A method for calculating the vertical bearing capacity of ultra-long pile groups in extremely deep silty soft soil.

Abstract

This invention relates to the field of geotechnical and bridge foundation engineering technology, and in particular provides a method for calculating the vertical bearing capacity of ultra-long pile groups in ultra-deep silty soft soil. The method includes parameter acquisition and inversion, and the construction of a three-dimensional saturated soft soil model. u - p The method employs a coupled model to simulate the construction-consolidation-immersion time sequence, construct and couple the transmission of multi-source traffic dynamic loads, and perform constitutive modeling of pile-soil interface bonding-slippage-softening, identification and redistribution of negative skin friction and neutral point. It also assesses the energy efficiency of pile groups and evaluates the reduction in cyclic dynamic effects. Furthermore, it obtains static and dynamic expressions and algorithms for vertical bearing capacity, and develops consistency criteria for service settlement, DAF (Dynamic Aspect-Oriented Fallout), and reliability. The method enables automated optimization of design and operation parameters, with software system and data flow implementation. It allows for optional implementation and standard compatibility, result verification, and full-lifecycle application. This method accurately characterizes the spectral characteristics and transmission paths of multi-source traffic dynamic loads and quantifies the energy dissipation and efficiency changes of pile groups.

Description

Technical Field

[0001] This invention relates to the field of geotechnical and bridge foundation engineering technology, and in particular to a method for calculating the vertical bearing capacity of ultra-long pile groups in ultra-deep silty soft soil. Background Technology

[0002] Deep, marine silty soft soils are widely distributed in coastal deltas and marine-continental transition zones. They exhibit typical engineering properties such as high natural water content, large initial porosity, low permeability, high compressibility, slow consolidation rate, low shear strength, and significant structural and susceptibility characteristics. Under the combined effects of long-term loads, environmental hydrological changes, and operational dynamic loads, the pile-soil interaction in this type of stratum exhibits strong nonlinearity, strong time-varying characteristics, and strong coupling, posing significant challenges to the safety assessment and life design of pile foundations for large-span transportation infrastructure.

[0003] Firstly, the issues of negative skin friction and neutral point migration are prominent. Under the consolidation of soft soil by its own weight, the surcharge of the subgrade, and the long-term load of the superstructure, the surface and foundation soils settle. The displacement of ultra-long pile tops is usually minimally constrained by the superstructure, resulting in relative displacement between the pile and the soil. The soil along the pile pulls the pile downwards, generating negative skin friction (also known as downward pull or drag force) pointing towards the pile tip. When the groundwater level rises suddenly, or when cofferdams leak or temporary flooding occurs, the effective stress of the soil drops sharply, shear strength decreases, and the consolidation history is reset. The peak area of ​​negative skin friction may shift upwards and amplify. Simultaneously, the neutral point (the depth at which the relative displacement between the pile and the soil is zero) migrates with time and water level conditions, leading to systematic changes in the axial force distribution of the pile, the reaction force at the pile top, and the mobilization pattern of the pile tip resistance. Negative skin friction not only depletes the available reserve of positive skin friction on the pile side and reduces the vertical bearing capacity reserve, but also induces alternating tension and compression in the local area of ​​the pile, causing fatigue accumulation and crack initiation, among other durability problems.

[0004] Secondly, the pile group effect leads to a significant reduction in bearing capacity and deformation response. In ultra-deep silty soft soil, the soil between piles is in a competitive state of high-pressure compaction and shear weakening. Due to the stress superposition and radial displacement limitation of the soil between piles, the mobilization process of pile side resistance exhibits mutual competition and lag, and the efficiency of pile group is lower than that of single pile. The uneven load distribution between the central pile and the edge piles is aggravated, often resulting in a basin-shaped response pattern where the central pile has a higher peak axial force and greater settlement, while the edge piles are relatively safe. For ultra-long piles with L / D≥50, the formation and release of pile side friction are more dispersed along the path, and the end resistance is more sensitive to the control of pile end settlement. The superposition of the pile group effect and the ultra-long pile effect not only affects the assessment of ultimate bearing capacity but also significantly increases the difficulty of controlling service settlement and differential settlement.

[0005] Finally, the spectral coupling effect of multi-source traffic dynamic loads has not been fully characterized. The dynamic loads of intercity trains and expressway vehicles exhibit significant speed dependence and spectral distribution characteristics: variations in axle load, train formation, and vehicle speed lead to energy distribution within the 1-20 Hz frequency band and wideband superposition. Furthermore, wheel-rail irregularities, road surface unevenness, and bridge modes collectively shape the input spectrum. After being transmitted through the bridge deck / road surface-superstructure-pile cap-pile-soil path, the dynamic load forms a non-stationary, non-Gaussian time-varying effect at the pile top, causing coupling between cyclic shear stress and pore pressure fluctuations at the pile-soil interface. This may lead to local strength reduction, stiffness degradation, and amplified cumulative settlement. Especially during heavy rain or storm surges, the pore pressure dissipation capacity of saturated soft soil decreases, and the effective stress further decreases. The superposition of multi-source dynamic loads and sudden rises in water level amplifies the peak and cumulative effects of pile top displacement and pile internal forces. Summary of the Invention

[0006] In view of this, the present invention provides a method for calculating the vertical bearing capacity of ultra-long pile groups in ultra-deep silty soft soil. This method can accurately characterize the spectral characteristics and transmission path of multi-source traffic dynamic loads, quantify the energy dissipation and efficiency changes of pile groups, and use the synergy of multiple indicators as a consistency criterion to provide scientific, verifiable and reusable technical support for the design and operation phases.

