time sequence triggering matrix is ​​obtained. S5: Based on the layered liquefaction timing triggering matrix, a pile-soil interface strength degradation model is constructed, and the pile side friction and pile end resistance parameters are time-varyingly corrected to obtain the time-varying degradation distribution of pile-soil interface strength. S6: Based on the time history distribution field of the cyclic shear stress of the soil layer and the time-varying degradation distribution of the pile-soil interface strength, the degree of damage to the soil during vibration is calculated using the cyclic cumulative damage model, and the cumulative damage factor of the soil vibration is obtained. S7: Based on the time-varying degradation distribution of the pile-soil interface strength and the cumulative damage factor of soil vibration, a pile group interaction model is established, the reduction effect of the single pile bearing capacity in the pile group system is calculated, and the pile group interaction reduction coefficient is obtained. S8: Based on the time-varying degradation distribution of the pile-soil interface strength, the cumulative damage factor of soil vibration, and the reduction coefficient of pile group interaction, calculate the change in vertical bearing capacity of the pile group foundation during the entire vibration process, and obtain the time history curve of the vertical bearing capacity of the pile group. S9: Based on the time history curve of the vertical bearing capacity of the pile group, extract the bearing capacity at key moments and compare it with the initial bearing capacity to determine the bearing capacity correction coefficient, and obtain the vertical bearing capacity correction coefficient of the pile group considering the vibration time effect.

2. The method for correcting the vertical bearing capacity of pile foundations for liquefiable silty soil considering vibration time effects according to claim 1, characterized in that: S1 includes the following steps: S101: Based on the original vibration acceleration time history data, the baseline correction method is used to eliminate low-frequency drift and obtain the preliminary correction vibration time program sequence; S102: Based on the preliminary correction vibration time program sequence, a bandpass filtering method is used to remove noise interference to obtain a filtered vibration time program sequence; S103: Based on the filtered vibration time program sequence, interpolation discretization is performed using a time step uniform processing method to obtain a vibration time program sequence with equal step size. S104: Based on the constant step vibration time program sequence, the amplitude normalization method is used for standardization processing to obtain the standardized vibration acceleration time program sequence.

3. The method for correcting the vertical bearing capacity of pile foundations for liquefiable silty soil considering vibration time effects according to claim 1, characterized in that: S2 includes the following steps: S201: Based on the standardized vibration acceleration time sequence, establish a layered soil parameter model; S202: Based on the layered soil parameter model, construct a dynamic response calculation model; S203: Based on the dynamic response calculation model and the standardized vibration acceleration time sequence, perform seismic response analysis to obtain shear stress time history dataset; S204: Based on the shear stress time history dataset, spatial distribution reconstruction is performed to obtain the soil cyclic shear stress time history distribution field.

4. The method for correcting the vertical bearing capacity of pile foundations for liquefiable silty soil considering vibration time effects according to claim 1, characterized in that: S3 includes the following steps: S301: The program sequence for calculating the cyclic stress ratio based on the time history distribution field of the cyclic shear stress in the soil layer; S302: Based on the program sequence of the cyclic stress ratio, construct a calculation model for pore pressure growth; S303: Based on the pore pressure growth calculation model, perform cumulative calculations to obtain the pore water pressure growth sequence; S304: Normalize the pore water pressure growth sequence to obtain the pore water pressure ratio time history evolution field.

5. The method for correcting the vertical bearing capacity of pile foundations for liquefiable silty soil considering vibration time effects according to claim 1, characterized in that: S4 includes the following steps: S401: Determine the liquefaction discrimination threshold parameter based on the pore water pressure ratio time history evolution field; S402: Perform time step comparison based on the liquefaction discrimination threshold parameter to obtain the liquefaction trigger time sequence; S403: Determine the liquefaction duration interval based on the liquefaction trigger time series, and obtain liquefaction duration interval data; S404: Construct a matrix representation based on the liquefaction duration interval data to obtain a hierarchical liquefaction timing trigger matrix.

6. The method for correcting the vertical bearing capacity of pile foundations for liquefiable silty soil considering vibration time effects according to claim 1, characterized in that: S5 includes the following steps: S501: Based on the layered liquefaction timing triggering matrix, identify the soil layers affected by liquefaction and obtain the set of soil layers affected by liquefaction; S502: Based on the liquefaction-affected soil layer set, establish an initial pile-soil interface strength model; S503: Based on the initial pile-soil interface strength model and liquefaction time information, update the parameters to obtain a time-varying interface strength parameter set; S504: Based on the time-varying interface strength parameter set, spatial mapping is performed to obtain the time-varying degradation distribution of pile-soil interface strength.

7. The method for correcting the vertical bearing capacity of pile foundations for liquefiable silty soil considering vibration time effects according to claim 1, characterized in that: S6 includes the following steps: S601: Based on the time history distribution field of the cyclic shear stress in the soil layer, the program sequence for calculating shear strain is obtained; S602: Extract strain amplitude based on the shear strain time sequence to obtain strain amplitude dataset; S603: Based on the strain amplitude dataset and the time-varying degradation distribution of the pile-soil interface strength, damage accumulation calculation is performed to obtain a damage accumulation calculation sequence; S604: Based on the damage accumulation calculation sequence, normalization processing is performed to obtain the soil vibration cumulative damage factor.

8. The method for correcting the vertical bearing capacity of pile foundations for liquefiable silty soil considering vibration time effects according to claim 1, characterized in that: S7 includes the following steps: S701: Extract the geometric parameters of the pile group based on the time-varying degradation distribution of the pile-soil interface strength to obtain the pile group geometric parameter set; S702: Calculate the pile spacing influence based on the geometric parameter set of the pile group to obtain the pile spacing influence coefficient; S703: Based on the pile spacing influence coefficient and the soil vibration cumulative damage factor, a coupled calculation is performed to obtain the intermediate coefficient of pile group interaction; S704: Based on the intermediate coefficient of the pile group interaction, a reduction process is performed to obtain the pile group interaction reduction coefficient.

9. The method for correcting the vertical bearing capacity of pile foundations for liquefiable silty soil considering vibration time effects according to claim 1, characterized in that: S8 includes the following steps: S801: Calculate the pile side friction based on the time-varying degradation distribution of the pile-soil interface strength, and obtain the pile side friction time program sequence; S802: Based on the pile side friction time sequence and the soil vibration cumulative damage factor, a modified pile side friction sequence is obtained; S803: Calculate the pile end resistance based on the modified pile side friction sequence and the pile group interaction reduction coefficient to obtain the pile end resistance sequence; S804: Based on the superposition of the modified pile side friction sequence and the pile end resistance sequence, the time history curve of the vertical bearing capacity of the pile group is obtained.

10. The method for correcting the vertical bearing capacity of pile foundations for liquefiable silty soil considering vibration time effects according to claim 1, characterized in that: S9 includes the following steps: S901: Extract feature values ​​based on the time history curve of the vertical bearing capacity of the pile group to obtain a set of key bearing capacity feature values; S902: Based on the set of key bearing capacity characteristic values, a comparative calculation is performed to obtain a bearing capacity ratio sequence; S903: Based on the bearing capacity ratio sequence, perform statistical analysis to obtain the calculated value of the bearing capacity correction coefficient; S904: Based on the calculated value of the bearing capacity correction coefficient, encapsulate and output to obtain the vertical bearing capacity correction coefficient of the pile group considering the vibration time effect.

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