CN110750863B - Foundation pile wave impedance inversion analysis method based on cubic B spline interpolation function - Google Patents
Foundation pile wave impedance inversion analysis method based on cubic B spline interpolation function Download PDFInfo
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Abstract
The invention discloses a foundation pile wave impedance inversion analysis method based on a cubic B spline interpolation function, which comprises the following steps: obtaining a pile top particle vibration speed test curve; calculating equivalent knocking force pulse according to the test curve and pile top wave impedance; dispersing the foundation pile into a plurality of pile units; calculating a damping pot coefficient in a pile-soil interaction model of each pile unit pile side by using shear waves of each layer of soil around the pile; constructing two time domain analysis windows in a pile top particle vibration speed test curve, taking interface wave impedance in the windows as optimization parameters, and obtaining other pile unit wave impedance in the windows by using a cubic B spline interpolation function according to the optimization parameters; obtaining pile top particle vibration speed response calculation curves by pile unit wave impedance and equivalent knocking force pulse; and when the calculation curve and the test curve reach the optimal matching, obtaining the corresponding wave impedance change profile in the time domain analysis window. The invention provides an analysis method for quantitatively analyzing the degree and range of the impedance change of foundation piles.
Description
Technical Field
The invention relates to the field of foundation pile structural integrity testing. More particularly, the invention relates to a foundation pile wave impedance inversion analysis method based on a cubic B-spline interpolation function, which is suitable for foundation pile engineering of urban buildings, bridges, wharfs and the like.
Background
Foundation piles are often adopted for engineering foundations of urban buildings, bridges, wharfs and the like, wherein bored piles are common. Quality problems such as separation of aggregate from concrete, mud inclusion, necking, cracking, breaking and the like often occur during pore-forming and concrete pouring processes under the influence of complex geological conditions such as weak layers, water flowing layers, construction processes and the like in construction sites. The foundation pile belongs to a masking project, the foundation pile quality detection is very important for the safety of an upper building, and the foundation pile quality detection is currently carried out by a drilling coring method, a sound wave test method and a knocking-echo method.
The drilling coring is to core the pile, the quality of the foundation pile at the coring position is judged through core sample analysis, and a plurality of coring positions are needed to be needed for objectively damaging the position, so that the pile body such as honeycomb briquette is required to be grouted and reinforced, and the process is time-consuming and labor-consuming. The acoustic wave test can provide a CT image of the wave velocity change of foundation piles in the test areas, so that the quantitative description of the concrete quality in the test areas can be realized, but the method needs to embed a plurality of test pipes in advance, and meanwhile, a plurality of test data of different test points are needed to be obtained, so that the test workload is huge. The pile head is tapped, the excited stress wave propagates downwards along the pile body, when the pile body wave impedance changes relatively, the wave will reflect at the wave impedance change interface, the sensor is used to receive the reflected wave particle vibration response to obtain particle vibration speed response test time curve, and the position and property (the impedance is increased and decreased) of the defect are determined through the phase and amplitude analysis of the reflected wave particle vibration speed signal. However, this analysis is qualitative and has a large human impact because: (1) Stress wave attenuation can be caused by pile-soil interaction, under the condition of the same pile geometric dimension and pile circumference soil property, even if the section relative wave impedance change degree is the same, the depth is different, the reflected wave signal energy received by the pile top is different, the shallow part has stronger reflected energy relative to the deep part, and even multiple reflection can occur; (2) The reflected waveform and amplitude are not only related to the relative degree of the relative wave impedance change at the abnormal position of the pile body, but also related to the pile body wave impedance change form (gradual change or abrupt change), and the relative degree of the wave impedance change is difficult to determine by the reflected wave amplitude; (3) The pile body can generate multiple reflections at the first abnormal position, the reflected waves can be coherent or incoherent with the reflected waves at the second abnormal position, the coherent interaction leads to the enhancement of the reflected wave amplitude value at the second abnormal position, and the incoherent interaction leads to the weakening of the reflected wave amplitude value at the second abnormal position. These factors can cause that qualitative analysis based on reflected wave phase and reflected wave amplitude cannot make objective judgment on pile body structural integrity, and influence the safety assessment of the upper engineering, so quantitative analysis on pile body structural integrity is very important for foundation pile quality and safety assessment of the upper engineering.
However, the test signal is also affected by various interferences such as the amplitude frequency and phase frequency characteristics of the sensor, the reinforcement cage and the like, all of which affect the quality of the test signal, the signal contains some false and distorted components, and in addition, the wave equation discrete algorithm also introduces discrete errors. Under the influence of theoretical model errors, test errors and discrete errors, even if the matching degree of the test and calculation curves is high, the calculated value and the actual value of the wave impedance may be greatly different, and particularly in the case that curve change is insensitive to the wave impedance change, the result is even wrong.