[0007] In a first aspect, the present invention provides a method for calculating the vertical bearing capacity of ultra-long pile groups in ultra-deep silty soft soil, the method comprising:

[0008] Step 1: Parameter acquisition and inversion, and construction of three-dimensional saturated soft soil. u - p Coupled model;

[0009] Step 2: Conduct time-series simulation of construction-consolidation-immersion, and construct and couple the dynamic load of multi-source traffic.

[0010] Step 3: Bond-slip-softening constitutive model of pile-soil interface, identification and redistribution update of negative skin friction and neutral point;

[0011] Step 4: Determine the energy efficiency of the pile group and assess the reduction of cyclic dynamic effects;

[0012] Step 5: Obtain the static and dynamic expressions and algorithms for vertical bearing capacity;

[0013] Step 6: Perform consistency criteria for service settlement, DAF, and reliability;

[0014] Step 7: Automated optimization of design and operation parameters, implementation of software systems and data flows;

[0015] Step 8: Optional implementation and standard compatibility, result verification and full lifecycle application.

[0016] Optionally, the parameter acquisition and inversion in step 1 includes: parameter identification following a closed loop of experiment-monitoring-inversion-verification;

[0017] First, with consolidation, triaxial CU / CD, and shear wave velocity V... s Initial values ​​for indoor or in-situ tests: MCC parameters {λ,κ,M,e0,p} c}、SSC creep parameters {C α}, initial shear modulus G max =ρV s 2 And configure the degradation curve G / G max =F(γ); Interface parameters {δ,c a ,κ soft The results were derived from the regression of the side resistance of the test piles and the back-inference of the pile strain monitoring.

[0018] Secondly, a hierarchical inversion method was adopted. The first layer used static load tests to fit the load-displacement curve at the pile top and the axial force distribution in the pile body; the second layer used consolidation settlement time history to fit c v The third layer is damped by dynamic measurement constraints and the dynamic boundary; the inversion objective function is to take the multi-index weighted least squares or Bayesian posterior maximization to control the error of key response quantities within ±10%, and output the parameter covariance.

[0019] Optionally, in step 1, three-dimensional saturated soft soil is constructed. u - p The coupled model includes:

[0020] The soil is treated using Biot's two-phase media theory:

[0021] Displacement equilibrium, ;

[0022] Conservation of mass ;

[0023] Where σ′=D:ε is given by MCC / SSC, and α is the Biot coefficient; the pile and the pile cap adopt solid elements, and the pile-soil interface element is inserted with zero thickness, with no tension in the normal direction, Coulomb limit in the tangential direction and softening;

[0024] Regarding the boundaries, a free field or viscoelastic boundary is applied at the bottom to absorb outward radiated waves, and the permeability of the side boundaries is switched according to the working conditions; spatial discretization satisfies the requirement of 8-10 elements for the pile diameter span; the equivalent thickness of the interface is approximately D / 20; and the consolidation step in time is Δt ≤ 0.2h. min 2 / c v In the dynamic analysis, explicit integration is performed with Δt ≤ T. min / 20 or implicitly adaptive.

[0025] Optionally, the time-series simulation of construction-consolidation-immersion in step 2 reflects the loading history, which includes:

[0026] ① Apply structural constraints and self-weight during the pile and cap construction stages; ② Load the subgrade or superstructure and enter long-term consolidation, give the seepage boundary according to the site drainage conditions, and solve for pore pressure dissipation and effective stress evolution; ③ Trigger the scenario of sudden rise in water level or immersion, introduce it through water head jump or infiltration flux boundary, reset the pore pressure field and cause effective stress reduction and strength degradation; ④ Use the current state as the initial field for subsequent dynamic loads; Update the pile-soil relative displacement, lateral resistance and neutral point position before the end of each stage to provide time-varying initial values ​​for the next stage.

[0027] Optionally, the multi-source traffic dynamic load construction and coupling transfer in step 2 includes:

[0028] Vehicle and train loads are statistically described using power spectral density S(ω) and speed-axle load. Broadband, non-stationary time histories are generated through spectral representation or pseudo-excitation, considering the energy distribution of wheel-rail irregularities or road surface irregularities in the 1-20Hz frequency band. The load coupling paths are sequentially bridge deck or road surface, main beam or bridge deck, abutment, pile group, and foundation, and are superimposed and transferred in the time domain. When the dominant frequency approaches the structural or foundation mode, the resonant neighborhood is checked using modal participation factor, damping ratio, and contact stiffness. For moving trains, a moving axle load-spatiotemporal mapping P(t) = ∑P is used. i δ(x v i t), and coupled with the interaction of the track or bridge surface to ensure the consistency of the input spectrum with the transfer spectrum.

[0029] Optionally, the pile-soil interface bond-slip-softening constitutive model in step 3 includes:

[0030] Peak interfacial shear strength ;

[0031] The softening segment index degrades. The normal direction adopts a contact-compression, cracking-free approach; the tangential direction adopts a three-stage approach of bond-slip-residual, with damage parameters D(N,γ) introduced under cyclic action. cyc )∈[0,1];

[0032] For δ, c a Update dynamically. ;

[0033] At the algorithm level, the tangential displacement increment and the bonding state are updated according to the returned mapping to ensure numerical stability and consistency with the algorithm. u - p Consistency of coupling.

[0034] Optionally, step 3, which involves identifying and redistributing negative friction and neutral point, includes:

[0035] The neutral point is initially determined by the pile-soil relative displacement Δw(z) = 0, and then verified by the sign change of the pile axial force derivative dN / dz; piecewise linear interpolation is used to lock the depth z. n ;

[0036] Side resistance distribution ;

[0037] Feedback is provided online from constitutive and stress paths;

[0038] Negative friction region [0, z] n Integrating, After immersion in water, σ is changed through the water head field. v ′ and K-path, causing f s Redistribution and z n Move up; the algorithm automatically refreshes at the end of each stage. And serve as the initial condition for the next stage.

