CN111553107B - Random earthquake response analysis and safety evaluation method for pile foundation of liquefiable field - Google Patents
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Abstract
The invention discloses a method for random earthquake response analysis and safety evaluation of a liquefiable site pile foundation, which comprises the following steps: computing a representative set of time course samples that generate a random seismic acceleration processAccording to the standard reaction spectrumFor representative time course sample setsCorrecting; establishing a liquefiable site-pile foundation integral finite element model; and (5) inputting the representative earthquake motion acceleration time course sample into a finite element model to complete analysis and evaluation of pile foundations and field soil in random earthquake motion. According to the invention, a certain amount of acceleration time courses of random earthquake vibration are selected, a liquefiable site-pile foundation integral finite element model is input, the liquefiable site-pile foundation earthquake reaction analysis is completed, probability safety evaluation is made, and a basis is provided for pile foundation based on the behavior earthquake-proof design.
Description
Technical Field
The invention relates to the technical field of earthquake motion analysis and evaluation, in particular to a method for random earthquake response analysis and safety evaluation of a liquefiable site pile foundation.
Background
The earthquake causes the liquefaction of the field soil, and the earthquake damage forms such as uneven settlement, lateral deformation, sliding and the like are generated, which are the main reasons for the earthquake damage of the pile foundation. In 1964, a large number of pile foundations produced excessive displacement at the boundary between the liquefaction zone and the non-liquefaction zone, and the pile foundations produced serious damage in the region; in 1976, the large earthquake of Tangshan, the place of a factory building of the ocean petroleum institute of Tianjin Xingang, the liquefied lateral expansion, the excessive lateral displacement of a pile foundation bearing platform and a large number of cracks of the excavated foundation pile occur; in 1995, the earthquake of the Japanese Massa Medicata Fermentata was caused by the liquefaction of the foundation, which resulted in excessive lateral displacement of the foundation of the large bridge pile in the western harbor. The analysis of the interaction of pile soil power in the liquefaction field has important significance for the earthquake-resistant research of engineering structures and is focused by students at home and abroad. Wilson, tang Liang and Ling Xianchang respectively perform a centrifuge vibration table and a vibration table test to study the dynamic interaction and seismic response characteristics of pile foundations of the liquefaction site. Xu Chengshun, du Xiuli, et al, have studied pile-soil-structure dynamic interactions under horizontal seismic excitation in liquefiable-nonliquefiable sites using a large shaker deck series of experiments. And carrying out numerical simulation analysis on the pile soil centrifuge vibration table model test by using a dynamic nonlinear p-y model through Ross W.Boulonger Varun. Wang Rui, zhang Jianmin, zhao Cheng, sulfur rain and the like perform numerical simulation on the pile foundation of the liquefaction site by adopting a three-dimensional nonlinear finite element method, and analyze the dynamic response of the surrounding soil and the pile foundation. Wang Xiaowei a OpenSees program is adopted to establish a two-dimensional integral finite element model of the pile-soil-pier, and control parameters affecting the seismic response of the bridge structure of the liquefaction site are analyzed. The method belongs to a deterministic analysis method, and uses deterministic seismic acceleration records as input to perform site-pile foundation seismic reaction power time course analysis.
The generation of the earthquake motion has the characteristics of randomness and uncertainty and can be regarded as a primary sample function implementation of a random process; under the random earthquake motion excitation effect, the earthquake response of the field-pile foundation has randomness, so that the earthquake motion is described by adopting a random process theory, and the earthquake response of the field-pile foundation is more reasonable by adopting the random vibration theory. Wang Zhihua and the like, a non-stationary random earthquake motion model and a virtual excitation method are applied, and the dynamic response of the bridge pier, the pile foundation and the soil is analyzed. Zhou Aigong and the like perform random seismic response analysis and parameter sensitivity analysis of pile-soil systems based on a virtual excitation method and an equivalent linearization method. The liquefiable field soil has strong nonlinearity in earthquake reaction, and the virtual excitation method is suitable for random vibration analysis of a linear system; meanwhile, the equivalent linearization method adopts unchanged shear modulus and damping ratio in the whole earthquake motion duration period, can not reflect the actual change of the rigidity of the soil body, and the random earthquake response analysis method based on the equivalent linearization method and the virtual excitation method is not suitable for the random earthquake response analysis of the single pile foundation of the liquefaction field. In recent years, probability density evolution theory proposed by the university of homotaxis Li Jie and Chen Jianbing professor team has been successfully applied to nonlinear stochastic power analysis of various complex structures and geotechnical engineering, so that it is necessary to perform stochastic seismic response analysis on liquefaction site-pile foundation by adopting a model reflecting nonlinear deformation characteristics of soil liquefaction and probability density evolution theory, and perform probabilistic evaluation.