Disclosure of Invention
The invention aims to solve the problems of the existing waveform fitting technology, and provides the inversion analysis method for the wave impedance of the foundation pile, which can quantitatively analyze the degree and the range of the wave impedance of the foundation pile, provide reasonable basis for foundation pile quality evaluation and ensure the safety of the upper engineering.
To achieve these objects and other advantages and in accordance with the purpose of the invention, there is provided a method of inversion analysis of a foundation pile wave impedance based on a cubic B-spline interpolation function, comprising the steps of:
s1, testing a foundation pile by adopting a knocking-echo method to obtain a pile top particle vibration speed response test curve;
s2, discretizing the foundation pile into N e Pile units with equal length and uniform section;
s3, constructing a first analysis window and a second analysis window in a region where pile body reflection signals appear in the pile top particle vibration velocity response time-course curve;
s4, equally dividing the pile units corresponding to the first analysis window into N according to the range of the pile units corresponding to the time range where the first analysis window is located and the number of the pile units s Taking N in the first analysis window from each pile unit section s The wave impedance of interfaces of +1 pile unit sections is used as a fitting analysis optimization parameter, and the fitting analysis optimization parameter is interpolated through a cubic B spline interpolation function to obtain the wave impedance of interfaces of other pile units in the first analysis window;
s5, performing the step in S4 on the pile units in the second analysis window to obtain the wave impedance of interfaces of other pile units in the second analysis window;
s6, calculating equivalent knocking force pulse according to the first bell-shaped pulse and pile top wave impedance in the pile top particle vibration speed response test curve;
s7, determining shear wave velocities of soil of each layer according to soil properties of soil layers around the piles, and calculating damping pot coefficients in a pile-soil interaction model of each pile unit pile side according to the shear wave velocities;
s8, based on a one-dimensional fluctuation theory, according to the calculated equivalent knocking force pulse, wave impedance of each pile unit interface in the first analysis window and the second analysis window and damping kettle coefficients in pile-soil interaction models of the pile side and the pile bottom of each pile unit, calculating the vibration speed of each pile unit interface by a fluctuation differential equation characteristic line solving method, and obtaining a pile top particle vibration speed response calculation curve.
Preferably, in the method for inverting and analyzing the impedance of the foundation pile based on the cubic B-spline interpolation function, in the step S2, the number N of pile units e The calculation method of (2) is as follows:
s21, obtaining the time difference T between the occurrence of the peak value of the knocking pulse signal and the occurrence of the peak value of the reflected wave signal at the bottom of the pile from the pile top particle vibration speed response test curve, and calculating the average wave speed of the wave in the pile according to the pile length and the time difference
Wherein L is pile length;
s22, calculating the sampling point number N from the starting point of the knocking pulse signal to the starting point of the pile bottom reflected wave signal according to the pile top particle vibration speed response sampling period deltat:
N＝T/Δt
s23, presetting the number of pile units to be N 0 From N 0 Calculating the preset length delta L of the pile unit 0 ：
ΔL 0 ＝L/N 0
S24, calculating the propagation time delta tau of the reflected wave back and forth in the pile unit:
s25, calculating sampling points M corresponding to the back-and-forth propagation time of the reflected wave in the unit:
M＝int(Δτ/Δt)+1
wherein the symbol int () in the formula represents rounding the calculation value in brackets;
s26, calculating the time delta tau required for the wave to make a round trip in the pile unit again by using the sampling point number M 1 ；
Δτ 1 ＝MΔt
S27, by Deltaτ 1 Recalculating pile unit length DeltaL by average wave velocity 1 ：
S28, calculating the number N of the actual pile units e ：
N e ＝int(L/ΔL 1 )+1。
Preferably, in the method for performing inversion analysis on the impedance of the foundation pile based on the cubic B-spline interpolation function, in the step S4, pile units in the first analysis window are equally divided into N s The method of individual pile unit sections is as follows:
s41, calculating the number N of pile units in the first analysis window 1 ：
Wherein N is 1,0 And N 1,1 Respectively starting pile units and ending pile units corresponding to the pile top particle vibration speed response test curves of the first analysis window; t is t 1,0 And t 1,1 Respectively starting time and ending time corresponding to the pile top particle vibration speed response test curve of the first analysis window;
due to N 1 ＝N 1,1 -N 1,0 Therefore:
s42, will be spentThe pile units in the first analysis window are equally divided into N s Pile unit sections, each section comprising a number delta N of pile units within the pile unit section s,1 The calculation method of (2) is as follows:
s43, recalculating a termination pile unit N in the first analysis window 1,1 ；
N 1,1 ＝N 1,0 +ΔN s,1 ×N s 。
Preferably, in the method for performing inversion analysis on the impedance of the foundation pile based on the cubic B-spline interpolation function, in the step S4, interpolation processing is performed on the fitting analysis optimization parameter by using the cubic B-spline interpolation function, and the method comprises the following steps:
a. interface position with first window wave impedance as optimization parameter
j＝1,…,N t And wave impedance
The control point positions and the wave impedances are calculated respectively as follows:
wherein N is t ＝N s +1，N t ×N t Order matrix
b. performing cubic B-spline interpolation on each pile unit section, wherein the expression of the cubic B-spline interpolation function is as follows:
wherein the interpolation function in the equation
In the above, xi is E [0,1 ]]；p i Representing the control point parameter of the ith section S i (ζ) represents a spline function after interpolation of the i-th segment control point parameter, and p is taken for the initial segment i=1 in the cubic B-spline interpolation 0 ＝p 1 For termination segment i=n s Taking out
Dividing a variable xi change interval into M equal parts, wherein the interval delta xi=1/M;
c. taking xi m =Δζ×m, m=0, 1, …, M, p i Respectively using
Instead, interpolation point locations and wave impedances can be obtained, specifically:
for the initial segment (i=1), the mth interpolation point positions and wave impedances are respectively
For the termination segment (i=n s ) The m-th interpolation point positions and the wave impedances are respectively
For the middle ith section, i is more than 1 and less than N s The m-th interpolation point positions and the wave impedances are respectively
d. Judging the position of the subsection where the kth interface is positioned and the adjacent interpolation point:
symbol i represents the segment number of the kth interface, n and n+1 represent the numbers of two adjacent interpolation points of the kth interface respectively;
calculating the kth interface wave impedance from Duan Naxiang adjacent interpolation point wave impedance:
preferably, in the method for inversion analysis of the impedance of the foundation pile based on the cubic B-spline interpolation function, the method for calculating the equivalent striking force pulse from the first bell pulse of the pile top particle vibration velocity test curve in S6 is as follows:
wherein T is d The duration of the rising period of the bell-shaped pulse, namely the time interval from the starting point to the peak point of the bell-shaped pulse; v (V) m (t) is the pile top particle vibration speed at the moment t; z is Z top ＝(ρcA) top And expressing pile top wave impedance, wherein ρ, c and A are pile top concrete density, wave speed and sectional area respectively.
Preferably, in the method for inversion analysis of foundation pile wave impedance based on cubic B-spline interpolation function, the step S7 of determining shear wave velocity of each layer of soil according to soil property of soil around the pile, and calculating a damping pot coefficient in a pile-soil interaction model of each pile unit pile side comprises the following steps:
s71, according to the soil property of the soil layer around the pile, according to a shear wave speed value range in the soil property suggested in the aseismic design specification of the railway engineering of GB50111-2006, taking the middle value of the shear wave speed value range as the shear wave speed of the soil layer, and calculating the damping kettle coefficient of the ith pile unit section of the soil layer according to the following formula:
J s,i ＝l i ρ s,i c s,i
wherein l i The circumference of the section of the ith pile unit of the foundation pile is the circumference; ρ s,i C s,i Respectively representing the density and shear wave velocity of the soil layer where the section is positioned;
s72, pile bottom damping pot coefficient J t The calculation method of (1) is as follows:
J t ＝β t Z t
wherein Z is t For wave impedance of pile bottom section, Z t ＝(ρcA) t ；β t And the coefficient is determined by matching the pile bottom reflected wave response test curve with the calculation curve.
Preferably, the method for inverting and analyzing the impedance of the foundation pile based on the cubic B-spline interpolation function further comprises the following steps:
and S9, optimizing and analyzing the wave impedance of each pile unit interface in the first analysis window and the second analysis window, and obtaining a wave impedance profile according to optimized data.
Preferably, in the method for performing inversion analysis on the wave impedance of the foundation pile based on the cubic B-spline interpolation function, in S9, performing an optimization analysis on the wave impedance of each pile unit interface in the first analysis window and the second analysis window includes the following steps:
s91, based on a one-dimensional fluctuation theory, obtaining a pile top particle vibration velocity response calculation curve by utilizing an equivalent knocking force pulse, pile soil interaction damping kettle coefficients and pile body wave impedance by utilizing a differential equation characteristic line solving method, and establishing an objective function taking analysis window wave impedance as an optimization parameter by using the particle vibration velocity test curve and calculation curve difference:
wherein: v m,i ,v c,i Respectively measuring a particle vibration speed test value and a calculated value corresponding to reflection at the ith section of the pile unit; n (N) 2,0 And N 2,1 Respectively starting pile units and ending pile units corresponding to the pile top particle vibration speed response test curves of the second analysis window;
s92, interface wave impedance
Performing analysis optimization, wherein the delta difference value of the objective function delta of the current step and the later step is smaller than the set error delta ε ＝10 -4 And (5) terminating the calculation to obtain the pile body wave impedance profile.