[0039] Optionally, the energy determination of the pile group efficiency in step 4 includes:

[0040] Characterizing interactions using strain energy: ;

[0041] in, ;

[0042] To distinguish between the effects of side resistance and end resistance, ζ is defined. s , ζ b Used to correct the effective contribution of side and end resistance, making α s α b This refers to the energy share coefficient.

[0043] The calculation process is as follows: Under the same top load and boundary conditions, calculate the energy of a single pile and a group of piles respectively, and statistically analyze the energy of different s / D, arrangements, degrees of consolidation, and frequency bands. Changes are processed to form a database and used for rapid prediction via response surface methodology or machine learning regression; in the design, real-time calculated values ​​are prioritized, while database values ​​serve as priors and verification.

[0044] Optionally, the assessment of the reduction in cyclic dynamic effects in step 4 includes:

[0045] Cyclic dynamic effect reduction ΔR cyc Evaluate, It is used to characterize the intensity decay of the interface under broadband, non-stationary cycling; the coefficient α is calibrated in two steps:

[0046] (1) Indoor interface cyclic direct shear or ring shear test to obtain τ cyc-N- Degradation curve; (2) On-site dynamic measurement inversion fine-tuning, using an extended form, ;

[0047] in, m and n are fitted experimentally to ensure sensitivity to high cycle counts and large shear strain amplitudes; if pore pressure accumulation is considered, then superimposed... .

[0048] Optionally, step 5 includes:

[0049] Instantaneous value of bearing capacity ;

[0050] The design value adopts the statistical lower limit: the quantile within the time window T. ;

[0051] The algorithm flow is as follows: a) complete the stage update; b) gradually integrate within the dynamic time history to obtain R. v dyn (t); c. Calculate the characteristic values ​​of peak value, root mean square, and 5th percentile; d. Output instantaneous-statistical-design triple values ​​for use in determining bearing capacity and reliability.

[0052] The technical solution provided by this invention includes parameter acquisition and inversion, and the construction of a three-dimensional saturated soft soil model. u - p This method employs a coupled model to perform time-series simulations of construction, consolidation, and immersion; construct and couple the transmission of multi-source traffic dynamic loads; define the pile-soil interface adhesion-slippage-softening constitutive model; identify and redistribute negative skin friction and neutral point; determine the energy efficiency of pile groups and assess the reduction of cyclic dynamic effects; obtain static and dynamic expressions and algorithms for vertical bearing capacity; establish consistency criteria for service settlement, DAF (Displacement Aspect Ratio), and reliability; automate the optimization of design and operation parameters; and implement the software system and data flow. It offers optional implementation and standard compatibility, result verification, and life-cycle application. This method can uniformly describe immersion or water level rise-negative skin friction-neutral point migration-pile group effect-dynamic load amplification at three-dimensional, temporal, and multi-field coupled levels. It accurately characterizes the spectral characteristics and transmission paths of multi-source traffic dynamic loads, quantifies the energy dissipation and efficiency changes of pile groups, and uses multi-index synergy as a consistency criterion, providing scientific, verifiable, and reusable technical support for design and operation. Attached Figure Description

[0053] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0054] Figure 1 A flowchart illustrating the method for calculating the vertical bearing capacity of ultra-long pile groups in ultra-deep silty soft soil, as provided in an embodiment of the present invention;

[0055] Figure 2 This is a schematic diagram of a three-dimensional pile-soft soil-superstructure calculation model provided in an embodiment of the present invention;

[0056] Figure 3 This is a constitutive curve diagram of interface adhesion-slippage-softening provided in an embodiment of the present invention;

[0057] Figure 4 This is a schematic diagram of the distribution of negative friction resistance and the migration of the neutral point before and after immersion in water, provided in an embodiment of the present invention.

[0058] Figure 5 This is a schematic diagram of the input of vehicle-train coupled load spectrum and time history provided in an embodiment of the present invention;

[0059] Figure 6 The group pile efficiency η provided in the embodiments of the present invention g Unified evaluation diagram for energy determination and bearing capacity. Detailed Implementation

[0060] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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, 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.

[0061] It should be understood that the described embodiments are merely some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0062] The terminology used in the embodiments of this invention is for the purpose of describing particular embodiments only and is not intended to limit the invention. The singular forms “a,” “the,” and “the” used in the embodiments of this invention are also intended to include the plural forms unless the context clearly indicates otherwise.

[0063] It should be understood that the term "and / or" used in this article is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, or B existing alone. Additionally, the character " / " in this article generally indicates that the preceding and following related objects have an "or" relationship.

[0064] Depending on the context, the word "if" as used here can be interpreted as "when," "when," "in response to determination," or "in response to detection." Similarly, depending on the context, the phrase "if determination" or "if detection (of the stated condition or event)" can be interpreted as "when determination," "in response to determination," "when detection (of the stated condition or event)," or "in response to detection (of the stated condition or event)."

[0065] Figure 1 The flowchart below shows the calculation method for the vertical bearing capacity of ultra-deep silty soft soil ultra-long pile groups provided in the embodiments of the present invention. Figure 1 As shown, the method includes:

[0066] Terminology and Scope of Application of this Invention: The term "marine ultra-deep silty soft soil" emphasizes the common characteristics of being thick, soft, saturated, and having slow drainage. Typical indicators include a thickness ≥ 40 m, high liquid limit, high e0, and c. u The low permeability coefficient leads to significant consolidation aging and time-varying strength. The constraint conditions for ultra-long piles are L / D ≥ 50 and L ≥ 50 m to ensure the full manifestation of the mechanical characteristics of lateral resistance dominance and end resistance control. The regularly arranged multi-pile system makes the soil confinement effect between piles significantly different from that between the center and edge piles. This invention covers both the new construction and operational phases and can be extended to sites with similar constitutive and hydrological responses, such as brackish water zones, river deltas, and tidal flat backfill areas.

