CN114996803B - High-precision method for detecting integrity of semi-embedded large-diameter friction pile by using low strain method - Google Patents
High-precision method for detecting integrity of semi-embedded large-diameter friction pile by using low strain method Download PDFInfo
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Abstract
The invention belongs to the technical field of dynamic pile measurement, and particularly relates to a high-precision method for detecting the integrity of a semi-buried large-diameter friction pile by using a low-strain method. The pile top speed reflection wave curve semi-analytic solution is obtained by establishing a semi-embedded large-diameter friction pile three-dimensional mechanical model and solving by utilizing a mathematical means, the distribution rule of the pile top speed reflection wave curve high-frequency interference components at the radial position of the pile top is analyzed on the basis, a method for eliminating the pile top speed reflection wave curve high-frequency interference components is provided based on the rule, pile foundation integrity detection precision can be improved by eliminating the high-frequency interference components, the influence of pile bottom soil fluctuation effect of the semi-embedded large-diameter friction pile on the vibration characteristics of the pile bottom is considered, and the three-dimensional virtual soil pile model suitable for the semi-embedded large-diameter friction pile is provided for the first time, so that the pile top speed reflection wave curve three-dimensional virtual soil pile model has good applicability. The invention has good application prospect for the power design of the guide pile and the improvement of the accuracy of the integrity of the low-strain detection pile body.
Description
Technical Field
The invention belongs to the technical field of dynamic pile measurement, and particularly relates to a high-precision method for detecting the integrity of a semi-buried large-diameter friction pile by using a low-strain method.
Background
The low strain method is a mainstream method for detecting the integrity of the foundation pile at present, and related foundation pile detection specifications which are currently implemented in China, including application ranges, equipment requirements, field technical requirements and data analysis and judgment of the low strain method are clearly standardized by railways, highways, buildings and the like.
The low strain method is generally defined as follows: the method is a detection method for evaluating the integrity of the pile to be inspected by applying low-energy impact load to the pile top, actually measuring acceleration (or speed) response time-course curve and applying time domain and frequency domain analysis of a one-dimensional linear fluctuation theory. Namely, the low strain method is a detection method based on a shock elastic wave.
When the elastic wave propagates along the pile body, the change of the cross section or the material change (such as pile bottom, broken pile or serious segregation) or the change of the pile body cross section (such as diameter reduction or diameter expansion) is reflected as the change of the mechanical impedance (generally, Z is used to represent the mechanical impedance of the material, z=ρca, where a is the cross section area), and the propagation characteristic of the wave changes at this time, namely, the reflection and transmission phenomena occur. The transmitted wave continues to propagate forward, the reflected wave propagates towards the wave source, and the specific characteristics of the impedance difference position can be determined by picking up the reflected wave signal and analyzing the wave characteristics. This is the principle of the low strain method, which is also commonly referred to as the low strain reflected wave method, because it uses reflected wave signals.
Various diseases of the pile body, such as diameter reduction, diameter expansion, segregation, pile breaking and the like, can be distinguished through the characteristics of the reflected waves. According to stress wave theory, there are the following rules:
wherein V is particle velocity, subscript I, R denotes incident wave, reflected wave, Z 1 、Z 2 Generalized wave impedance (Z) of upper and lower portions of the reflection interface 1 ＝ρ 1 C 1 A 1 ,Z 2 ＝ρ 2 C 2 A 2 ,A 1 ,A 2 The sectional areas of the upper pile body and the lower pile body of the interface are respectively).
(1) When the pile body is defect-free, Z 2 ＝Z 1 ，V R =0, no reflected wave exists in the pile body, and only the pile bottom reflected wave exists;
(2) Z when the pile body has defects 2 <Z 1 ，V R And V is equal to 1 The same number, namely on the actually measured time domain curve, the reflected wave is in phase with the incident wave; conversely, when the pile body has increased wave impedance due to expanding diameter, Z 2 >Z 1 ，V R And V is equal to 1 The opposite sign, i.e. on the measured real domain curve, the reflected wave is opposite to the incident wave.
As a theoretical basis of the low strain reflection wave method, there have been many studies on the theory of pile-soil longitudinal coupling vibration, which mostly simplify the pile into one-dimensional bars, i.e., waves propagate only in the longitudinal direction (pile length direction) of the pile. The pile foundation is simplified into a one-dimensional slender rod piece based on the pile foundation stress wave detection theory of the one-dimensional fluctuation theory, the wave is assumed to propagate longitudinally, and the wave propagation in the transverse direction is not considered.