Disclosure of Invention
The invention aims to solve the technical problem of providing a method for random earthquake response analysis and safety evaluation of a liquefiable site pile foundation, which can be used for more accurately analyzing the liquefiable site and evaluating probability safety.
In order to solve the technical problems, the invention provides a method for random earthquake response analysis and safety evaluation of a liquefiable site pile foundation, which comprises the following steps:
(1) Computing a representative set of time course samples that generate a random seismic acceleration process
(2) Determining a representative set of time course samplesAverage reaction spectrum/>And standard reaction spectrumIf the errors meet the regulations, outputting a representative earthquake motion acceleration time course sample set, and if the errors do not meet the regulations, entering the step (3);
(3) Correcting the evolution power spectrum density, and repeating the steps (1) - (2);
(4) Establishing a liquefiable field-pile foundation integral finite element model based on OpenSees platforms according to centrifuge test data;
(5) And (3) inputting the representative earthquake motion acceleration time course sample output in the step (2) into the finite element model in the step (4), and completing the analysis and evaluation of the soil and pile foundation in random earthquake motion.
Further, the representative set of time course samples in step (1)Based on Priesley non-stationary random process evolution spectrum representation theory.
Further, a representative time course of the seismic acceleration process in step (1)Calculated from equation 1:
Where ω n =nΔω.
Further, { X n,Yn } (n=1, 2, … N) is based on a random variable functionGenerating a mapped orthonormal random variable, wherein the random variable Θ obeys a uniform distribution among [ -pi, pi ]/>Is arbitrarily constant.
Further, the modification of the evolving power spectral density in step (3) is achieved by equation 2:
where ω c is the cut-off frequency.
Further, there are at least 100 representative seismic samples output in step (2).
Further, in the step (5), inversion is performed on the output representative earthquake motion acceleration time course sample to obtain bedrock acceleration records.
Further, probability information of the single pile in random vibration reaction is analyzed.
Further, the distribution information of the soil in the field in the random earthquake motion reaction is analyzed.
Further, probability information of the field soil in random earthquake motion reaction is analyzed.
Compared with the prior art, the method for random earthquake reaction analysis and safety evaluation of the liquefiable field pile foundation has the advantages that a certain amount of acceleration time courses of random earthquake vibration are selected, a liquefiable field-pile foundation integral finite element model is input, random earthquake reaction analysis of the liquefiable field-pile foundation is completed, probability safety evaluation is carried out, and basis is provided for the design of pile foundation based on performance earthquake resistance.
Drawings
FIG. 1 is a flow chart of the present invention;
FIGS. 2a, 2b, 2c, 2d, 2e, 2f are random seismic response probability information for a single pile foundation of the present invention;
FIGS. 3a, 3b are plot-of-land random seismic response distributions of the invention;
Fig. 4a, 4b, 4c, 4d, 4e, 4f are plot random seismic response probability information for the present invention.
Detailed Description
The present invention will be further described with reference to the accompanying drawings and specific examples, which are not intended to be limiting, so that those skilled in the art will better understand the invention and practice it.
Referring to fig. 1, a flow chart of the method for random earthquake response analysis and safety evaluation of liquefiable site pile foundation according to the invention comprises the following steps:
(1) Computing a representative set of time course samples that generate a random seismic acceleration process
(2) Determining a representative set of time course samplesAverage reaction spectrum/>And standard reaction spectrumIf the errors meet the regulations, outputting a representative earthquake motion acceleration time course sample set, and if the errors do not meet the regulations, entering the step (3);
(3) Correcting the evolution power spectrum density, and repeating the steps (1) - (2);
(4) Establishing a liquefiable field-pile foundation integral finite element model based on OpenSees platforms according to centrifuge test data;
(5) And (3) inputting the representative earthquake motion acceleration time course sample output in the step (2) into the finite element model in the step (4), and completing the analysis and evaluation of the soil and pile foundation in random earthquake motion.