The invention avoids the defects of the traditional waveform fitting analysis method, builds two analysis windows in the time region where the abnormal reflected wave of the pile body appears in the test signal, selects some interface wave impedance as fitting analysis optimization parameters according to equal unit intervals in the windows, calculates other interface wave impedance in the window region by the interface wave impedance values of the cubic B-spline, thus avoiding the influence of theoretical model errors, test errors and discrete errors on fitting analysis, improving the sensitivity of calculation curves to the change of the optimization parameters in the curve fitting process, improving the analysis precision, and deducing the quantitative analysis of the foundation pile wave impedance to be applied in foundation pile engineering.
Additional advantages, objects, and features of the invention will be set forth in part in the description which follows and in part will become apparent to those having ordinary skill in the art upon examination of the following or may be learned from practice of the invention.
Drawings
FIG. 1 is a plot of pile top particle vibration velocity response test time course according to the present invention;
FIG. 2 is a schematic illustration of pile unit segments of a first analysis window and a second analysis window according to the present invention;
FIG. 3 is a schematic structural view of a pile-soil interaction model according to the present invention;
FIG. 4 is a graph showing the velocity response of vibration of particles at the top of a pile according to the present invention, wherein V m (t) is a test curve, V c And (t) is a calculation curve.
Detailed Description
The present invention is described in further detail below with reference to the drawings to enable those skilled in the art to practice the invention by referring to the description.
The embodiment of the invention provides a foundation pile wave impedance inversion analysis method based on a cubic B spline interpolation function, which comprises the following steps of:
s1, testing a foundation pile by adopting a knocking-echo method to obtain a pile top particle vibration speed response test curve;
s2, discretizing the foundation pile into N e Pile units with equal length and uniform section;
wherein the number of pile units N e The calculation method of (2) is as follows:
s21, obtaining the time difference T between the occurrence of the peak value of the knocking pulse signal and the occurrence of the peak value of the reflected wave signal at the bottom of the pile from the pile top particle vibration speed response test curve, and calculating the average wave speed of the wave in the pile according to the pile length and the time difference
Wherein L is pile length;
s22, calculating the sampling point number N from the starting point of the knocking pulse signal to the starting point of the pile bottom reflected wave signal according to the pile top particle vibration speed response sampling period deltat:
N＝T/Δt
s23, presetting the number of pile units to be N 0 From N 0 Calculating the preset length delta L of the pile unit 0 ：
ΔL 0 ＝L/N 0
S24, calculating the propagation time delta tau of the reflected wave back and forth in the pile unit:
s25, calculating sampling points M corresponding to the back-and-forth propagation time of the reflected wave in the unit:
M＝int(Δτ/Δt)+1
wherein the symbol int () in the formula represents rounding the calculation value in brackets;
s26, calculating the time delta tau required for the wave to make a round trip in the pile unit again by using the sampling point number M 1 ；
Δτ 1 ＝MΔt
S27, by Deltaτ 1 Recalculating pile unit length DeltaL by average wave velocity 1 ：
S28, calculating the number N of the actual pile units e ：
N e ＝int(L/ΔL 1 )+1。
S3, constructing a first analysis window and a second analysis window in a region where pile body reflection signals appear in the pile top particle vibration velocity response time-course curve;
s4, setting the first analysis window according to the range of the pile units and the number of the pile units corresponding to the time range of the first analysis windowPile units corresponding to the openings are equally divided into N s Taking N in the first analysis window from each pile unit section s The wave impedance of interfaces of +1 pile unit sections is used as a fitting analysis optimization parameter, and the fitting analysis optimization parameter is interpolated through a cubic B spline interpolation function to obtain the wave impedance of interfaces of other pile units in the first analysis window;
specifically, the pile units in the first analysis window are equally divided into N s The method of individual pile unit sections is as follows:
s41, calculating the number N of pile units in the first analysis window 1 ：
Wherein N is 1,0 And N 1,1 Respectively starting pile units and ending pile units corresponding to the pile top particle vibration speed response test curves of the first analysis window; t is t 1,0 And t 1,1 Respectively starting time and ending time corresponding to the pile top particle vibration speed response test curve of the first analysis window;
due to N 1 ＝N 1,1 -N 1,0 Therefore:
s42, equally dividing the pile units in the first analysis window into N s Pile unit sections, each section comprising a number delta N of pile units within the pile unit section s,1 The calculation method of (2) is as follows:
s43, recalculating the first analysis windowIs a termination pile unit N of (1) 1,1 ；
N 1,1 ＝N 1,0 +ΔN s,1 ×N s ；
Specifically, the fitting analysis optimization parameters are subjected to interpolation processing through a cubic B spline interpolation function, and the method comprises the following steps:
a. interface position with first window wave impedance as optimization parameter
j＝1,…,N t And wave impedance +.>
The control point positions and the wave impedances are calculated respectively as follows:
wherein N is t ＝N s +1，N t ×N t Order matrix
And->
