Time-varying failure probability analysis method for pile-anchor support system

Abstract

The application discloses a time-varying failure probability analysis method for a row pile-anchor rod supporting system, and belongs to the technical field of geotechnical engineering and underground structure engineering. The technical problem to be solved is that there is a lack of risk quantification means in the failure probability level. The technical solution points are as follows: a row pile resistance model, an anchor rod resistance model, a soil pressure model and a groundwater pressure model are constructed, a static limit state function is converted into a time-varying limit state function; row pile resistance parameters, anchor rod resistance parameters, soil pressure parameters and groundwater parameters are set, a time-varying limit state function is output, and a row pile-anchor rod supporting system failure probability change graph is output; according to the failure probability change graph, instantaneous failure probability and cumulative failure probability are counted, and the reliability and failure risk of the row pile-anchor rod supporting system are analyzed.

Description

Technical Field

[0001] This invention belongs to the field of geotechnical engineering and underground structure engineering technology, specifically involving a time-varying failure probability analysis method for a pile-anchor support system based on probability statistics theory. It is applicable to the safety assessment and risk control of support structures in deep foundation pit engineering, underground engineering and complex environmental conditions. Background Technology

[0002] The pile-anchor support system is widely used in urban deep foundation pit engineering due to its clear stress distribution, mature construction methods, and strong adaptability. However, existing engineering design and safety assessment methods generally have the following shortcomings: 1. Based on deterministic design: Traditional support structure design often adopts the safety factor method, which only checks a certain most unfavorable working condition, making it difficult to reflect the random fluctuations and degradation patterns of structural performance during long-term service.

[0003] 2. Ignoring the time-varying characteristics of structural performance; factors such as concrete carbonization of piles, steel corrosion, anchor stress relaxation, interface degradation of anchorage sections, soil consolidation creep, and groundwater level fluctuations can all lead to the decrease of the support system's resistance over time and the gradual accumulation of load effects. Traditional static methods cannot reflect the above processes.

[0004] 3. Lack of risk quantification methods at the level of failure probability; existing methods are unable to quantitatively provide key engineering questions such as "when will the pile-anchor support system fail", "what is the probability of failure", and "when will the risk accumulate rapidly" within its service life, making it difficult to provide a scientific basis for operation and maintenance decisions.

[0005] Therefore, there is an urgent need to propose a failure probability analysis method for pile-anchor support systems that can simultaneously consider the randomness of multiple factors, time-varying degradation effects, and the impact of extreme events. Summary of the Invention

[0006] The purpose of this invention is to provide: A time-varying failure probability analysis method for pile-anchor support systems is proposed to address the technical problem of lacking risk quantification methods at the failure probability level.

[0007] To solve the above-mentioned technical problems, the present invention provides the following technical solution: A time-varying failure probability analysis method for a pile-anchor support system includes the following steps: S1. Perform stress analysis on the pile-anchor support system to determine the initial active earth pressure and initial hydrostatic pressure of the pile-anchor support system; S2. An equivalent stress analysis is performed on the pile-anchor support system, and a static limit state function is constructed based on the resistance system and the action effect system. S3. Construct a pile resistance model by combining the initial pile resistance, attenuation coefficient, and random disturbance term of pile resistance; S4. Combining the initial resistance of a single anchor bolt, the number of anchor bolts, the anchor bolt resistance degradation model, and the anchor bolt resistance random disturbance term, construct the anchor bolt resistance model; S5. Combine the initial active earth pressure, time growth term, and random disturbance term of the pile-anchor support system to construct an earth pressure model; and construct a groundwater pressure model by equating the groundwater level to the resultant force of water pressure acting on the pile-anchor support system per unit width. S6. Using the pile resistance model, anchor resistance model, earth pressure model, and groundwater pressure model constructed in the preceding steps, the static limit state function is transformed into a time-varying limit state function; S7. Set the pile resistance parameters, anchor resistance parameters, earth pressure parameters, and groundwater parameters, output the time-varying limit state function substituted into step S6, and output the failure probability variation diagram of the pile-anchor support system. S8. Based on the failure probability change graph described in step S7, calculate the instantaneous failure probability and cumulative failure probability, and analyze the reliability and failure risk of the pile-anchor support system.

[0008] Further, in step S2, the static limit state function is constructed, specifically: S2. An equivalent stress analysis is performed on the pile-anchor support system, and a static limit state function is constructed based on the resistance system and the action effect system; specifically: S21. The structural failure caused by insufficient overall bearing capacity of the combined pile and anchor system is selected as the failure mode; S22. In this failure mode, perform equivalent stress analysis to summarize the stress of the pile-anchor system into a resistance system and an action effect system; S23. The difference between the total resistance of the resistance system and the total effect of the action system is the static limit state function.