The invention takes the liquefaction site single pile random vibration reaction as an example, and represents a time-course sample setBased on Priesley non-stationary random process evolution spectrum representation theory, the method can be specifically expressed as follows:
where ω n＝nΔω,Xn,Yn (n=1, 2, … N) is a standard orthogonal random variable, The power spectrum density is the evolution of the single side of the random vibration acceleration process. /(I)The formula is:
It follows that a (t, ω) is the time-frequency modulation function and G (ω) is the single-sided power spectral density of the steady-ground-shock acceleration process. G (ω) is represented by the formula
The result shows that S 0 is a spectrum intensity factor, omega g、ωf is the excellent circle frequency of the field soil and the bedrock respectively, and zeta g、ζf is the damping ratio of the field soil and the bedrock respectively.
From a representative set of time course samplesCan calculate the average reaction spectrum/>The building earthquake-resistant design Specification specifies a canonical response spectrum/>Average reaction Spectrum/>And canonical response spectrumFitting errors exist between the two reaction spectra, and in order to meet the requirements on target reaction spectra in building anti-seismic design specifications, average reaction spectra/>The correction is performed, and the average reaction spectrum is calculated from a representative set of time-course samples, which is derived from the evolving power spectral density, so that the evolving power spectral density needs to be corrected. For specific correction formulas, refer to formula 2:
where ω c is the cut-off frequency.
Further, generating standard orthogonal random variables to satisfy the generation of random seismic acceleration time course, the invention is based on random variable functionGenerating random function variablesRandom function variable/>Mapping to a standard orthogonal random variable { X n,Yn } (n=1, 2, … N), where the random variable Θ obeys a uniform distribution between [ -pi, pi ]/>Is arbitrarily constant. The invention adopts a spectrum representation-random function method of a non-stationary process to generate a non-stationary random earthquake acceleration time course record, and then the record is corrected to be in accordance with a target reaction spectrum of building earthquake-proof design rule, thereby obtaining a representative random earthquake acceleration time course set/>Can be used as the time course record of the earth acceleration. Because the representative time-course sample set is generated by random variables, there can be countless records, but the calculated amount is too large when the analysis and evaluation are carried out, and at least 100 representative time-course records are randomly output, and in particular, 144 time-course records are selected in the invention for facilitating the calculation and simultaneously ensuring the specific randomness characteristic.
The finite element model in the prior art is generally a deterministic seismic vibration numerical simulation model, in this embodiment, a single pile random seismic vibration reaction of a liquefiable field is simulated, and a liquefiable field-pile foundation integral finite element model is established based on a OpenSees platform according to centrifuge test data. Specifically, a Pressure Depend Multi Yield 02 model in OpenSees material warehouse is adopted, an elastic beam unit is used for simulating pile foundations, a quad Up unit is used for simulating sand, equal-altitude nodes on the left side and the right side are restrained by adopting an Equal DOF command, acceleration boundaries are adopted at the bottom, a zero-length unit is adopted for respectively connecting piles and soil nodes, pyliq and Tzliq1 materials are endowed to the zero-length unit, and dynamic interaction between pile and soil is simulated. The finite element model is determined by comparing the numerical simulation with pile body bending moment, pore water pressure and soil layer acceleration time course change in centrifuge test data.
And inputting the 144 obtained time course records into the liquefiable site-pile foundation integral finite element model, analyzing and evaluating different information, and ensuring the simulation precision of random vibration, thereby ensuring the accuracy and reliability of analysis and evaluation and providing basis for the design of pile foundation based on the behavior earthquake resistance.
The invention takes 8-degree earthquake fortification intensity, class II sites, the design basic acceleration is 0.2g, the maximum value alpha max of the horizontal earthquake motion influence coefficient is 0.45, the time step delta t of the representative earthquake motion acceleration time course is 0.01s, the truncated term number N is 1600, the frequency interval delta omega is 0.15rad/s, and the site soil characteristic period Tg＝0.4s,ωg＝15.71s-1,ζg＝0.72,ωf＝0.1ωg,ζf＝ζg as an example for analysis and evaluation.