Respectively representing a control point position vector and a wave impedance vector;
b. performing cubic B-spline interpolation on each pile unit section, wherein the expression of the cubic B-spline interpolation function is as follows:
wherein the interpolation function in the equation
In the above, xi is E [0,1 ]]；p i Representing the control point parameter of the ith section S i (ζ) represents a spline function after interpolation of the i-th segment control point parameter, and p is taken for the initial segment i=1 in the cubic B-spline interpolation 0 ＝p 1 For termination segment i=n s Taking out
Dividing a variable xi change interval into M equal parts, wherein the interval delta xi=1/M;
c. taking xi m =Δζ×m, m=0, 1, …, M, p i Respectively using
Instead, interpolation point locations and wave impedances can be obtained, specifically:
for the initial segment (i=1), the mth interpolation point positions and wave impedances are respectively
For the termination segment (i=n s ) The m-th interpolation point positions and the wave impedances are respectively
For the middle ith section，1＜i＜N s The m-th interpolation point positions and the wave impedances are respectively
d. Judging the position of the subsection where the kth interface is positioned and the adjacent interpolation point:
symbol i represents the segment number of the kth interface, n and n+1 represent the numbers of two adjacent interpolation points of the kth interface respectively;
calculating the kth interface wave impedance from Duan Naxiang adjacent interpolation point wave impedance:
s5, performing the step in S4 on the pile units in the second analysis window to obtain the wave impedance of interfaces of other pile units in the second analysis window;
s6, calculating equivalent knocking force pulse according to the first bell-shaped pulse and pile top wave impedance in the pile top particle vibration speed response test curve;
specifically, the method for calculating the equivalent knocking force pulse by the first bell-shaped pulse of the pile top particle vibration speed test curve comprises the following steps:
wherein T is d The duration of the rising period of the bell-shaped pulse, namely the time interval from the starting point to the peak point of the bell-shaped pulse; v (V) m (t) is the pile top mass point at the moment tVibration speed; z is Z top ＝(ρcA) top And expressing pile top wave impedance, wherein ρ, c and A are pile top concrete density, wave speed and sectional area respectively.
S7, determining shear wave velocities of soil of each layer according to soil properties of soil layers around the piles, and calculating damping pot coefficients in a pile-soil interaction model of each pile unit pile side according to the shear wave velocities;
specifically, according to soil property of soil around the pile, determining shear wave velocity of each layer of soil, and calculating a damping pot coefficient in a pile-soil interaction model of each pile unit pile side comprises the following steps:
s71, according to the soil property of the soil layer around the pile, according to a shear wave speed value range in the soil property suggested in the aseismic design specification of the railway engineering of GB50111-2006, taking the middle value of the shear wave speed value range as the shear wave speed of the soil layer, and calculating the damping kettle coefficient of the ith pile unit section of the soil layer according to the following formula:
J s,i ＝l i ρ s,i c s,i
wherein l i The circumference of the section of the ith pile unit of the foundation pile is the circumference; ρ s,i C s,i Respectively representing the density and shear wave velocity of the soil layer where the section is positioned;
s72, pile bottom damping pot coefficient J t The calculation method of (1) is as follows:
J t ＝β t Z t
wherein Z is t For wave impedance of pile bottom section, Z t ＝(ρcA) t ；β t And the coefficient is determined by matching the pile bottom reflected wave response test curve with the calculation curve.
S8, calculating the vibration speed of each pile unit interface by a wave differential equation characteristic line solving method according to the calculated equivalent knocking force pulse, the wave impedance of each pile unit interface in the first analysis window and the second analysis window and damping kettle coefficients in pile-soil interaction models of the pile side and the pile bottom of each pile unit, and obtaining a pile top particle vibration speed response calculation curve;
and S9, optimizing and analyzing the wave impedance of each pile unit interface in the first analysis window and the second analysis window, and obtaining a wave impedance profile according to optimized data.
Specifically, the optimizing analysis of the wave impedance of each pile unit interface in the first analysis window and the second analysis window comprises the following steps:
s91, based on a one-dimensional fluctuation theory, obtaining a pile top particle vibration velocity response calculation curve by utilizing an equivalent knocking force pulse, pile soil interaction damping kettle coefficients and pile body wave impedance by utilizing a differential equation characteristic line solving method, and establishing an objective function taking analysis window wave impedance as an optimization parameter by using the particle vibration velocity test curve and calculation curve difference:
wherein: v m,i ,v c,i Respectively measuring a particle vibration speed test value and a calculated value corresponding to reflection at the ith section of the pile unit; n (N) 2,0 And N 2,1 Respectively starting pile units and ending pile units corresponding to the pile top particle vibration speed response test curves of the second analysis window;
s92, interface wave impedance
Performing analysis optimization, wherein the delta difference value of the objective function delta of the current step and the later step is smaller than the set error delta ε ＝10 -4 And (5) terminating the calculation to obtain the pile body wave impedance profile.