[0009] Furthermore, the total resistance of the resistance system is: ; The total load on the system is: ; The static limit state function is then defined as: ; in: The total load borne by the pile-anchor support system in year t; The total resistance of the pile-anchor support system in year t; The resistance provided by the piles in year t; The resistance provided by the anchor bolt in year t; The force exerted by the soil on the pile-anchor support system in year t; The force exerted by groundwater on the pile-anchor support system in year t.

[0010] Further, in step S3, a pile resistance model is constructed, specifically: The bearing capacity of piles under a certain failure mode is equivalent to a scalar resistance value. , representing the maximum equivalent resistance capacity that the piles can provide in year t; By employing an exponential function, introducing a decay coefficient, and a random disturbance term for the pile resistance, the maximum equivalent resistance capacity is solved, characterized as follows: : ; Initial ultimate resistance of piles; : Annual attenuation coefficient of pile resistance; : Random disturbance term of pile resistance, used to characterize the uncertainty of material properties and construction quality.

[0011] Further, in step S4, the anchor bolt resistance model is constructed, specifically: Based on the equivalent resistance model of multiple anchor bolts, the stabilizing effect provided by multiple anchor bolts at a certain moment is equivalent to the resistance provided by the anchor bolts in year t. This value represents the total equivalent resistance that the anchor system can provide in year t; The initial total resistance of the anchor system is calculated by multiplying the initial resistance of a single anchor bolt by the number of bolts. The total equivalent resistance is characterized by the equivalent initial total resistance, the exponential function, the attenuation coefficient, and the random disturbance term of the anchor bolt resistance; the expression for the total equivalent resistance is as follows: ; in: Number of anchor bolts; Initial resistance of a single anchor bolt; : Annual attenuation coefficient of anchor bolt resistance; : Random disturbance term of anchor bolt resistance.

[0012] Furthermore, in step S5, an earth pressure model is constructed by combining the initial active earth pressure, time growth term, and random disturbance term of the pile-anchor support system; the earth pressure model is characterized by the expression for the force exerted by the soil on the pile-anchor support system in year t. ; in: Initial active earth pressure; : Annual growth coefficient of earth pressure; Earth pressure random disturbance term.

[0013] Furthermore, in step S5, the groundwater level is equivalent to the resultant force of water pressure acting on the pile-anchor support system per unit width, thus constructing a groundwater pressure model; the expression for the force exerted by groundwater on the pile-anchor support system in year t is used to characterize the groundwater pressure model: ; ; : The density of water; If the height from the bottom of the pile-anchor support system to the groundwater surface is ≤0, then water pressure is not calculated. : Average groundwater level over many years; : Seasonal changes in groundwater level; Random related items for groundwater level; Sudden increases in water level caused by extreme environmental events.

[0014] Furthermore, the seasonal variation of groundwater level This is used to simulate annual periodic water level changes, with water levels rising during the rainy season and falling during the dry season; the seasonal variation of groundwater levels is also included. The expression is as follows: ; Where A represents the seasonal water level amplitude.

[0015] Furthermore, groundwater level stochastic correlation items ,expression: ; ; Time correlation coefficient; Intensity of interannual random disturbances.

[0016] Furthermore, the sudden increase in water level caused by extreme environmental events ,expression: Using Poisson distribution Describe the frequency of extreme events. The number of extreme events; The average rate at which extreme events occur, when When an extreme event is determined to have occurred; In the event of an extreme event, the water level increase... Follows an exponential distribution: ; It represents the mean of the exponential distribution, i.e., the average level of water level increments.

[0017] Further, in step S6, the static limit state function is transformed into a time-varying limit state function through equivalent processing; specifically: ; .

[0018] The present invention has at least the following beneficial effects: 1. The purpose of this invention is to provide a time-varying failure probability analysis method for a pile-anchor support system. By constructing a pile resistance model, an anchor resistance model, an earth pressure model, a groundwater pressure model, and a time-varying limit state function, the method enables a quantitative assessment of the failure probability of the pile-anchor support system throughout its entire service life.

[0019] 2. This method can: reflect the degradation law of the resistance of piles and anchors over time; consider the random evolution of active earth pressure and groundwater pressure and the influence of extreme events; calculate the instantaneous failure probability and cumulative failure probability at any service time; and provide quantitative basis for support structure design optimization, operation monitoring and maintenance decision-making.