[0067] Step 1: Obtain and invert parameters, and construct a three-dimensional saturated soft soil up-coupled model.

[0068] In this embodiment of the invention, the parameter acquisition and inversion in step 1 includes: parameter identification following a closed loop of experiment-monitoring-inversion-verification;

[0069] First, with consolidation, triaxial CU / CD, and shear wave velocity V... s Initial values ​​for indoor or in-situ tests: MCC parameters {λ,κ,M,e0,p} c}、SSC creep parameters {C α}, initial shear modulus G max =ρV s 2 And configure the degradation curve G / G max =F(γ); Interface parameters {δ,c a ,κ soft The results were derived from the regression of the side resistance of the test piles and the back-inference of the pile strain monitoring.

[0070] Secondly, a hierarchical inversion method was adopted. The first layer used static load tests to fit the load-displacement curve at the pile top and the axial force distribution in the pile body; the second layer used consolidation settlement time history to fit c vThe third layer constrains the damping and dynamic boundary with dynamic measurements (acceleration, DAF, strain); the inversion objective function takes multi-index weighted least squares or Bayesian posterior maximization to control the error of key response quantities within ±10%, and outputs parameter covariance to achieve uncertainty quantification.

[0071] In embodiments of the present invention, such as Figure 2 As shown, in step 1, three-dimensional saturated soft soil is constructed. u - p The coupled model includes:

[0072] The soil is treated using Biot's two-phase media theory:

[0073] Displacement equilibrium, ;

[0074] Conservation of mass ;

[0075] Where σ′=D:ε is given by MCC / SSC, and α is the Biot coefficient; the pile and the pile cap adopt solid elements, and the pile-soil interface element is inserted with zero thickness, with no tension in the normal direction, Coulomb limit in the tangential direction and softening;

[0076] Regarding the boundaries, a free field or viscoelastic boundary is applied at the bottom to absorb outward radiated waves, and the permeability of the side boundaries is switched according to the working conditions; spatial discretization satisfies the requirement of 8-10 elements for the pile diameter span; the equivalent thickness of the interface is approximately D / 20; and the consolidation step in time is Δt ≤ 0.2h. min 2 / c v In the dynamic analysis, explicit integration takes Δt ≤ T. min / 20 or implicit adaptive, to avoid high-frequency spurious vibrations.

[0077] Step 2: Conduct time-series simulation of construction-consolidation-immersion, and construct and couple the dynamic load of multi-source traffic.

[0078] In this embodiment of the invention, the time-series simulation of construction-consolidation-immersion in step 2 reflects the loading history, and includes:

[0079] ① Apply structural constraints and self-weight during the pile and cap construction stages; ② Load the subgrade or superstructure and enter long-term consolidation, give the seepage boundary according to the site drainage conditions, and solve for pore pressure dissipation and effective stress evolution; ③ Trigger the scenario of sudden rise in water level or immersion, introduce it through water head jump or infiltration flux boundary, reset the pore pressure field and cause effective stress reduction and strength degradation; ④ Use the current state as the initial field for subsequent dynamic loads; Update the pile-soil relative displacement, lateral resistance and neutral point position before the end of each stage to provide time-varying initial values ​​for the next stage, avoiding static and dynamic disconnection.

[0080] In this embodiment of the invention, step 2, the construction and coupling transfer of multi-source traffic dynamics, includes:

[0081] Vehicle and train loads are statistically described using power spectral density S(ω) and speed-axle load. Broadband, non-stationary time histories are generated through spectral representation or pseudo-excitation, considering the energy distribution of wheel-rail irregularities or road surface irregularities in the 1-20Hz frequency band. The load coupling paths are sequentially bridge deck or road surface, main beam or bridge deck, abutment, pile group, and foundation, and are superimposed and transferred in the time domain. When the dominant frequency approaches the structural or foundation mode, the resonant neighborhood is checked using modal participation factor, damping ratio, and contact stiffness. For moving trains, a moving axle load-spatiotemporal mapping P(t) = ∑P is used. i δ(x v i t), and coupled with the interaction of the track or bridge surface to ensure the consistency of the input spectrum with the transfer spectrum.

[0082] Step 3: Bond-slip-softening constitutive model of pile-soil interface, identification and redistribution update of negative friction and neutral point.

[0083] In embodiments of the present invention, such as Figure 3 As shown, the pile-soil interface bond-slip-softening constitutive model in step 3 includes:

[0084] Peak interfacial shear strength ;

[0085] The softening segment index degrades. The normal direction adopts a contact-compression, cracking-free approach; the tangential direction adopts a three-stage approach of bond-slip-residual, and damage parameters D(N,γ) are introduced under cyclic action. cyc )∈[0,1];

[0086] For δ, c a Update dynamically. ;

[0087] At the algorithm level, the tangential displacement increment and the bonding state are updated according to the returned mapping to ensure numerical stability and consistency with the algorithm. u - p Consistency of coupling.

[0088] In embodiments of the present invention, such as Figure 4 and 5 As shown, step 3, the identification and redistribution update of negative friction and neutral point, includes:

[0089] The neutral point is initially determined by the pile-soil relative displacement Δw(z) = 0, and then verified by the sign change of the pile axial force derivative dN / dz; piecewise linear interpolation is used to lock the depth z. n ;

[0090] Side resistance distribution ;

[0091] Feedback is provided online from constitutive and stress paths;

[0092] Negative friction region [0, z] n Integrating, After immersion in water, σ is changed through the water head field. v ′ and K-path, causing f s Redistribution and z n Move up; the algorithm automatically refreshes at the end of each stage. And serve as the initial condition for the next stage.

[0093] Step 4: Determine the energy efficiency of the pile group and assess the reduction of the cyclic dynamic effect.