In addition, as shown in fig. 1-4, the present invention also provides a test example, wherein in fig. 1-4, the meanings represented by the reference numerals are as follows: 1. normalizing the pile unit wave impedance; 2. equivalent wave impedance of pile bottom soil; 3. knocking pulse; 4. reflecting waves at the pile bottom; 5. a first analysis window; 6. a second analysis window; 7. a first analysis window in-pile unit; 8. a first analysis window in-pile unit; 9. a second analysis window in-pile unit; 10. AA, BB, CC, DD, EE in B spline interpolation is used for optimizing pile unit interfaces for analysis; 11. a pile unit; 12. pile side resistance; 13. pile side pile soil interaction damping kettle model; 14. pile bottom pile soil interaction damping pot model; 15. pile unit numbering; 16. calculating a pile top particle vibration speed calculation curve; 17. pile top particle vibration speed test curves; 18. pile cell wave impedance profile.
The test example comprises the following steps:
step A: dispersing pile bodies;
(a) And the length of the necking model pile is 8m, the radius R=0.2 m of the pile top section, a necking is arranged in the range of 4m-4.5m from the pile top, the equivalent radius of the necking section is 0.18m, and the surrounding soil of the pile is backfill soil. The measuring accelerometer is stuck at the position near 2/3R from the pile center by using plasticine, a hand hammer is used for knocking at the pile center, a foundation pile dynamic measuring instrument records particle vibration acceleration signals, and the sampling time interval deltat=2×10 -5 s, integrating the acceleration signals to obtain particle vibration velocity response signals, and performing 2000Hz low-pass filtering on the signals, wherein the processed signals are shown in figure 1;
(b) The average wave speed c=3341 m/S is obtained by the S21 according to the time difference of the striking pulse (first pulse) of the test signal and the reflection wave crest value of the pile bottom;
(c) Dispersing piles into 80 equal-length pile units according to the S22 to S28, and calculating the corresponding time for the reflected wave of each interface of the ith unit to reach the pile top to obtain the normalized wave impedance of each interface in the time domain, as shown in figure 1;
and (B) step (B): constructing an analysis window;
(1) In-phase reflected wave signals appear after knocking pulses in the test signals, a mouse is dragged from the initial time position of the abnormal reflected signals of the pile body to the direction of reflected waves of the pile bottom by pressing a right mouse button, when a window of the mouse covers main reflected signals, the right mouse button is loosened to obtain a first analysis window, a second analysis window is constructed in a subsequent section no matter whether reflection exists or not, and the initial unit, the termination unit and the unit number in the window are determined according to the step S41, as shown in fig. 1.
(2) Dividing the window unit into 4 sections, wherein the number of units in each section is the same, and taking the wave impedance of the first interface, the last interface and each section of interface in the window as fitting analysis optimization parameters, as shown in figure 2. From these interface wave impedances, the other interface wave impedances within the window are calculated as cubic B-spline functions from said step a to said step d.
(3) Pile-soil interaction was simulated with a damping pot, as shown in FIG. 3, with pile periphery backfill density ρ s =1800 kg/m3, shear wave velocity c s =80m/S, the pile side damping pot coefficient is calculated according to the step S71, the pile bottom damping pot coefficient is calculated according to the step S72, and the undetermined coefficient beta t And the pile bottom reflected wave matching determines that the pile bottom damping kettle parameters only influence the pile bottom reflected wave and the response calculation curve of the subsequent reflected wave, and do not influence the calculation of the response curve before the pile bottom reflected wave and the impedance analysis of the pile body wave.
(4) And S8, obtaining the time variation of the equivalent knocking force pulse according to the step, and obtaining a particle vibration speed response calculation value by utilizing a differential equation characteristic line solving method based on a one-dimensional fluctuation theory and by using the equivalent knocking force, pile-soil interaction model damping kettle parameters and pile unit wave impedance variation. Constructing an objective function according to the step S91, wherein the calculated value difference of the objective function in the current and later steps is smaller than the set error delta ε ＝10 -4 And (5) ending the optimization analysis to obtain the wave impedance profile. Compared with a calculation curve, the pile top particle vibration speed test curve is shown in fig. 4, and the wave impedance change range and degree obtained by the method are close to the model setting parameters.
Although embodiments of the present invention have been disclosed above, it is not limited to the details and embodiments shown, it is well suited to various fields of use for which the invention is suited, and further modifications may be readily made by one skilled in the art, and the invention is therefore not to be limited to the particular details and examples shown and described herein, without departing from the general concepts defined by the claims and the equivalents thereof.