[0020] 3. For the first time, time-varying reliability is organically combined with the overall stability of the pile-anchor system; 4. It can simultaneously consider the effects of resistance degradation, load increase, and extreme events; 5. The output is the failure probability, with a high degree of risk quantification; 6. Applicable to the design, construction, and operation and maintenance phases; 7. It has strong engineering applicability, clear calculation methods, and can be directly implemented through programming. Attached Figure Description

[0021] Figure 1 This is a simplified force diagram of the pile-anchor support system of the present invention; Figure 2This is a flowchart illustrating the programming process of the present invention. Figure 3 This is a graph showing the change in failure probability of the pile-anchor support system of the present invention; Figure 4 This is the most unfavorable cross-sectional view of the pile-support structure of the Daxing project according to the present invention; Figure 5 This is a graph showing the change in failure probability of the pile-anchor support system for the Daxing project according to the present invention. Detailed Implementation

[0022] The following non-limiting embodiments are intended to enable those skilled in the art to gain a more comprehensive understanding of the present invention, but do not limit the invention in any way. The following content is merely an exemplary description of the scope of protection claimed by the present invention, and those skilled in the art can make various changes and modifications to the present invention based on the disclosed content, and such changes should also fall within the scope of protection claimed by the present invention.

[0023] This invention provides a method for analyzing the time-varying failure probability of a pile-anchor support system, comprising the following steps: S1. Perform a stress analysis on the pile-anchor support system to determine the initial active earth pressure and initial hydrostatic pressure. The initial hydrostatic pressure refers to the water pressure generated by the initial groundwater level. Specifically: like Figure 1 As shown, to simplify the mechanical analysis of the complex pile-anchor support system, a classic pile-anchor support system is selected, with a 1m width used as the support unit. Within each support unit, one pile and three layered anchors are arranged, with the anchors and piles working in tandem. Earth pressure and water pressure increase with depth; Pwatermax is the maximum water pressure at the bottom of the pile, and Psoilmax is the maximum earth pressure at the bottom of the pile.

[0024] To ensure the safety and conservatism of the simulation data, the moment when the foundation pit excavation is completed is selected as the most unfavorable stress condition. The favorable lateral active earth pressure exerted by the soil within the foundation pit on the piles is ignored in the calculation, and the initial groundwater head outside the pit is set to h. Based on these assumptions, a stress analysis is conducted on the support unit to clarify the distribution and quantitative values ​​of the active earth pressure and hydrostatic pressure borne by the piles on the soil-facing surface, providing a physical model and initial load data for subsequent reliability simulation of the support system.

[0025] S2. An equivalent stress analysis is performed on the pile-anchor support system, and a static limit state function is constructed based on the resistance system and the action effect system; specifically: S21. The structural failure caused by insufficient overall bearing capacity of the combined pile and anchor system is selected as the failure mode; S22. In this failure mode, an equivalent stress analysis is performed, and the stress of the pile-anchor system is summarized into a resistance system and an action effect system. The resistance system includes the passive resistance provided by the piles and the active tensile force provided by the anchors. The action effect system includes the active earth pressure, groundwater pressure, and additional effects caused by environmental and construction disturbances. S23. The difference between the total resistance of the resistance system and the total effect of the action system is the static limit state function.

[0026] 1) The role of the limit state function: In this invention, the role of the limit state function is to compare the comprehensive bearing capacity of the pile-anchor support system at a certain service moment with the external forces, thereby determining whether the system has failed at that moment.

[0027] 2) Failure modes in step S21: The pile-anchor support system may experience various failure modes: pile bending failure, anchor breakage or pullout, overall slippage of the retaining structure, and overall overturning of the retaining structure.

[0028] The failure mode selected in step S21 of this invention is structural failure caused by insufficient overall bearing capacity of the combined pile and anchor system. This mode can comprehensively reflect the combined effect of the piles and anchors, avoid over-refinement of local components, enhance model stability, and is suitable for long-term, time-varying reliability analysis.

[0029] 3) Equivalent force analysis in step S22: From a mechanical perspective, the function of the pile-anchor system can be summarized as a resistance system and an action-effect system. The resistance system mainly includes the passive resistance provided by the piles and the active tensile force provided by the anchors. The action-effect system mainly includes active earth pressure, groundwater pressure, and additional effects caused by environmental and construction disturbances.