The existing pile foundation low-strain reflected wave method has higher precision for slender piles (small-diameter piles) and lower precision for large-diameter piles. The method is based on pile foundation one-dimensional fluctuation theory, and when the method is applied to a semi-buried large-diameter pile, the influence of the three-dimensional fluctuation effect of the pile body is ignored, so that the existence of high-frequency interference components on a pile top speed reflection wave curve cannot be considered, the accuracy of the integrity detection of the large-diameter pile can be greatly reduced, the method for reducing the high-frequency interference components is provided in the existing building foundation pile detection technical specification, namely, the detection point is preferably at the position 2/3 radius from the pile center, practice proves that the high-frequency interference components are minimum at the position 2/3 radius from the pile center, but the method can only reduce the influence of the high-frequency interference, but cannot eliminate the high-frequency interference components, and the detection accuracy still needs to be improved.
Disclosure of Invention
The invention aims to solve the problem of providing a high-precision method for detecting the integrity of a semi-embedded large-diameter friction pile by using a low strain method, which is characterized in that a pile top velocity reflection wave curve semi-analytical solution is obtained by establishing a three-dimensional mechanical model of the semi-embedded large-diameter friction pile and solving by using a mathematical means, the distribution rule of high-frequency interference components of the pile top velocity reflection wave curve in the radial position of the pile top is analyzed on the basis, and the method for eliminating the high-frequency interference components of the pile top velocity reflection wave curve is provided on the basis of the rule, so that the pile foundation integrity detection precision can be improved by eliminating the high-frequency interference components.
A high-precision method for detecting the integrity of a semi-embedded large-diameter friction pile by using a low strain method comprises the following specific steps:
s1, utilizing a plane strain model to establish a longitudinal vibration control equation of soil body at the pile side and the pile bottom;
s2, establishing a longitudinal vibration control equation of the half-buried large-diameter friction pile and the three-dimensional virtual soil pile by using a viscoelastic three-dimensional axisymmetry theory;
s3, establishing boundary conditions of a pile side soil-semi-embedded large-diameter friction pile-three-dimensional virtual soil pile-pile bottom soil coupling vibration system;
s4, solving 2 vibration equations in the steps S1 and S2 by using mathematical means such as Laplace transformation and separation variables, and solving to obtain a pile top velocity reflection wave curve analysis solution of the semi-buried large-diameter pile by combining continuous displacement and stress balance conditions on the interface of the pile and the soil body in the step S3;
s5, utilizing MATLAB programming program to obtain a numerical calculation example of a theoretical solution of a pile top velocity reflection wave curve of the half-buried large-diameter friction pile based on the pile body three-dimensional viscoelastic fluctuation theory, and providing a method for eliminating the pile top velocity reflection wave curve high-frequency interference component by combining calculation results based on the analysis of the distribution rule of the high-frequency interference component on the pile top of the half-buried large-diameter pile;
s6, when the integrity of the semi-embedded large-diameter pile is detected on site, detecting points are arranged according to analysis of pile top distribution rules of the large-diameter pile in the step S5, velocity reflection wave curves collected at the two detecting points are overlapped, and the integrity of the large-diameter pile is judged based on the overlapped reflection wave curves, so that high-precision evaluation of the integrity of the semi-embedded large-diameter pile is achieved.
Further, in the step S1, a control equation for longitudinal vibration of soil bodies at the pile side and the pile bottom is established by using a plane strain model, and is as follows:
wherein u is SS For vertical displacement of soil body at pile side, u ES For the vertical displacement of the soil body at the bottom of the pile G SS 、η SS And ρ SS Respectively shear modulus, viscous damping coefficient and density of pile-side soil mass, G ES 、η ES And ρ ES Shear modulus, viscous damping coefficient and density of pile bottom soil body。
Further, in the step S2, a longitudinal vibration control equation of the semi-embedded large-diameter friction pile and the three-dimensional virtual soil pile is established by using a viscoelastic three-dimensional axisymmetry theory, and is as follows:
in the method, in the process of the invention,for the vertical displacement of the half-embedded large-diameter friction pile, < > for>And->Respectively, the Lame constant, the shear modulus, the viscous damping coefficient and the density of the semi-embedded large-diameter friction pile, < >> And->The elastic modulus and poisson ratio of the semi-embedded large-diameter friction pile are respectively shown, and the related parameters of subscripts j=1, 2, j=1 and j=2 respectively represent the exposed section and the embedded section of the semi-embedded large-diameter friction pile, u FP Is the vertical displacement lambda of the three-dimensional virtual soil pile ES 、G ES 、η ES And ρ ES Respectively the Lame constant, the shear modulus, the viscous damping coefficient and the density lambda of pile foundation soil ES ＝E ES μ ES /(1+μ ES )(1-2μ ES )，G ES ＝E ES /2(1+μ ES )，E ES Sum mu ES The elastic modulus and poisson ratio of pile foundation soil are respectively.