Claims (8)
1. The foundation pile wave impedance inversion analysis method based on the cubic B spline interpolation function is characterized by comprising the following steps of:
s1, testing a foundation pile by adopting a knocking-echo method to obtain a pile top particle vibration speed response test curve;
s2, discretizing the foundation pile into N e Pile units with equal length and uniform section;
s3, constructing a first analysis window and a second analysis window in a region where pile body reflection signals appear in the pile top particle vibration velocity response time-course curve;
s4, equally dividing the pile units corresponding to the first analysis window into N according to the range of the pile units corresponding to the time range where the first analysis window is located and the number of the pile units s Taking N in the first analysis window from each pile unit section s The wave impedance of interfaces of +1 pile unit sections is used as a fitting analysis optimization parameter, and the fitting analysis optimization parameter is interpolated through a cubic B spline interpolation function to obtain the wave impedance of interfaces of other pile units in the first analysis window;
s5, performing the step in S4 on the pile units in the second analysis window to obtain the wave impedance of interfaces of other pile units in the second analysis window;
s6, calculating equivalent knocking force pulse according to the first bell-shaped pulse and pile top wave impedance in the pile top particle vibration speed response test curve;
s7, determining shear wave velocities of soil of each layer according to soil properties of soil layers around the piles, and calculating damping pot coefficients in a pile-soil interaction model of each pile unit pile side according to the shear wave velocities;
s8, based on a one-dimensional fluctuation theory, according to the calculated equivalent knocking force pulse, wave impedance of each pile unit interface in the first analysis window and the second analysis window and damping kettle coefficients in pile-soil interaction models of the pile side and the pile bottom of each pile unit, calculating the vibration speed of each pile unit interface by a fluctuation differential equation characteristic line solving method, and obtaining a pile top particle vibration speed response calculation curve.
2. The method for inversion analysis of the impedance of foundation piles based on a cubic B-spline interpolation function as set forth in claim 1, wherein in said S2, the number N of pile units e The calculation method of (2) is as follows:
s21, obtaining the time difference T between the occurrence of the peak value of the knocking pulse signal and the occurrence of the peak value of the reflected wave signal at the bottom of the pile from the pile top particle vibration speed response test curve, and calculating the average wave speed of the wave in the pile according to the pile length and the time difference
Wherein L is pile length;
s22, calculating the sampling point number N from the starting point of the knocking pulse signal to the starting point of the pile bottom reflected wave signal according to the pile top particle vibration speed response sampling period deltat:
N＝T/Δt
s23, presetting the number of pile units to be N 0 From N 0 Calculating the preset length delta L of the pile unit 0 ：
ΔL 0 ＝L/N 0
S24, calculating the propagation time delta tau of the reflected wave back and forth in the pile unit:
s25, calculating sampling points M corresponding to the back-and-forth propagation time of the reflected wave in the unit:
M＝int(Δτ/Δt)+1
wherein the symbol int () in the formula represents rounding the calculation value in brackets;
s26, calculating the time delta tau required for the wave to make a round trip in the pile unit again by using the sampling point number M 1 ；
Δτ 1 ＝MΔt
S27, by Deltaτ 1 Recalculating pile unit length DeltaL by average wave velocity 1 ：
S28, calculating the number N of the actual pile units e ：
N e ＝int(L/ΔL 1 )+1。
3. The method for inversion analysis of the impedance of foundation piles based on a cubic B-spline interpolation function as set forth in claim 2, wherein in S4, pile units in said first analysis window are equally divided into N s The method of individual pile unit sections is as follows:
s41, calculating the number N of pile units in the first analysis window 1 ：
Wherein N is 1,0 And N 1,1 Respectively starting pile units and ending pile units corresponding to the pile top particle vibration speed response test curves of the first analysis window; t is t 1,0 And t 1,1 Respectively starting time and ending time corresponding to the pile top particle vibration speed response test curve of the first analysis window;
due to N 1 ＝N 1,1 -N 1,0 Therefore:
s42, equally dividing the pile units in the first analysis window into N s Pile unit sections, each section comprising a number delta N of pile units within the pile unit section s,1 The calculation method of (2) is as follows:
s43, re-countingCalculating a termination pile unit N in the first analysis window 1,1 ；
N 1,1 ＝N 1,0 +ΔN s,1 ×N s 。
4. A method for inverting the impedance of a foundation pile based on a cubic B-spline interpolation function as set forth in claim 3, wherein the step of interpolating the fitting analysis optimization parameters by the cubic B-spline interpolation function in S4 comprises the steps of:
a. interface position with first window wave impedance as optimization parameter
j＝1,…,N t And wave impedance +.>
The control point positions and the wave impedances are calculated respectively as follows:
wherein N is t ＝N s +1，N t ×N t Order matrix