[0030] In step S23, To make it suitable for probabilistic analysis, this invention simplifies the pile-anchor system as follows: Total resistance of the resistance system: ; The total effect of the system: ; The static limit state function is then defined as: .

[0031] in: The total load borne by the pile-anchor support system in year t; The total resistance of the pile-anchor support system in year t; The resistance provided by the piles in year t; The resistance provided by the anchor bolt in year t; The force exerted by the soil on the pile-anchor support system in year t; The force exerted by groundwater on the pile-anchor support system in year t; : At that time, it was determined that the support system had failed.

[0032] In the overall stability analysis, the equivalent model system treats the piles and anchors as co-bearing components, which facilitates the introduction of randomness and time-varying characteristics, and transforms the static limit state function into a time-varying limit state function.

[0033] S3. Construct a pile resistance model by combining the initial pile resistance, attenuation coefficient, and random disturbance term of the pile resistance; specifically: 1. The necessity of modeling the pile resistance model: In the pile-anchor support system, the piles are the main load-bearing components, bearing bending moments and shear forces caused by active earth pressure. The performance of the piles directly determines the safety of the system. Therefore, in this invention, the pile resistance is modeled as an independent and core resistance component.

[0034] 2. Analysis of the resistance composition of pile groups; The ability of piles to resist external loads mainly comes from: the strength and stiffness of the pile material, the pile-soil interaction, and the structural geometric parameters.

[0035] During long-term service, the resistance of pile walls is not constant, but rather exhibits initial stability followed by gradual decline in the middle and later stages. The main reasons include: concrete carbonation, freeze-thaw cycles, and aging; steel reinforcement corrosion leading to a reduction in effective cross-section; and the long-term effects of groundwater and corrosive media.

[0036] 3. Equivalent simplification at the mechanical level; This invention focuses on the evolution of trends, probabilities, and risks, rather than the precise distribution of internal forces under a single working condition. Therefore, this invention does not directly perform refined finite element analysis, but instead adopts an equivalent resistance model.

[0037] The bearing capacity of piles under a certain failure mode (such as overall stability, anti-sliding, and anti-overturning) is equivalent to a scalar resistance value. , representing the maximum equivalent resistance capacity that the piles can provide in year t.

[0038] 4. Construction of the pile resistance model; 1) Initial ultimate resistance of the piles; Initial ultimate resistance of piles This represents the maximum lateral resistance, or equivalent resistance to sliding or overturning, that a pile system (considering only the piles) can provide under extreme conditions during the initial service phase (t=0), without considering material degradation, environmental erosion, and long-term effects. It can be determined through calculations using standard formulas, finite element analysis, or field tests.

[0039] 2) Selection of resistance degradation model; Based on the characteristics of pile resistance degradation, the basic requirements for the resistance degradation model are: monotonically decreasing; slow change in the early stage; significant cumulative effect in the later stage; and simple and calculable mathematical form.

[0040] Because the exponential function can naturally reflect the long-term accumulation of deterioration and is widely used in the durability modeling of concrete structures to meet the resistance degradation characteristics, the exponential function is chosen as the functional form of the resistance degradation model.

[0041] Introducing attenuation coefficient , which represents the annual decay rate of the pile resistance, comprehensively reflecting the damage to the resistance caused by the decay of concrete strength, the rate of steel corrosion, and the intensity of environmental erosion.

[0042] 3) Random disturbance term of pile resistance; In real-world engineering projects, there are significant differences in construction quality among different pile groups. Geological conditions vary along depth and space, and material properties exhibit statistical dispersion. Therefore, it is necessary to introduce stochastic modeling.

[0043] Random disturbance term of pile resistance It comprehensively reflects the disturbance situation of the resistance force by disturbance conditions such as pile diameter deviation, pile length deviation, concrete strength dispersion, reinforcement position and reinforcement deviation, and pile-soil contact condition differences.

[0044] 4) The resistance of the pile wall gradually decreases with service time, and its mathematical model can be summarized as follows: ; in: Initial ultimate resistance of piles; : Annual attenuation coefficient of pile resistance; : Random disturbance term of pile resistance, used to characterize the uncertainty of material properties and construction quality.

[0045] S4. Combining the initial resistance of a single anchor bolt, the number of anchor bolts, the anchor bolt resistance degradation model, and the anchor bolt resistance random disturbance term, construct an anchor bolt resistance model; specifically: 1. The necessity of constructing an anchor bolt resistance model: In a pile-anchor support system, the anchor bolt is an active load-bearing component. It reduces the bending moment of the piles through prestressing or passive tension, providing additional stabilizing force and suppressing structural displacement. Therefore, in this invention, the anchor bolt resistance is modeled as an independent, degenerate resistance component.