[0094] In embodiments of the present invention, such as Figure 6 As shown, the energy determination of the group pile efficiency in step 4 includes:

[0095] Characterizing interactions using strain energy: ;

[0096] in, ;

[0097] To distinguish between the effects of side resistance and end resistance, ζ is defined. s , ζ b Used to correct the effective contribution of side and end resistance, making α s α b This refers to the energy share coefficient.

[0098] The calculation process is as follows: Under the same top load and boundary conditions, calculate the energy of a single pile and a group of piles respectively, and statistically analyze the energy of different s / D, arrangements, degrees of consolidation, and frequency bands. Changes are processed to form a database and used for rapid prediction via response surface methodology or machine learning regression; in the design, real-time calculated values ​​are prioritized, while database values ​​serve as priors and verification.

[0099] In this embodiment of the invention, the assessment of the reduction in cyclic dynamic effects in step 4 includes:

[0100] Cyclic dynamic effect reduction ΔR cyc Evaluate, It is used to characterize the intensity decay of the interface under broadband, non-stationary cycling; the coefficient α is calibrated in two steps:

[0101] (1) Indoor interface cyclic direct shear or ring shear test to obtain τ cyc -N- Degradation curve; (2) On-site dynamic measurement (acceleration / pile strain) inversion fine-tuning, using extended form, ;

[0102] in, m and n are fitted experimentally to ensure sensitivity to high cycle counts and large shear strain amplitudes; if pore pressure accumulation is considered, then superimposed... .

[0103] Step 5: Obtain the static-dynamic expressions and algorithms for vertical bearing capacity.

[0104] In this embodiment of the invention, step 5 includes:

[0105] Instantaneous value of bearing capacity ;

[0106] The design value adopts the statistical lower limit: the quantile within the time window T. ;

[0107] Compared with the design vertical load SLC, the algorithm flow is as follows: a) complete the stage update; b) gradually integrate over the dynamic time history to obtain R. v dyn (t); c. Calculate the characteristic values ​​of peak value, root mean square, and 5th percentile; d. Output instantaneous-statistical-design triple values ​​for use in determining bearing capacity and reliability.

[0108] Step 6: Perform service settlement, DAF and reliability consistency criteria.

[0109] In this embodiment of the invention, the service settlement S is the control amount of the absolute or differential settlement of the pile cap or pile top; the dynamic amplification factor... Defined by the ratio of static and dynamic displacements under the same load conditions; reliability analysis is based on... Let X be a performance function containing random variables {δ, c}. a ,κ soft ,K,λ,κ,M,q b The failure probability P is obtained using FORM / IS or Monte Carlo methods. f and The consistency criterion is:

[0110] ;

[0111] When the three are inconsistent, iterate the parameters or operating strategies in the order of first satisfying safety and then optimizing economy.

[0112] Step 7: Design and operational parameter automation optimization, software system and data flow implementation.

[0113] In this embodiment of the invention, {L, s / D, layout type, pier stiffness, speed limit v, peak shift rate} are used as design variables. The objectives are to maximize bearing capacity margin, minimize settlement, minimize cost, and optimize robustness. The constraints are criterion satisfaction and upper and lower structural limits. NSGA-II or multi-objective particle swarm optimization algorithms are used to evaluate robustness in the outer nested scenario set Ω = {normal water level, sudden rainstorm rise, storm surge}. Each candidate scheme is calculated under each scenario. S, DAF, β are aggregated in worst-case or CVaR; output the Pareto front and recommended range (if the efficiency gain decreases after the critical pile distance ≈ 4.0-4.5D, it indicates that the benefit of further increasing the distance is limited), and give the minimum cost set of the operation strategy (speed limit / peak shift).

[0114] In this embodiment of the invention, the system architecture adopts a modular + database design: modules such as parameter inversion, 3D modeling, time-series load conditions, dynamic load input, coupled solution, energy efficiency, unified assessment, reliability, and report visualization are connected through unified data specifications (such as JSON / Parquet); inputs include survey databases, indoor tests, and monitoring sensors (settlement, pore pressure, acceleration, pile strain), and the middle platform implements versioning and traceability; the solution engine supports parallel computing and breakpoint continuation; post-processing outputs standardized reports and traceable layers (lateral resistance / neutral point evolution, energy cloud map, spectral transfer function) of bearing capacity-settlement-DAF-β-recommendation; and provides APIs to connect with BIM / CIM platforms and operation and maintenance monitoring systems to form an integrated engineering digital foundation.

[0115] Step 8: Optional implementation and standard compatibility, result verification and full lifecycle application.

[0116] In this embodiment of the invention, when computing power or cycle time is limited, a one-dimensional Winkler curve equivalent in energy to the three-dimensional result is constructed: The mapping is transformed into p–y / t–z / q–z curve reduction coefficients, which quickly completes the initial screening and layout optimization; the final decision is verified by three-dimensional coupling and monitoring inversion; the system has a built-in automatic mapping layer with the current specifications (bearing capacity partial factor, settlement limit, train / vehicle load value), and provides a three-dimensional comparison report of specifications, engineering and this invention to ensure compliance in review and feasibility in implementation.

[0117] In this embodiment of the invention, the entire lifecycle is divided into three stages:

[0118] I. Pre-design assessment: Rapidly compare and select solutions under multiple water levels and dynamic load scenarios, and form a three-dimensional index matrix of technical, economic and robust indicators;

[0119] II. Rolling during construction: Monitoring data is integrated according to the phased pile-cap-backfilling rhythm, parameters are periodically inverted, and real-time updates and judgment criteria are implemented. Construction organization and pile spacing / reinforcement details are adjusted as necessary.