b. performing cubic B-spline interpolation on each pile unit section, wherein the expression of the cubic B-spline interpolation function is as follows:
wherein the interpolation function in the equation
In the above, xi is E [0,1 ]]；p i Representing the control point parameter of the ith section S i (ζ) represents a spline function after interpolation of the i-th segment control point parameter, and p is taken for the initial segment i=1 in the cubic B-spline interpolation 0 ＝p 1 For termination segment i=n s Taking out
Dividing a variable xi change interval into M equal parts, wherein the interval delta xi=1/M;
c. taking xi m =Δζ×m, m=0, 1, …, M, p i Respectively using
Instead, interpolation point locations and wave impedances can be obtained, specifically:
for the initial segment i=1, the m-th interpolation point positions and wave impedances are respectively
For termination segment i=n s The m-th interpolation point positions and the wave impedances are respectively
For the middle ith section, i is more than 1 and less than N s The m-th interpolation point positions and the wave impedances are respectively
d. Judging the position of the subsection where the kth interface is positioned and the adjacent interpolation point:
symbol i represents the segment number of the kth interface, n and n+1 represent the numbers of two adjacent interpolation points of the kth interface respectively;
calculating the kth interface wave impedance from Duan Naxiang adjacent interpolation point wave impedance:
5. the method for inversion analysis of foundation pile wave impedance based on cubic B-spline interpolation function according to claim 1, wherein the method for calculating equivalent striking force pulse from the first bell-shaped pulse of pile top particle vibration velocity test curve in S6 is as follows:
wherein T is d For the duration of the rising period of the bell-shaped pulse, i.e. the time between the start point and the peak point of the bell-shaped pulseA partition; v (V) m (t) is the pile top particle vibration speed at the moment t; z is Z top ＝(ρcA) top And expressing pile top wave impedance, wherein ρ, c and A are pile top concrete density, wave speed and sectional area respectively.
6. The method for inversion analysis of foundation pile wave impedance based on cubic B-spline interpolation function according to claim 1, wherein S7 determines shear wave velocities of soil of each layer according to soil property of soil around the pile, and calculates damping pot coefficients in pile-soil interaction model of each pile unit pile side comprises the following steps:
s71, according to the soil property of the soil layer around the pile, according to a shear wave speed value range in the soil property suggested in the aseismic design specification of the railway engineering of GB50111-2006, taking the middle value of the shear wave speed value range as the shear wave speed of the soil layer, and calculating the damping kettle coefficient of the ith pile unit section of the soil layer according to the following formula:
wherein l i The circumference of the section of the ith pile unit of the foundation pile is the circumference; ρ s,i C s,i Respectively representing the density and shear wave velocity of the soil layer where the section is positioned;
s72, pile bottom damping pot coefficient J t The calculation method of (1) is as follows:
J t ＝β t Z t
wherein Z is t For wave impedance of pile bottom section, Z t ＝(ρcA) t ；β t And the coefficient is determined by matching the pile bottom reflected wave response test curve with the calculation curve.
7. A method of inversion analysis of the impedance of a foundation pile based on a cubic B-spline interpolation function as claimed in any one of claims 1 to 6, further comprising:
and S9, optimizing and analyzing the wave impedance of each pile unit interface in the first analysis window and the second analysis window, and obtaining a wave impedance profile according to optimized data.
8. The method for inverting the wave impedance of the foundation pile based on the cubic B-spline interpolation function according to claim 7, wherein the optimizing the wave impedance of each pile unit interface in the first analysis window and the second analysis window in S9 comprises the steps of:
s91, based on a one-dimensional fluctuation theory, obtaining a pile top particle vibration velocity response calculation curve by utilizing an equivalent knocking force pulse, pile soil interaction damping kettle coefficients and pile body wave impedance by utilizing a differential equation characteristic line solving method, and establishing an objective function taking analysis window wave impedance as an optimization parameter by using the particle vibration velocity test curve and calculation curve difference:
wherein: v m,i ,v c,i Respectively measuring a particle vibration speed test value and a calculated value corresponding to reflection at the ith section of the pile unit; n (N) 2,0 And N 2,1 Respectively starting pile units and ending pile units corresponding to the pile top particle vibration speed response test curves of the second analysis window;
s92, interface wave impedance
Performing analysis optimization, wherein the delta difference value of the objective function delta of the current step and the later step is smaller than the set error delta ε ＝10 -4 And (5) terminating the calculation to obtain the pile body wave impedance profile. />
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| CN109138004A (en) * | 2018-08-27 | 2019-01-04 | 武汉工程大学 | A kind of analysis method of more hammering combined signal inverting pile bearing capacities |
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