Further, in the step S3, a boundary condition of a pile side soil-semi-embedded large-diameter friction pile-three-dimensional virtual soil pile-pile bottom soil coupling vibration system is established, and soil displacement is reduced to zero at radial infinity:
u ES | r→∞ ＝u SS | r→∞ ＝0 (5)
the surface shear stress of the exposed section of the semi-embedded large-diameter pile is zero, and the displacement and stress of pile side soil and the embedded section of the semi-embedded large-diameter friction pile, pile bottom soil and the three-dimensional virtual soil pile at the pile radius are equal:
in the method, in the process of the invention,τ SS 、τ FP and τ ES Shear stress of a half-embedded large-diameter friction pile exposed section, an embedded section, pile side soil, a three-dimensional virtual soil pile and pile bottom soil respectively +.>
The boundary conditions of the pile top of the half-embedded large-diameter friction pile are as follows:
in the middle ofThe positive stress of the large-diameter friction pile is p (t) g (r) which is the uniformly distributed exciting force generated by the exciting hammer;
the vertical displacement of the center of the half-embedded large-diameter friction pile is limited:
the vertical displacement of the three-dimensional virtual soil pile at the bedrock is zero:
u FP (z,r,t)| z＝H ＝0 (11)
further, the step S4 includes the following specific steps:
step 1, soil mass displacement solving
Laplace transform is performed on the formula (1) and the formula (2):
in the method, in the process of the invention,U SS (r, ω) and U ES (r, ω) are u SS (r, t) and u ES A pull-type transformation of (r, t), ω excitation circle frequency;
the general solution of equations (12) and (13) after considering boundary condition equation (5) is:
U SS (r,ω)＝A SS K 0 (q SS r) (14)
U ES (r,ω)＝A ES K 0 (q ES r) (15)
in which A SS And A ES To be determined as coefficient, K 0 () The bessel function is modified for the second zero order,
the soil shear stress is expressed as:
k in the formula 1 () Correcting the Bessel function for the second class first order;
step 2, carrying out Laplacian transformation on the vibration control equation of the half-buried large-diameter friction pile, and decomposing the equation by utilizing a separation variable method
Performing laplace transform on formula (3):
in the method, in the process of the invention,is->Is a pull-type transformation of (2);
by adopting a separation variable method, the method enablesEquation (18) can be written as:
wherein the method comprises the steps ofAnd->Then it is possible to obtain:
as can be seen from the formula (19),and->The following relationship is satisfied:
the general solution of equations (20) and (21) is:
wherein the method comprises the steps ofIs a coefficient to be determined;
considering boundary condition (10), the basic solution of pile body displacement, positive stress and shear stress is as follows:
step 3, solving displacement of exposed section of semi-embedded large-diameter friction pile
When j=2, the boundary condition expression (6) is considered to be available:
due toIt is possible to obtain:
solving (28) to obtainN eigenvalues of>Will->Substitution (22) available->
Thus, according to the superposition principle, the displacement and the positive stress of the exposed section of the semi-embedded large-diameter friction pile can be expressed as:
in the middle ofAnd->Is a series of pending coefficients.
Step 4, solving displacement of embedded section of semi-embedded large-diameter friction pile
When j=2, the boundary condition expression (7) is considered, and the expressions (14), (24), (16), and (26) are substituted to be available:
the combined type (31) and (32) can be obtained:
in the middle of N eigenvalues>Can be obtained by solving the transcendental equation (33), will +.>Substitution (22) available->
According to the superposition principle, the displacement and the normal stress of the embedded section of the semi-embedded large-diameter friction pile can be expressed as follows:
in the middle ofAnd->Is a series of undetermined coefficients;
step 5, solving the displacement of the three-dimensional virtual soil pile
Performing laplace variation on the formula (4):
u in FP Is u FP Is a pull-type transformation of (2);
by adopting a separation variable method, U is led to FP ＝Z FP (z)·R FP (r), equation (36) can be written as:
wherein the method comprises the steps ofAnd->Then it is possible to obtain:
the general solution of equation (38) is:
wherein C is FP ,D FP ,E FP ,F FP Is a coefficient to be determined;
the displacement of the center of the three-dimensional virtual soil pile is limited, and the displacement, the normal stress and the shear stress of the pile body of the three-dimensional virtual soil pile can be basically solved as follows:
further consider the boundary condition equation (8), and substituting equations (15), (17), (41), (43) into the equation:
the combined type (44) and (45) can be obtained:
in the middle ofβ FP N eigenvalues>Can be obtained by solving the transcendental equation (46), will +.>Substitution (39) is available->
According to the superposition principle, the displacement and the positive stress of the three-dimensional virtual soil pile can be expressed as follows:
in the middle ofAnd->Is a series of undetermined coefficients;
step 6, introducing boundary conditions of pile tops of half-embedded large-diameter friction piles and pile bottoms of three-dimensional virtual soil piles
Substituting the formulas (30) and (47) into the boundary condition formulas (9) and (11) can obtain:
wherein P (ω) is the Laplace transform of P (t);
step 7, consider orthogonality of Bessel function
Bessel function I 0 () Has the following orthogonality:
multiplying simultaneously on both sides of equations (49) and (50) by the orthogonality of equations (51) and (52), respectivelyAndand in interval [0, r 0 ]The integral is carried out on the two components to obtain the following components:
in the middle of
Step 8, introducing displacement and stress continuous conditions on the interfaces of the exposed section and the embedded section of the half-embedded large-diameter friction pile and the embedded section and the three-dimensional virtual soil pile
Step 9, simultaneously solving each undetermined coefficient
The six equations, six unknowns, of the combined type (53) - (58) can be solved to obtain two undetermined coefficients related to the exposed section of the semi-embedded large-diameter friction pile:
in the middle of
Step 10, pile top frequency domain analysis solution of semi-embedded large-diameter friction pile
The displacement and speed frequency domain analysis solution of the semi-embedded large-diameter friction pile can be obtained through the solution, and is as follows:
V P (z,r,ω)＝iωU P (z,r,ω) (62)
step 11, semi-time domain semi-resolution solution of pile top of semi-embedded large-diameter friction pile
The semi-resolution solution of the pile top displacement and the speed time domain response of the semi-embedded large-diameter friction pile can be obtained by using inverse discrete Fourier transform:
u P (z,r,t)＝IFT[U P (z,r,ω)] (63)
where IFT is the inverse fourier transform, which can be implemented by MATLAB,the theoretical solution of the pile top speed reflection wave curve is obtained.