[0120] III. Operational Period Review: Check DAF, settlement and β on an annual / pre-flood cycle. In scenarios where static load is qualified but dynamic load is critical, prioritize the combination of speed limit / peak shifting and drainage and dewatering. If still insufficient, implement local reinforcement (external grouting, pile cap stiffening, side pile replacement, etc.). Record the entire process and archive it. Set trigger thresholds to automatically issue early warnings and generate disposal orders.

[0121] An example of this invention: It has been applied in a cross-sea expressway project in a coastal city. This expressway consists of a bridge system jointly constructed by an intercity rail line and an urban expressway. The marine silty soft soil at the bridge site is 48.6–61.3 m thick, grayish-black with high water content, has a liquid limit of 54–68%, a natural water content of 47%–62%, and a permeability coefficient of approximately 1.1 × 10⁻⁶ m. -8 The stratum has a consolidation rate of m / s and is extremely slow, belonging to an ultra-soft and compressible stratum. The bridge pier abutment uses a square pile group consisting of nine ultra-long piles with a diameter of 1.2m, each 78m long, with a net pile spacing of 4.8m (approximately 4.0D). The superstructure traffic live load is jointly generated by intercity trains traveling at 200 km / h and a six-lane expressway traveling at 80 km / h, with a design traffic volume of 1200 vehicles / hour in both directions. During the construction and operation phases, the project faces the adverse scenario of long-term consolidation, sudden rise in water level, and broadband dynamic load superposition. The traditional equivalent static load method cannot provide a consistent static-dynamic safety criterion, resulting in problems such as bearing capacity assessment deviation and dispersion of control indicators.

[0122] To implement the method of this invention, initial parameter values ​​were first established through field investigation and laboratory tests. The soil constitutive model was a modified Cambridge model (MCC), and the key parameters after inversion were λ=0.245, κ=0.045, critical state slope M=1.22, and initial void ratio e0=2.10; the permeability coefficient of saturated soft soil was 1.1×10⁻⁶. -8 m / s. The pile-soil interface bond-slip-softening model was comprehensively inverted through static load pile testing, pile strain, and acoustic transmission. The friction angle δ = 22°, and the bond strength c... a =8.0 kPa, exponential softening coefficient κ soft =32m -1 The dynamic parameters are determined by monitoring the bridge deck acceleration and pile top vibration to determine the damping ratio, and matched with the modal participation coefficients in the target frequency band of 1–20 Hz, forming a parameter closed loop of monitoring-inversion-verification. The relative error of the calculated-measured key response is controlled within ±10%.

[0123] The three-dimensional calculation model uses saturated soil u - pThe coupling theory is used to create a refined integrated model of the bridge deck, abutment, pile group, and foundation. Zero-thickness contact elements are inserted at the pile-soil interface, and a free field or viscoelastic artificial boundary is set at the bottom. The side boundaries switch seepage conditions according to the consolidation and dynamic stages. The working condition sequence follows the actual engineering history: after the pile and abutment construction is completed, traffic preloading and 6-month long-term consolidation are carried out, followed by a flooding scenario where the groundwater level rises by 1.8m due to heavy rain. Finally, the coupled loads of intercity trains and highway vehicles are input under this updated state. The dynamic load input generates time histories using spectral representation. The main frequency of intercity trains is 1.5–10 Hz with a peak of about 4 Hz, and the main frequency of highway vehicles is 2–16 Hz with a peak of about 7 Hz. The two have significant frequency band overlap in the 4–10 Hz range. The time histories are transferred to the pile top through the superstructure-abutment-pile group-foundation path, ensuring the consistency between the input spectrum and the transferred spectrum.

[0124] Under the effects of consolidation and immersion, the pile-soil relative displacement drives the redistribution of negative skin friction, with the neutral point shifting from 35.2 m before consolidation to 37.1 m after consolidation. When the water level rises by 1.8 m, due to the decrease in effective stress and the change in the lateral pressure path, the neutral point significantly shifts upward to 30.6 m, and the peak value of negative skin friction increases from 28.6 kPa to 61.5 kPa. The depth of negative skin friction influence extends to approximately 25 m above the pile length. This evolution process directly leads to changes in the axial force distribution and end resistance mobilization patterns of the pile. If the neutral point and net lateral resistance value are not updated, significant deviations in load assessment will occur. This invention identifies the neutral point using the zero point of the pile-soil relative displacement and automatically updates the lateral resistance, axial force, and neutral point at the end of each stage, ensuring that subsequent dynamic load analysis starts from the true initial state.

[0125] To characterize the interaction of pile groups, this invention defines pile group efficiency using strain energy. Under the same top load and boundary conditions, comparing the strain energy distribution of a single pile and a group of piles, the strain energy U of a single pile is... single The total strain energy of the pile group is 742.5 kJ. group The value is 4785.2 kJ. =(U group / 9) / U single ≈0.716. This value is lower than the empirical reduction factor of 0.80–0.85, reflecting that the efficiency reduction of ultra-long piles is more significant under dense pile arrangement and soft soil confinement conditions. A unified bearing capacity expression is introduced, and the dynamic reduction term ΔR is calculated by combining the interface cyclic shear stress statistics. cyc After two-stage calibration—indoor circulating direct shear and on-site dynamic testing—the ΔR of this invention... cyc Take 310 kN.

[0126] According to the static-dynamic unified calculation formula of this invention, the bearing capacity is calculated as follows: An assessment was conducted; under the control combination of immersion in water and multiple dynamic loads, the positive resistance R of the pile side was... side + =5800kN, negative frictional force R side - =1350kN, pile end resistance R b =1050kN, substitute into =0.716 and ΔR cyc =310kN, thus obtaining R v dyn ≈3555kN. Compared with the design vertical load SLC=2970kN, the bearing capacity meets the specified target; at the same time, the dynamic amplification factor DAF for pile top displacement and pile cap settlement is 1.13, and the maximum settlement S max =34.6mm (limit 40mm), reliability index β=3.41 (target ≥3.10), all three criteria passed, avoiding the disconnect between static load qualification and dynamic load criticality assessment.