[0046] 2. Analysis of anchor bolt resistance composition; The effective resistance of a single anchor rod in an engineering project mainly comes from: the strength of the rod material, the bonding performance between the anchor section and the soil (or rock), the level of prestress, and the locking effect.

[0047] During long-term service, anchor bolts typically exhibit early stress loss and later performance degradation. The main causes include steel corrosion, interface deterioration of the anchorage section, soil creep, and relaxation effects caused by long-term loads.

[0048] 3. Equivalent simplification at the mechanical level; Because of the significant differences in anchor length, angle, and geological conditions, the stress distribution in the anchorage section is complex. Long-term probabilistic analysis focuses on overall stability. Therefore, this invention employs a group anchor equivalent resistance model, rather than detailed modeling of each anchor and segment individually. The stabilizing effect provided by multiple anchors at a given moment is equivalent to... This value represents the total equivalent resistance that the anchor system (including only the anchors) can provide in year t.

[0049] 4. Construction of mathematical models; 1) Initial resistance of a single anchor bolt; Initial resistance of a single anchor bolt This represents the effective pull-out resistance of a single anchor bolt during the initial service phase (t = 0). It can be determined through field pull-out tests, calculations using standard formulas, or design-specified values.

[0050] 2) Group anchor effect and number of anchor bolts; Anchor bolts are typically arranged in rows or groups, and their total resistance is not simply "resistance of a single bolt × number of bolts." However, in overall stability analysis, a more robust approach can usually be used. (Initial resistance of a single anchor bolt × number of anchor bolts) is used as the equivalent initial total resistance. The weakening effect of the group anchors can be reflected by the random disturbance term.

[0051] 3) Anchor bolt resistance degradation model; Anchor bolts are underground concealed works, and their performance degrades significantly over time and they are highly unrepairable. Therefore, it is necessary to introduce a time-varying anchor bolt resistance degradation model.

[0052] Because the exponential function can reflect the trend of anchor performance gradually decreasing over time, and is consistent with the form of the pile resistance model, facilitating the coupling of the pile-anchor support system, the exponential function is chosen as the functional form of the anchor resistance degradation model. Specifically, .

[0053] As the attenuation coefficient, it can comprehensively reflect the attenuation of anchor bolt resistance caused by steel corrosion, attenuation of anchoring section bonding performance, and long-term stress relaxation of anchor bolt.

[0054] 4) Random disturbance term of anchor bolt resistance; Introducing random disturbance terms of anchor bolt resistance It is used to comprehensively reflect the impact of uncertainties such as anchorage length deviation, grouting quality difference, and stratum inhomogeneity on anchor resistance, making the modeling effect more consistent with the actual engineering situation.

[0055] 5) The final form of the anchor bolt resistance model; ; in: Number of anchor bolts; Initial resistance of a single anchor bolt; : Annual attenuation coefficient of anchor bolt resistance; : Random disturbance term of anchor bolt resistance.

[0056] This anchor resistance model incorporates time evolution characteristics, random uncertainty, and the combined effect of multiple anchors, and can comprehensively reflect the decline of anchor resistance over time.

[0057] S5. Combine the initial active earth pressure, time growth term, and random disturbance term of the pile-anchor support system to construct an earth pressure model; and construct a groundwater pressure model by equating the groundwater level to the resultant force of water pressure acting on the pile-anchor support system per unit width. 1. Earth pressure model; 1) Modeling objectives and basic assumptions; The goal of the local pressure model is to describe the process by which the active earth pressure of a pile-anchor support system gradually increases over time due to factors such as soil consolidation, creep, changes in the surrounding environment, and construction disturbances.

[0058] To ensure the computability and engineering applicability of the earth pressure model, the following assumptions are made: The research object is the equivalent resultant active earth pressure of the pile-anchor support system; the active earth pressure has been integrated in the vertical direction and is represented by the equivalent concentrated force; during long-term service, the active earth pressure shows a slow increasing trend; uncertainties such as soil parameters, construction quality, and measurement errors can be described by random variables.

[0059] 2) Initial active earth pressure ; Initial active earth pressure The meaning is the equivalent resultant of active earth pressures borne by the support structure in its initial state, which can be determined by calculation or numerical simulation using Rankine or Coulomb earth pressure theory. It represents the soil load level at the beginning of the excavation and when the support system is put into use, excluding long-term consolidation and environmental effects.