Further, in the step S5, a MATLAB writing program is used to perform numerical calculation analysis on the formula (64), so as to obtain a numerical calculation of a pile top velocity reflected wave curve theoretical solution based on the pile body three-dimensional viscoelastic fluctuation theory, and based on the numerical calculation, the distribution rule of the high-frequency interference component on the pile top of the large-diameter pile is analyzed.
Further, the amplitudes of the high-frequency interference components at the positions of the radial 0.5 radius and the radial 0.8 radius of the pile top are opposite, and the high-frequency interference components are eliminated by adding the pile top velocity reflection wave curves at the positions of the radial 0.5 radius and the radial 0.8 radius.
Further, when the S6 is used for detecting the integrity of the semi-embedded large-diameter pile on site, the used exciting hammer is any one of transient exciting equipment and steady exciting equipment; the transient excitation equipment comprises a force hammer and a hammer pad, wherein the force hammer and the hammer pad can excite wide pulses and narrow pulses, and the force hammer can be provided with a force sensor; the steady-state excitation equipment is an electromagnetic steady-state vibration exciter, the excitation force of the steady-state vibration exciter is adjustable, and the sweep frequency range is 10 Hz-2000 Hz.
Further, when the S6 is used for detecting the integrity of the semi-embedded large-diameter pile on site, an excitation point is selected at the center of the pile, the speed reflection wave curves of the position, 0.5 radius and 0.8 radius, of the pile top of the semi-embedded large-diameter pile are actually measured at the position, 0.5 radius and 0.8 radius, of the detection point are measured, and the speed reflection wave curves of the position, 0.5 radius and 0.8 radius, of the pile top of the semi-embedded large-diameter pile are overlapped, so that a final judging curve of the integrity of the semi-embedded large-diameter pile is obtained.
Compared with the prior art, the invention has the following advantages:
according to the pile-top speed reflection wave curve semi-analytic solution, a pile-top speed reflection wave curve semi-analytic solution is obtained by establishing a semi-embedded large-diameter friction pile three-dimensional mechanical model and solving by utilizing a mathematical means, the pile-top speed reflection wave curve high-frequency interference component distribution rule at the radial position of the pile top is analyzed on the basis, a method for eliminating the pile-top speed reflection wave curve high-frequency interference component is provided based on the rule, and pile-top integrity detection precision can be improved by eliminating the high-frequency interference component;
the invention provides a three-dimensional virtual soil pile model suitable for a half-embedded large-diameter friction pile for the first time for more accurately simulating the vibration characteristic of the half-embedded large-diameter friction pile, namely, considering that a part of a pile body is exposed in the air and a part of the pile body is embedded in the soil, and considering the soil body of the pile bottom in the radius range as a three-dimensional virtual soil pile, the model has the advantages of being capable of well considering the influence of the fluctuation effect of the soil body of the pile bottom of the half-embedded large-diameter friction pile on the vibration characteristic of the half-embedded large-diameter friction pile and having good applicability;
the invention provides a method capable of well eliminating high-frequency interference components based on an analysis method, which can greatly improve the integrity judgment precision when the integrity of a large-diameter pile is detected by using a low-strain method.
Drawings
FIG. 1 is a flow chart of an embodiment of the present invention;
FIG. 2 is a three-dimensional mechanical model of a half-embedded large-diameter friction pile constructed by the invention;
FIG. 3 shows the distribution rule of the high-frequency interference components in the pile top of the semi-embedded large-diameter pile;
FIG. 4 shows the field detection excitation point and detection point arrangement position of the present invention;
Detailed Description
The drawings are for illustrative purposes only; it should be understood that the following examples are presented for the purpose of illustrating the invention only and are not to be construed as limiting the invention in any way as may be desired to facilitate the description of the invention and to simplify the description.