[0127] To verify the effectiveness of the project, a comparison was made between the traditional equivalent static load method and the method of this invention: The traditional method uses an empirical pile group coefficient of 0.82 and ignores cyclic reduction, resulting in a bearing capacity of approximately 3820 kN, which is 7%–9% more optimistic than the results consistent with the measured and inverted calculations. Furthermore, the DAF (Density Aspect Ratio) is not quantified, making it difficult to provide a basis for speed limiting and peak-shifting strategies. This invention provides a unified bearing capacity of 3555 kN under the same data and boundary conditions, and simultaneously generates DAF=1.13 and β=3.41. The calculated results and field monitoring show a better than ±10% agreement in pile top acceleration, peak axial force, and displacement components, forming a consistent criterion for bearing capacity, settlement, and reliability. Based on sensitivity analysis, if the pile spacing is increased from 4.0D to 4.8D… The R value can be increased from approximately 0.716 to around 0.78. v dyn The speed will be increased by about 6% to 8%, and the maximum settlement will be reduced by about 12%. If the operating speed of intercity trains is limited from 200 km / h to 180 km / h, the DAF will be reduced from 1.13 to about 1.09, which can achieve a higher operational safety margin without changing the civil engineering structure.

[0128] Based on the overall project implementation results, this invention has achieved three significant benefits in this project. First, in terms of safety, the unified three-dimensional criteria for load-bearing capacity, DAF, and β ensure consistency between design and operation and maintenance standards, allowing for risk identification under extreme conditions to be implemented at the design stage, and providing a quantitative basis for operational speed / peak-shifting strategies. Second, in terms of economy, based on... With ΔR cycThe accurate identification avoids overly conservative reinforcement and redundant pile lengths. Cost comparisons show that single-pier pile groups save approximately 3% to 5% in materials and labor time, demonstrating considerable cost-effectiveness after large-scale engineering implementation. Thirdly, in terms of replicability, the parameter inversion and status update processes can be completed using conventional survey and in-service monitoring data, without requiring additional specialized testing equipment, making it easily reusable in other marine soft soil bridge sites, port areas, and near-shore seawall projects.

[0129] This invention relates to static and dynamic analysis, negative skin friction assessment, and bearing capacity calculation of pile group foundations. It is particularly applicable to the design, evaluation, and operational safety determination of ultra-long pile group foundations in ultra-deep marine silty soft soil layers under the superimposed loads of intercity railways and expressways. It can achieve verifiable static-dynamic integrated assessment on ultra-long pile groups in ultra-deep silty soft soil, providing direct quantitative basis for subsequent design optimization (pile spacing, pile length, pile cap stiffness) and operation management (speed limit, peak shifting, drainage and dewatering strategies), and has broad engineering application value.

[0130] The technical solution provided by this invention includes parameter acquisition and inversion, and the construction of a three-dimensional saturated soft soil model. u - p This method employs a coupled model to perform time-series simulations of construction, consolidation, and immersion; construct and couple the transmission of multi-source traffic dynamic loads; define the pile-soil interface adhesion-slippage-softening constitutive model; identify and redistribute negative skin friction and neutral point; determine the energy efficiency of pile groups and assess the reduction of cyclic dynamic effects; obtain static and dynamic expressions and algorithms for vertical bearing capacity; establish consistency criteria for service settlement, DAF, and reliability; automate the optimization of design and operation parameters; and implement the software system and data flow. It offers optional implementation and standard compatibility, result verification, and life-cycle application. This method can uniformly describe immersion or water level rise-negative skin friction-neutral point migration-pile group effect-dynamic load amplification at three-dimensional, temporal, and multi-field coupled levels. It accurately characterizes the spectral characteristics and transmission paths of multi-source traffic dynamic loads, quantifies the energy dissipation and efficiency changes of pile groups, and uses multiple indicators (bearing capacity-settlement-reliability) as consistency criteria, providing scientific, verifiable, and reusable technical support for design and operation.