[0060] 3) Time growth item ; Long-term engineering measurements show that cohesive soils undergo consolidation and creep, while sandy soils exhibit changes in density. Furthermore, construction and traffic loads from surrounding areas cause additional stress accumulation. Therefore, active earth pressure is not constant. A time-growth term is introduced to reflect the slow increase in active earth pressure during long-term service.

[0061] 4) Earth pressure random disturbance term ; The random disturbance term of earth pressure is used to describe the spatial variability of soil physical and mechanical parameters, earth pressure calculation model errors, construction deviations, and measurement and statistical errors on earth pressure calculation.

[0062] 4) Final form; Active earth pressure varies with time and exhibits randomness; the earth pressure model is ultimately expressed as: ; in: Initial active earth pressure; : Annual growth coefficient of earth pressure; Earth pressure random disturbance term.

[0063] 2. Groundwater pressure model; In pile-anchor support systems, groundwater pressure is often one of the main controlling factors leading to instability and sudden accidents. The goal of this local groundwater pressure model is to construct a groundwater level evolution model that simultaneously reflects the influence of trends, randomness, and extreme events, and to transform it into an equivalent water pressure acting on the pile-anchor support system. The groundwater level is equivalent to the resultant force of water pressure acting on the support structure per unit width, and its calculation expression is as follows: ; ; in: : The density of water; If the height from the bottom of the pile-anchor support system to the groundwater surface is ≤0, then water pressure is not calculated. Initial groundwater level, representing the multi-year average groundwater level; : Seasonal changes in groundwater level; Random related items for groundwater level; Sudden increases in water level caused by extreme environmental events.

[0064] 1) Seasonal changes in groundwater level ; The simulation shows annual cyclical water level changes, with water levels rising during the rainy season and falling during the dry season.

[0065]

[0066] A: Seasonal water level fluctuations.

[0067] 2) Random related items of groundwater level ;

[0068]

[0069] Time correlation coefficient; Intensity of interannual random disturbances.

[0070] 3) Sudden increases in water level caused by extreme environmental events ; Using Poisson distribution Describe the frequency of extreme events. The average rate at which events occur, when At that time, it is determined that an extreme event has occurred.

[0071] In the event of an extreme event, the water level increase... Follows an exponential distribution: , It represents the mean of the exponential distribution, i.e., the average level of water level increments.

[0072] S6. Using the pile resistance model, anchor resistance model, earth pressure model, and groundwater pressure model constructed in the preceding steps, the static limit state function is transformed into a time-varying limit state function;

[0073]

[0074] S7. Set the pile resistance parameters, anchor resistance parameters, earth pressure parameters, and groundwater parameters, output the time-varying limit state function substituted into step S6, and output the failure probability variation diagram of the pile-anchor support system. S8. Based on the failure probability change graph described in step S7, calculate the instantaneous failure probability and cumulative failure probability, and analyze the reliability and failure risk of the pile-anchor support system.

[0075] Specifically: Based on classic engineering conditions, parameters are set and organized, with detailed explanations of the physical meaning and reasons for their values. During programming, values ​​can be assigned to relevant parameters according to the initial parameter table. The initial parameter table is shown in Table 1.

[0076] Table 1

[0077] Using MATLAB software, according to Figure 2 The flowchart steps are used to write code and analyze the changes in the failure probability of the pile-anchor support system over 50 years.

[0078] After running the code, a graph showing the change in failure probability of the pile-anchor support system can be obtained, such as... Figure 3 As shown, analysis of the change graph leads to the following conclusions: 1. The probability of instantaneous failure increases monotonically with time; The continuous degradation of the resistance of piles and anchors, and the accumulation of soil pressure and groundwater loads year by year, make the possibility of failure of the pile-anchor support system in any given year increasingly greater.

[0079] 2. The cumulative failure probability exhibits a typical S-shaped growth pattern; Growth was slow in the early stages, rose rapidly in the middle stages, and then approached 1 in the later stages.

[0080] 3. High reliability in the early service phase (0-10 years); The probability of instantaneous failure is low, and the pile-anchor support system has a sufficient safety margin, resulting in a low risk of failure. It is recommended to conduct a routine visual inspection annually, primarily checking for pile cracks, pile top displacement, and anchor head corrosion.