In order to more clearly illustrate the above objects, features and advantages of the present invention, the principles and features of the present invention will be described below with reference to the following examples, which are provided for the purpose of illustrating the present invention only and are not intended to limit the scope of the present invention. The specific conditions are not noted in the examples and are carried out according to conventional conditions or conditions recommended by the manufacturer. The apparatus or device used is not particularly pointed out or illustrated and is a conventional product available commercially.
As shown in FIG. 2, the three-dimensional mechanical model of the semi-embedded large-diameter friction pile is built. In the figure, the large-diameter pile is divided into a bare section, a buried section and a three-dimensional virtual soil pile from top to bottom, r 0 Radius of large diameter friction pile, H P 、H TFSP H is the length of the soil layer on the half-embedded large-diameter friction pile, the three-dimensional virtual soil pile and the bedrock respectively,for the exposed section length of the semi-buried pile, < >>Is the length of the embedded section of the semi-embedded pile. r is a radial coordinate, z is a vertical coordinate, and o is a coordinate origin. The invention provides a three-dimensional virtual soil pile model suitable for a half-embedded large-diameter friction pile for the first time for more accurately simulating the vibration characteristic of the half-embedded large-diameter friction pile, namely, considering that a part of a pile body is exposed in the air, a part of the pile body is embedded in the soil, and considering the soil body of the pile bottom within the radius range of the pile bottom as a three-dimensional virtual soil pile, the model has the advantage of being capable of well considering the half-embedded large-diameter pileThe pile friction pile bottom soil body fluctuation effect affects the vibration characteristics of the pile friction pile bottom soil body fluctuation effect.
As shown in fig. 1, a high-precision method for detecting the integrity of a semi-embedded large-diameter friction pile by using a low strain method comprises the following specific steps:
s1, utilizing a plane strain model to establish a pile side and pile bottom soil body longitudinal vibration control equation:
wherein u is SS For vertical displacement of soil body at pile side, u ES For the vertical displacement of the soil body at the bottom of the pile G SS 、η SS And ρ SS Respectively shear modulus, viscous damping coefficient and density of pile-side soil mass, G ES 、η ES And ρ ES Respectively shear modulus, viscous damping coefficient and density of pile bottom soil mass.
S2, establishing a longitudinal vibration control equation of the half-buried large-diameter friction pile and the three-dimensional virtual soil pile by using a viscoelastic three-dimensional axisymmetry theory:
in the method, in the process of the invention,for the vertical displacement of the half-embedded large-diameter friction pile, < > for>And->Respectively, the Lame constant, the shear modulus, the viscous damping coefficient and the density of the semi-embedded large-diameter friction pile, < >> And->The elastic modulus and poisson ratio of the semi-embedded large-diameter friction pile are respectively shown, and the related parameters of subscripts j=1, 2, j=1 and j=2 respectively represent the exposed section and the embedded section of the semi-embedded large-diameter friction pile, u FP Is the vertical displacement lambda of the three-dimensional virtual soil pile ES 、G ES 、η ES And ρ ES Respectively the Lame constant, the shear modulus, the viscous damping coefficient and the density lambda of pile foundation soil ES ＝E ES μ ES /(1+μ ES )(1-2μ ES )，G ES ＝E ES /2(1+μ ES )，E ES Sum mu ES The elastic modulus and poisson ratio of pile foundation soil are respectively.