[0131] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for calculating the vertical bearing capacity of ultra-long pile groups in ultra-deep silty soft soil, characterized in that, The method includes: Step 1: Parameter acquisition and inversion, and construction of three-dimensional saturated soft soil. u - p Coupled model; Step 2: Conduct time-series simulation of construction-consolidation-immersion, and construct and couple the dynamic load of multi-source traffic. Step 3: Bond-slip-softening constitutive model of pile-soil interface, identification and redistribution update of negative skin friction and neutral point; Step 4: Determine the energy efficiency of the pile group and assess the reduction of cyclic dynamic effects; Step 5: Obtain the static and dynamic expressions and algorithms for vertical bearing capacity; Step 6: Perform consistency criteria for service settlement, DAF, and reliability; Step 7: Automated optimization of design and operation parameters, implementation of software systems and data flows; Step 8: Optional implementation and standard compatibility, result verification and full lifecycle application; The pile-soil interface bonding-slipping-softening constitutive model in step 3 includes: Peak interfacial shear strength ; The softening segment index degrades. The normal direction adopts a contact-compression, cracking-free approach; the tangential direction adopts a three-stage approach of bond-slip-residual, and damage parameters D(N,γ) are introduced under cyclic action. cyc )∈[0,1]; For δ, c a Update dynamically. ; At the algorithm level, the tangential displacement increment and the bonding state are updated according to the returned mapping to ensure numerical stability and consistency with the algorithm. u - p Consistency of coupling; Step 3, the identification and redistribution update of negative friction and neutral point, includes: The neutral point is initially determined by the pile-soil relative displacement Δw(z) = 0, and then verified by the sign change of the pile axial force derivative dN / dz; piecewise linear interpolation is used to lock the depth z. n ; Side resistance distribution ; Feedback is provided online from constitutive and stress paths; Negative friction region [0, z] n Integrating, After immersion in water, σ is changed through the water head field. v ′ and K-path, causing f s Redistribution and z n Move up; the algorithm automatically refreshes at the end of each stage. And serve as the initial condition for the next stage; The energy determination of the pile group efficiency in step 4 includes: Characterizing interactions using strain energy: ; in, ; To distinguish between the effects of side resistance and end resistance, ζ is defined. s , ζ b Used to correct the effective contribution of side and end resistance, making α s α b This refers to the energy share coefficient. The calculation process is as follows: Under the same top load and boundary conditions, calculate the energy of a single pile and a group of piles respectively, and statistically analyze the energy of different s / D, arrangements, degrees of consolidation, and frequency bands. Changes are processed to form a database and used for rapid prediction via response surface methodology or machine learning regression; in the design, real-time calculated values ​​are prioritized, with database values ​​serving as priors and verification. The assessment of the reduction in cyclic dynamic effects in step 4 includes: Cyclic dynamic effect reduction ΔR cyc Evaluate, It is used to characterize the intensity decay of the interface under broadband, non-stationary cycling; the coefficient α is calibrated in two steps: (1) Indoor interface cyclic direct shear or ring shear test to obtain τ cyc -N- Degradation curve; (2) On-site dynamic measurement inversion fine-tuning, using an extended form, ; in, m and n are fitted experimentally to ensure sensitivity to high cycle counts and large shear strain amplitudes; if pore pressure accumulation is considered, then superimposed... .

2. The method according to claim 1, characterized in that, The parameter acquisition and inversion in step 1 includes: parameter identification following a closed loop of experiment-monitoring-inversion-verification; First, with consolidation, triaxial CU / CD, and shear wave velocity V... s Initial values ​​for indoor or in-situ tests: MCC parameters {λ,κ,M,e0,p} c }、SSC creep parameters {C α }, initial shear modulus G max =ρV s 2 And configure the degradation curve G / G max =F(γ); Interface parameters {δ,c a ,κ soft The results were derived from the regression of the side resistance of the test piles and the back-inference of the pile strain monitoring. Secondly, a hierarchical inversion method was adopted. The first layer used static load tests to fit the load-displacement curve at the pile top and the axial force distribution in the pile body; the second layer used consolidation settlement time history to fit c v The third layer is damped by dynamic measurement constraints and the dynamic boundary; the inversion objective function is to take the multi-index weighted least squares or Bayesian posterior maximization to control the error of key response quantities within ±10%, and output the parameter covariance.

3. The method according to claim 2, characterized in that, In step 1, three-dimensional saturated soft soil is constructed. u - p The coupled model includes: The soil is treated using Biot's two-phase media theory: Displacement equilibrium, ; Conservation of mass ; Where σ′=D:ε is given by MCC / SSC, and α is the Biot coefficient; the pile and the pile cap adopt solid elements, and the pile-soil interface element is inserted with zero thickness, with no tension in the normal direction, Coulomb limit in the tangential direction and softening; Regarding the boundaries, a free field or viscoelastic boundary is applied at the bottom to absorb outward radiated waves, and the permeability of the side boundaries is switched according to the working conditions; spatial discretization satisfies the requirement of 8-10 elements for the pile diameter span; the equivalent thickness of the interface is approximately D / 20; and the consolidation step in time is Δt ≤ 0.2h. min 2 / c v In the dynamic analysis, explicit integration is performed with Δt ≤ T. min / 20 or implicitly adaptive.

4. The method according to claim 3, characterized in that, The time-series simulation of construction-consolidation-immersion in step 2 reflects the loading history, and includes: ① Apply structural constraints and self-weight during the pile and cap construction stages; ② Load the subgrade or superstructure and enter long-term consolidation, give the seepage boundary according to the site drainage conditions, and solve for pore pressure dissipation and effective stress evolution; ③ Trigger the scenario of sudden rise in water level or immersion, introduce it through water head jump or infiltration flux boundary, reset the pore pressure field and cause effective stress reduction and strength degradation; ④ Use the current state as the initial field for subsequent dynamic loads; Update the pile-soil relative displacement, lateral resistance and neutral point position before the end of each stage to provide time-varying initial values ​​for the next stage.

5. The method according to claim 4, characterized in that, Step 2, the construction and coupling transfer of multi-source traffic dynamics, includes: Vehicle and train loads are statistically described using power spectral density S(ω) and speed-axle load. Broadband, non-stationary time histories are generated through spectral representation or pseudo-excitation, considering the energy distribution of wheel-rail irregularities or road surface irregularities in the 1-20Hz frequency band. The load coupling paths are sequentially bridge deck or road surface, main beam or bridge deck, abutment, pile group, and foundation, and are superimposed and transferred in the time domain. When the dominant frequency approaches the structural or foundation mode, the resonant neighborhood is checked using modal participation factor, damping ratio, and contact stiffness. For moving trains, a moving axle load-spatiotemporal mapping P(t) = ∑P is used. i δ(x v i t), and coupled with the interaction of the track or bridge surface to ensure the consistency of the input spectrum with the transfer spectrum.

6. The method according to claim 1, characterized in that, Step 5 includes: Instantaneous value of bearing capacity ; The design value adopts the statistical lower limit: the quantile within the time window T. ; The algorithm flow is as follows: a) complete the stage update; b) gradually integrate within the dynamic time history to obtain R. v dyn (t); c. Calculate the characteristic values ​​of peak value, root mean square, and 5th percentile; d. Output instantaneous-statistical-design triple values ​​for use in determining bearing capacity and reliability.

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