[0081] 4. The medium term (10-30 years) is a period of rapid accumulation of failure risks; The combined effects of structural degradation and random fluctuations in groundwater levels lead to a rapid increase in the cumulative failure probability, making this a critical period for the pile-anchor support system. It is recommended to conduct at least two specialized structural inspections annually, perform random pull-out tests on the anchors, and inspect and maintain the drainage and dewatering systems.

[0082] 5. The system's reliability becomes significantly insufficient in the later stages (30 years and beyond); The probability of instantaneous failure is high, and the cumulative failure probability is close to 1, indicating that failure is almost inevitable under long-term service conditions. It is recommended to establish a real-time monitoring system, assess the economic and safety feasibility of continued service, and implement overall renovation or demolition and reconstruction as appropriate.

[0083] Example This is the first landmark innovation base project of China Power Construction Corporation in Daxing District, covering an area of ​​82,500 square meters. The project utilizes a perimeter-lined pile-anchor support system with a design life of 50 years. Due to its proximity to major transportation arteries such as the South Fifth Ring Road and the Beijing-Kaifeng Expressway, the surrounding environment is sensitive. Failure of the pile-anchor support system could trigger a chain reaction of disasters, including foundation pit collapse, road subsidence, and building cracking, impacting not only the project's construction progress but also threatening the subsequent operational safety of the park. Therefore, a failure probability simulation analysis of the pile-anchor support system within its design life is necessary. This analysis can guide the identification of risk-sensitive parameters during the design and construction phases, provide a basis for maintenance and testing plans during the operation and maintenance phase, and improve the safety of the pile-anchor support system throughout its entire life cycle.

[0085] Follow these steps for detailed instructions: 1. The support structure was designed using the Lizheng deep foundation pit support structure design software; the most unfavorable interface and the most unfavorable working condition of the project were selected, such as... Figure 4 As shown, input the pile anchor design, soil type, excavation depth, and initial groundwater level. The software automatically calculates the initial active earth pressure based on this information. Initial hydrostatic pressure, initial resistance of a single anchor bolt Initial ultimate resistance of piles Internal force envelope diagrams, etc., were used to create the engineering parameter table for the Daxing project, as shown in Table 2.

[0086] Table 2

[0087] 2. A MATLAB program based on the method of this invention was used. The parameters were modified according to the engineering parameter table of the Daxing project. After running the code, a graph showing the change in the failure probability of the support structure of the Daxing project was obtained, as shown below. Figure 5 As shown.

[0088] Finally, it should be noted that the above content is only used to illustrate the technical solution of the present invention, and is not intended to limit the scope of protection of the present invention. Simple modifications or equivalent substitutions made by those skilled in the art to the technical solution of the present invention do not depart from the essence and scope of the technical solution of the present invention.

Claims

1. A time-varying failure probability analysis method for a pile-anchor support system, characterized in that, Includes the following steps: S1. Perform stress analysis on the pile-anchor support system to determine the initial active earth pressure and initial hydrostatic pressure of the pile-anchor support system; S2. An equivalent stress analysis is performed on the pile-anchor support system, and a static limit state function is constructed based on the resistance system and the action effect system. S3. Construct a pile resistance model by combining the initial pile resistance, attenuation coefficient, and random disturbance term of pile resistance; S4. Combining the initial resistance of a single anchor bolt, the number of anchor bolts, the anchor bolt resistance degradation model, and the anchor bolt resistance random disturbance term, construct the anchor bolt resistance model; S5. Combine the initial active earth pressure, time growth term, and random disturbance term of the pile-anchor support system to construct an earth pressure model; and construct a groundwater pressure model by equating the groundwater level to the resultant force of water pressure acting on the pile-anchor support system per unit width. S6. Using the pile resistance model, anchor resistance model, earth pressure model, and groundwater pressure model constructed in the preceding steps, the static limit state function is transformed into a time-varying limit state function; S7. Set the pile resistance parameters, anchor resistance parameters, earth pressure parameters, and groundwater parameters, output the time-varying limit state function substituted into step S6, and output the failure probability variation diagram of the pile-anchor support system. S8. Based on the failure probability change graph described in step S7, calculate the instantaneous failure probability and cumulative failure probability, and analyze the reliability and failure risk of the pile-anchor support system.

2. The time-varying failure probability analysis method for a pile-anchor support system according to claim 1, characterized in that, Step S2, construct the static limit state function, specifically: S2. An equivalent stress analysis is performed on the pile-anchor support system, and a static limit state function is constructed based on the resistance system and the action effect system; specifically: S21. The structural failure caused by insufficient overall bearing capacity of the combined pile and anchor system is selected as the failure mode; S22. In this failure mode, perform equivalent stress analysis to summarize the stress of the pile-anchor system into a resistance system and an action effect system; S23. The difference between the total resistance of the resistance system and the total effect of the action system is the static limit state function.