S3, establishing boundary conditions of a pile side soil-semi-embedded large-diameter friction pile-three-dimensional virtual soil pile-pile bottom soil coupling vibration system:
the soil displacement is reduced to zero at radial infinity:
u ES | r→∞ ＝u SS | r→∞ ＝0 (5)
the surface shear stress of the exposed section of the semi-embedded large-diameter pile is zero, and the displacement and stress of pile side soil and the embedded section of the semi-embedded large-diameter friction pile, pile bottom soil and the three-dimensional virtual soil pile at the pile radius are equal:
in the method, in the process of the invention,τ SS 、τ FP and τ ES Shear stress of a half-embedded large-diameter friction pile exposed section, an embedded section, pile side soil, a three-dimensional virtual soil pile and pile bottom soil respectively +.>
The boundary conditions of the pile top of the half-embedded large-diameter friction pile are as follows:
in the middle ofThe positive stress of the large-diameter friction pile is p (t) g (r) which is the uniformly distributed exciting force generated by the exciting hammer;
the vertical displacement of the center of the half-embedded large-diameter friction pile is limited:
the vertical displacement of the three-dimensional virtual soil pile at the bedrock is zero:
u FP (z,r,t)| z＝H ＝0 (11)
s4, solving 2 vibration equations in the steps S1 and S2 by using mathematical means such as Laplace transformation and separation variable, and solving to obtain a pile top velocity reflection wave curve analysis solution of the semi-buried large-diameter pile by combining continuous displacement and stress balance conditions on the pile and soil body interface in the step S3, wherein the method specifically comprises the following steps:
step 1, soil mass displacement solving
Laplace transform is performed on the formula (1) and the formula (2):
in the method, in the process of the invention,U SS (r, ω) and U ES (r, ω) are u SS (r, t) and u ES A pull-type transformation of (r, t), ω excitation circle frequency;
the general solution of equations (12) and (13) after considering boundary condition equation (5) is:
U SS (r,ω)＝A SS K 0 (q SS r) (14)
U ES (r,ω)＝A ES K 0 (q ES r) (15)
in which A SS And A ES To be determined as coefficient, K 0 () The bessel function is modified for the second zero order,
the soil shear stress is expressed as:
k in the formula 1 () Correcting the Bessel function for the second class first order;
step 2, carrying out Laplacian transformation on the vibration control equation of the half-buried large-diameter friction pile, and decomposing the equation by utilizing a separation variable method
Performing laplace transform on formula (3):
in the method, in the process of the invention,is->Is a pull-type transformation of (2);
by adopting a separation variable method, the method enablesEquation (18) can be written as:
wherein the method comprises the steps ofAnd->Then it is possible to obtain:
as can be seen from the formula (19),and->The following relationship is satisfied:
the general solution of equations (20) and (21) is:
wherein the method comprises the steps ofIs a coefficient to be determined;
considering boundary condition (10), the basic solution of pile body displacement, positive stress and shear stress is as follows:
step 3, solving displacement of exposed section of semi-embedded large-diameter friction pile
When j=2, the boundary condition expression (6) is considered to be available:
due toIt is possible to obtain:
solving (28) to obtainN eigenvalues of>Will->Substitution (22) available->
Thus, according to the superposition principle, the displacement and the positive stress of the exposed section of the semi-embedded large-diameter friction pile can be expressed as:
in the middle ofAnd->Is a series of pending coefficients.
Step 4, solving displacement of embedded section of semi-embedded large-diameter friction pile
When j=2, the boundary condition expression (7) is considered, and the expressions (14), (24), (16), and (26) are substituted to be available:
the combined type (31) and (32) can be obtained:
in the middle of N eigenvalues>Can be obtained by solving the transcendental equation (33), will +.>Substitution (22) available->
According to the superposition principle, the displacement and the normal stress of the embedded section of the semi-embedded large-diameter friction pile can be expressed as follows:
in the middle ofAnd->Is a series of undetermined coefficients; />
Step 5, solving the displacement of the three-dimensional virtual soil pile
Performing laplace variation on the formula (4):
u in FP Is u FP Is a pull-type transformation of (2);
by adopting a separation variable method, U is led to FP ＝Z FP (z)·R FP (r), equation (36) can be written as:
wherein the method comprises the steps ofAnd->Then it is possible to obtain:
the general solution of equation (38) is:
wherein C is FP ,D FP ,E FP ,F FP Is a coefficient to be determined;
the displacement of the center of the three-dimensional virtual soil pile is limited, and the displacement, the normal stress and the shear stress of the pile body of the three-dimensional virtual soil pile can be basically solved as follows:
further consider the boundary condition equation (8), and substituting equations (15), (17), (41), (43) into the equation:
the combined type (44) and (45) can be obtained:
in the middle ofβ FP N eigenvalues>Can be obtained by solving the transcendental equation (46), will +.>Substitution (39) is available->
According to the superposition principle, the displacement and the positive stress of the three-dimensional virtual soil pile can be expressed as follows:
/>
in the middle ofAnd->Is a series of undetermined coefficients;
step 6, introducing boundary conditions of pile tops of half-embedded large-diameter friction piles and pile bottoms of three-dimensional virtual soil piles
Substituting the formulas (30) and (47) into the boundary condition formulas (9) and (11) can obtain:
wherein P (ω) is the Laplace transform of P (t);
step 7, consider orthogonality of Bessel function
Bessel function I 0 () Has the following orthogonality:
by means of(51) And (52) are multiplied simultaneously on both sides of equations (49) and (50), respectivelyAndand in interval [0, r 0 ]The integral is carried out on the two components to obtain the following components:
in the middle of
Step 8, introducing displacement and stress continuous conditions on the interfaces of the exposed section and the embedded section of the half-embedded large-diameter friction pile and the embedded section and the three-dimensional virtual soil pile
Step 9, simultaneously solving each undetermined coefficient
The six equations, six unknowns, of the combined type (53) - (58) can be solved to obtain two undetermined coefficients related to the exposed section of the semi-embedded large-diameter friction pile:
in the middle of
Step 10, pile top frequency domain analysis solution of semi-embedded large-diameter friction pile
The displacement and speed frequency domain analysis solution of the semi-embedded large-diameter friction pile can be obtained through the solution, and is as follows:
V P (z,r,ω)＝iωU P (z,r,ω) (62)
step 11, semi-time domain semi-resolution solution of pile top of semi-embedded large-diameter friction pile
The semi-resolution solution of the pile top displacement and the speed time domain response of the semi-embedded large-diameter friction pile can be obtained by using inverse discrete Fourier transform:
u P (z,r,t)＝IFT[U P (z,r,ω)] (63)
where IFT is the inverse fourier transform, which can be implemented by MATLAB,the theoretical solution of the pile top speed reflection wave curve is obtained.