Because the representative time course sample set obtained in the embodiment is the acceleration record at the earth surface, and the seismic response of the single pile top and the bottom bedrock is reflected respectively, the output representative seismic acceleration time course sample is inverted based on the accurate dynamic stiffness matrix of the layered field soil layer and the bedrock half space in the embodiment, so that the bedrock acceleration record is obtained.
And analyzing probability information of the single pile in random vibration reaction. Specifically, a reaction spectrum amplification factor α=s Pile top /S Bedrock is defined, where S Pile top 、S Bedrock is the acceleration reaction spectrum values at the pile top and bedrock when the damping ratio is 0.05, and the probability density of the reaction spectrum amplification factor α is calculated. The probability density of the reaction spectrum amplification coefficient alpha, the representative acceleration time course sample and the bedrock acceleration record in the embodiment are brought into the finite element model, and a reaction spectrum amplification coefficient alpha probability density evolution curved surface (refer to fig. 2 (a)), a probability density contour line (refer to fig. 2 (b)), a pile body maximum bending moment envelope graph (refer to fig. 2 (c)), a pile body maximum horizontal displacement envelope graph (refer to fig. 2 (d)), a pile top horizontal displacement equivalent extremum event probability density function (refer to fig. 2 (e)), and a pile top horizontal displacement equivalent extremum event probability distribution (refer to fig. 2 (f)) at the period of 0.5s-1.5 can be obtained, wherein the equivalent extremum event distribution function (CDF) in fig. 2 (f) is the power reliability. From the above chart, it can be seen that: the probability density function of the pile top reaction spectrum amplification factor is an irregular curve, the maximum bending moment of the pile body in the embodiment appears in the loose sand layer by 2.6m, the maximum horizontal position of the pile body moves out of the existing pile top position, and when the horizontal displacement of the pile top reaches 10.6cm, the dynamic reliability is 95%.
And analyzing the distribution information of the field soil in the random vibration reaction. Specifically, the representative acceleration time-course sample in this embodiment is brought into the finite element model of the present invention, and the shear stress-shear strain and the ultra-static pore pressure ratio of the field soil in this embodiment are analyzed to obtain a hysteresis curve of the shear stress-shear strain of the field soil (see fig. 3 (a)), and the ultra-static pore pressure ratio distribution (see fig. 3 (b)). From the above chart, it can be seen that: the earthquake reaction of the liquefiable field shows strong nonlinear characteristics, the pore water pressure rises, the soil body effective stress is reduced, and the sandy soil shearing rigidity is reduced; the shear stress-shear strain hysteresis curve of the loose sand layer is plump, the ultra-static hole pressure ratio reaches more than 0.8, which indicates that part of the loose sand layer enters a liquefied state, the upper part of the pile body loses the lateral resistance of the surrounding soil of the pile body, and the bending moment of the pile body and the deformation of the pile body are increased; the shear stress-shear strain hysteresis curve of the dense sand layer is in a shuttle shape, and the ultra-static pore pressure ratio is below 0.4, which indicates that the dense sand layer does not enter a liquefaction state yet.
And analyzing probability information of the field soil in random vibration reaction. Specifically, the representative acceleration time course sample in this embodiment is brought into the finite element model of the present invention, and the surface subsidence probability density, the surface level maximum lateral shift, the surface subsidence probability density, and the cumulative probability in this embodiment are analyzed to obtain a surface subsidence probability density function surface (refer to fig. 4 (a)), a surface subsidence probability density contour line (refer to fig. 4 (b)), a surface horizontal displacement equivalent extremum event probability density (refer to fig. 4 (c)), a surface horizontal displacement equivalent extremum event probability distribution (refer to fig. 4 (d)), a surface subsidence equivalent extremum event probability density (refer to fig. 4 (e)), and a surface subsidence equivalent extremum event probability distribution (refer to fig. 4 (f)). From the above chart, it can be seen that: the earth surface subsidence probability density evolution function evolves with time, has different forms at different moments, has the characteristics of multimodal mountains, and mainly distributes earth surface horizontal lateral movement between [1,4] cm in the embodiment, and the limit value of the earth surface horizontal lateral movement with the power reliability reaching 95% is 3.3cm; the surface subsidence is mainly distributed between [1,1.5] cm, and the surface subsidence limit value with the power reliability reaching 95% is 1.5cm.