3. The time-varying failure probability analysis method for a pile-anchor support system according to claim 2, characterized in that, The total resistance of the resistance system is: ; The total load on the system is: ; The static limit state function is then defined as: ； in: The total load borne by the pile-anchor support system in year t; The total resistance of the pile-anchor support system in year t; The resistance provided by the piles in year t; The resistance provided by the anchor bolt in year t; The force exerted by the soil on the pile-anchor support system in year t; The force exerted by groundwater on the pile-anchor support system in year t.

4. The time-varying failure probability analysis method for a pile-anchor support system according to claim 3, characterized in that, Step S3, construct the pile resistance model, specifically: The bearing capacity of piles under a certain failure mode is equivalent to a scalar resistance value. , representing the maximum equivalent resistance capacity that the piles can provide in year t; By employing an exponential function, introducing a decay coefficient, and a random disturbance term for the pile resistance, the maximum equivalent resistance capacity is solved, characterized as follows: : ； Initial ultimate resistance of piles; : Annual attenuation coefficient of pile resistance; : Random disturbance term of pile resistance, used to characterize the uncertainty of material properties and construction quality.

5. The time-varying failure probability analysis method for a pile-anchor support system according to claim 4, characterized in that, Step S4, construct the anchor bolt resistance model, specifically: Based on the equivalent resistance model of multiple anchor bolts, the stabilizing effect provided by multiple anchor bolts at a certain moment is equivalent to the resistance provided by the anchor bolts in year t. This value represents the total equivalent resistance that the anchor system can provide in year t; The initial total resistance of the anchor system is calculated by multiplying the initial resistance of a single anchor bolt by the number of bolts. The total equivalent resistance is characterized by the equivalent initial total resistance, the exponential function, the attenuation coefficient, and the random disturbance term of the anchor bolt resistance; the expression for the total equivalent resistance is as follows: ； in: Number of anchor bolts; Initial resistance of a single anchor bolt; : Annual attenuation coefficient of anchor bolt resistance; : Random disturbance term of anchor bolt resistance.

6. The time-varying failure probability analysis method for a pile-anchor support system according to claim 5, characterized in that, In step S5, an earth pressure model is constructed by combining the initial active earth pressure, time growth term, and random disturbance term of the pile-anchor support system; the earth pressure model is characterized by the expression for the force exerted by the soil on the pile-anchor support system in year t. ； in: Initial active earth pressure; : Annual growth coefficient of earth pressure; Earth pressure random disturbance term.

7. The time-varying failure probability analysis method for a pile-anchor support system according to claim 6, characterized in that, In step S5, the groundwater level is equivalent to the resultant force of water pressure acting on the pile-anchor support system per unit width, and a groundwater pressure model is constructed. The groundwater pressure model is characterized by the expression for the force exerted by groundwater on the pile-anchor support system in year t: ； ； : The density of water; If the height from the bottom of the pile-anchor support system to the groundwater surface is ≤0, then water pressure is not calculated. : Average groundwater level over many years; : Seasonal changes in groundwater level; Random related items for groundwater level; Sudden increases in water level caused by extreme environmental events.

8. The time-varying failure probability analysis method for a pile-anchor support system according to claim 7, characterized in that, Seasonal changes in groundwater level This is used to simulate annual periodic water level changes, with water levels rising during the rainy season and falling during the dry season; the seasonal variation of groundwater levels is also included. The expression is as follows: ； Where A represents the seasonal water level amplitude.

9. The time-varying failure probability analysis method for a pile-anchor support system according to claim 7, characterized in that, Groundwater level random related items ,expression: ； ； Time correlation coefficient; Intensity of interannual random disturbances.

10. The time-varying failure probability analysis method for a pile-anchor support system according to claim 7, characterized in that, Water level surge caused by extreme environmental events ,expression: Using Poisson distribution Describe the frequency of extreme events. The number of extreme events; The average rate at which extreme events occur, when When an extreme event is determined to have occurred; In the event of an extreme event, the water level increase Follows an exponential distribution: ； It represents the mean of an exponential distribution, i.e., the average level of water level increments.

11. The time-varying failure probability analysis method for a pile-anchor support system according to claim 1, characterized in that, Step S6. Perform equivalent processing on the static limit state function to transform it into a time-varying limit state function; specifically: ； 。

Images