S5, obtaining a numerical calculation example of a theoretical solution of a pile top speed reflection wave curve of the half-buried large-diameter friction pile based on a pile body three-dimensional viscoelastic fluctuation theory by utilizing MATLAB programming, and providing a method for eliminating the pile top speed reflection wave curve high-frequency interference component by combining a calculation result based on the analysis of the distribution rule of the high-frequency interference component on the pile top of the half-buried large-diameter pile, wherein the method specifically comprises the following steps:
numerical calculation analysis is carried out on the formula (64) by utilizing MATLAB programming program, so that a numerical calculation example of pile top speed reflected wave curve theoretical solution based on pile body three-dimensional viscoelasticity fluctuation theory can be obtained, and the distribution rule of high-frequency interference components on the pile top of the large-diameter pile is analyzed based on the numerical calculation example, and is particularly shown in fig. 3. As can be seen from the figure, the radial direction of the pile top is 0.5r 0 And 0.8r 0 The amplitudes of the high-frequency interference components at the positions are opposite in sign, so that the phenomenon can be utilized by the method for measuring the radial direction by 0.5r 0 And 0.8r 0 The pile top velocity reflection wave curve at the position is added to eliminate high-frequency interference components, and the eliminated high-frequency interference components are shown as a black solid line in the figure, and compared with the method adopting only 2/3r in engineering 0 Pile-top velocity reflection wave curve at position (r=0.6r in the figure) 0 The line of (2) eliminates the influence of high-frequency interference components, and enhances the amplitude of the pile bottom reflected signal, thereby improving the accuracy of judging the integrity of the pile body of the large-diameter pile.
S6, when the integrity of the semi-buried large-diameter pile is detected on site, according to analysis of pile top distribution rules of the large-diameter pile in the step S5, the amplitudes of high-frequency interference components at the radial positions of 0.5 radius and 0.8 radius of the pile top are opposite in sign, and the high-frequency interference components are eliminated by adding the pile top velocity reflection wave curves at the radial positions of 0.5 radius and 0.8 radius. And the speed reflected wave curves acquired at the two detection points are overlapped, and the integrity of the large-diameter pile is judged based on the overlapped reflected wave curves, so that the high-precision evaluation of the integrity of the semi-embedded large-diameter pile is realized.
Selecting a detection instrument with main technical performance indexes meeting relevant regulations of the current industry standard J G/T3055 of foundation pile dynamic tester, wherein the used exciting hammer is any one of transient exciting equipment and steady exciting equipment; the transient excitation equipment comprises a force hammer and a hammer pad, wherein the force hammer and the hammer pad can excite wide pulses and narrow pulses, and the force hammer can be provided with a force sensor; the steady-state excitation equipment is an electromagnetic steady-state vibration exciter, the excitation force of the steady-state vibration exciter is adjustable, and the sweep frequency range is 10 Hz-2000 Hz.
Further, as shown in fig. 4, the excitation point is selected at the pile center, the velocity reflection wave curves at the positions of 0.5 radius and 0.8 radius from the pile center of the semi-embedded large-diameter pile are actually measured, and the velocity reflection wave curves at the positions of 0.5 radius and 0.8 radius from the pile top of the semi-embedded large-diameter pile are overlapped to obtain the final judging curve of the integrity of the semi-embedded large-diameter pile.
The equipment, instruments and the like used in the invention can be purchased in the market by adopting standard equipment and instruments which are conventional in the prior art unless explicitly stated otherwise, and the technical method which is not stated adopts the prior art.
Those of ordinary skill in the art will appreciate that the embodiments shown herein are intended to aid the reader in understanding the principles of the present invention and that the scope of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other modifications without departing from the spirit of the invention in light of the teachings of the present disclosure, and such modifications are still within the scope of the present invention.