According to the invention, a certain amount of acceleration time courses of random earthquake vibration are selected, a liquefiable site-pile foundation integral finite element model is input, a liquefiable site-pile foundation random earthquake reaction analysis flow is completed, pile foundation and site soil earthquake reaction probability information is obtained, a probability safety evaluation method is established, probability safety evaluation is made, and a basis is provided for the pile foundation based on the performance earthquake-proof design.
The above-described embodiments are merely preferred embodiments for fully explaining the present invention, and the scope of the present invention is not limited thereto. Equivalent substitutions and modifications will occur to those skilled in the art based on the present invention, and are intended to be within the scope of the present invention. The protection scope of the invention is subject to the claims.
Claims (5)
1. A random earthquake response analysis method for a liquefiable site pile foundation is characterized by comprising the following steps:
(1) Computing a representative set of time course samples that generate a random seismic acceleration process The representative time course sample set is an acceleration record at the earth surface;
(2) Determining a representative set of time course samples Average reaction spectrum/>And standard reaction spectrumIf the errors meet the regulations, outputting a representative earthquake motion acceleration time course sample set, and if the errors do not meet the regulations, entering the step (3);
(3) Correcting the evolution power spectrum density, and repeating the steps (1) - (2);
(4) Establishing a liquefiable field-pile foundation integral finite element model based on OpenSees platforms according to centrifuge test data;
(5) Inputting the representative earthquake motion acceleration time course sample output in the step (2) into the finite element model in the step (4), and completing the analysis and evaluation of the soil and pile foundation in random earthquake motion, wherein the method comprises the following steps: analyzing the distribution information of the field soil in random earthquake motion reaction; analyzing probability information of the field soil in random earthquake motion reaction; defining a reaction spectrum amplification coefficient alpha=S Pile top /S Bedrock , wherein S Pile top 、S Bedrock is the acceleration reaction spectrum value at the pile top and the bedrock when the damping ratio is 0.05, calculating the probability density of the reaction spectrum amplification coefficient alpha, inverting the output representative earthquake motion acceleration time course sample based on the accurate dynamic stiffness matrix of the layered field soil layer and the bedrock half space to obtain bedrock acceleration records, and analyzing the probability information of a single pile in random earthquake motion reaction according to the probability density of the reaction spectrum amplification coefficient alpha and the bedrock acceleration records to obtain the probability information of the single pile: the probability density function of pile-top reaction spectrum amplification factor is an irregular curve.
2. The method of random seismic response analysis of liquefiable field pile foundation of claim 1, wherein the representative set of time course samples of step (1)Based on Priestley non-stationary stochastic process evolution spectrum representation theory, the following is obtained:
......1
wherein, For unilateral evolution of power spectral density,/>Δω is the frequency interval,/>WhereinIs a standard orthogonal random variable.
3. The method for random earthquake response analysis of liquefiable field pile foundation according to claim 1, wherein the method comprises the steps of,Wherein/>Is based on random variable function/>Wherein/>Generating a mapped orthonormal random variable, wherein the random variable/>At/>Obeying uniform distribution among/>Is arbitrarily constant.
4. The method of random seismic response analysis of liquefiable field pile foundation of claim 1, wherein the modification of the evolving power spectral density in step (3) is accomplished by equation 2:
......2
wherein, Is the cut-off frequency.
5. The method of random seismic response analysis of liquefiable field pile foundation of claim 1, wherein the representative seismic samples output in step (2) are 100.
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| CN112115539A (en) * | 2020-09-23 | 2020-12-22 | 同济大学 | Seismic dynamic reliability analysis method for slope supporting structure |
| CN113379105B (en) * | 2021-05-21 | 2022-05-31 | 浙江大学 | Site earthquake liquefaction disaster rapid evaluation method based on artificial intelligence |
| CN113987632B (en) * | 2021-10-19 | 2023-07-21 | 武汉大学 | Method for predicting field liquefaction transverse displacement |
| CN114139381B (en) * | 2021-12-01 | 2024-07-05 | 北京交通大学 | Pile foundation damage census and evaluation method considering pile soil parameter uncertainty |
| CN116306099B (en) * | 2023-02-06 | 2024-05-10 | 武汉大学 | Random field-based evaluation method for lateral movement of liquefiable site reinforced by gravel piles |
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