Claims (9)
1. A high-precision method for detecting the integrity of a semi-embedded large-diameter friction pile by using a low-strain method is characterized by comprising the following specific steps:
s1, utilizing a plane strain model to establish a longitudinal vibration control equation of soil body at the pile side and the pile bottom;
s2, establishing a longitudinal vibration control equation of the half-buried large-diameter friction pile and the three-dimensional virtual soil pile by using a viscoelastic three-dimensional axisymmetry theory;
s3, establishing boundary conditions of a pile side soil-semi-embedded large-diameter friction pile-three-dimensional virtual soil pile-pile bottom soil coupling vibration system;
s4, solving 2 vibration equations in the steps S1 and S2 by using mathematical means such as Laplace transformation and separation variables, and solving to obtain a pile top velocity reflection wave curve analysis solution of the semi-buried large-diameter pile by combining continuous displacement and stress balance conditions on the interface of the pile and the soil body in the step S3;
s5, utilizing MATLAB programming program to obtain a numerical calculation example of a theoretical solution of a pile top velocity reflection wave curve of the half-buried large-diameter friction pile based on the pile body three-dimensional viscoelastic fluctuation theory, and providing a method for eliminating the pile top velocity reflection wave curve high-frequency interference component by combining calculation results based on the analysis of the distribution rule of the high-frequency interference component on the pile top of the half-buried large-diameter pile;
s6, when the integrity of the semi-embedded large-diameter pile is detected on site, two detection points are arranged according to analysis of pile top distribution rules of the large-diameter pile in the step S5, velocity reflection wave curves collected at the two detection points are overlapped, the integrity of the large-diameter pile is judged based on the overlapped reflection wave curves, and high-precision evaluation of the integrity of the semi-embedded large-diameter pile is achieved.
2. The high-precision method for detecting the integrity of a semi-embedded large-diameter friction pile by using a low strain method according to claim 1, wherein the construction of a pile side and pile bottom soil longitudinal vibration control equation by using a plane strain model in S1 is as follows:
wherein u is SS For vertical displacement of soil body at pile side, u ES For the vertical displacement of the soil body at the bottom of the pile G SS 、η SS And ρ SS Respectively shear modulus, viscous damping coefficient and density of pile-side soil mass, G ES 、η ES And ρ ES Respectively shear modulus, viscous damping coefficient and density of pile bottom soil mass.
3. The high-precision method for detecting the integrity of a semi-embedded large-diameter friction pile by using a low strain method according to claim 1, wherein the step S2 of establishing a longitudinal vibration control equation of the semi-embedded large-diameter friction pile and a three-dimensional virtual soil pile by using a viscoelastic three-dimensional axisymmetry theory is as follows:
in the method, in the process of the invention,for the vertical displacement of the half-embedded large-diameter friction pile, < > for>And->Respectively, the Lame constant, the shear modulus, the viscous damping coefficient and the density of the semi-embedded large-diameter friction pile, < >> And->Respectively are provided withFor the elastic modulus and poisson ratio of the semi-embedded large diameter friction pile, the subscripts j=1, 2, j=1, and j=2 relate to parameters representing the exposed and embedded sections, u FP Is the vertical displacement lambda of the three-dimensional virtual soil pile ES 、G ES 、η ES And ρ ES Respectively the Lame constant, the shear modulus, the viscous damping coefficient and the density lambda of pile foundation soil ES ＝E ES μ ES /(1+μ ES )(1-2μ ES )，G ES ＝E ES /2(1+μ ES )，E ES Sum mu ES The elastic modulus and poisson ratio of pile foundation soil are respectively.
4. The high-precision method for detecting the integrity of a half-embedded large-diameter friction pile by using a low strain method according to claim 1, wherein the boundary condition of a pile side soil-half-embedded large-diameter friction pile-three-dimensional virtual soil pile-pile bottom soil coupling vibration system is established in the step S3, and the soil displacement is reduced to zero at radial infinity:
u ES | r→∞ ＝u SS | r→∞ ＝0 (5)
the surface shear stress of the exposed section of the semi-embedded large-diameter pile is zero, and the displacement and stress of pile side soil and the embedded section of the semi-embedded large-diameter friction pile, pile bottom soil and the three-dimensional virtual soil pile at the pile radius are equal:
in the method, in the process of the invention,τ SS 、τ FP and τ ES Shear stress of a half-embedded large-diameter friction pile exposed section, an embedded section, pile side soil, a three-dimensional virtual soil pile and pile bottom soil respectively +.>
The boundary conditions of the pile top of the half-embedded large-diameter friction pile are as follows:
in the middle ofThe positive stress of the large-diameter friction pile is p (t) g (r) which is the uniformly distributed exciting force generated by the exciting hammer;
the vertical displacement of the center of the half-embedded large-diameter friction pile is limited:
the vertical displacement of the three-dimensional virtual soil pile at the bedrock is zero:
u FP (z,r,t)| z＝H ＝0 (11) 。
5. the high precision method for detecting the integrity of a semi-buried large diameter friction pile using a low strain method according to claim 1, wherein S4 comprises the following specific steps:
step 1, soil mass displacement solving
Laplace transform is performed on the formula (1) and the formula (2):
in the method, in the process of the invention,U SS (r, ω) and U ES (r, ω) are u SS (r, t) and u ES A pull-type transformation of (r, t), ω excitation circle frequency;
the general solution of equations (12) and (13) after considering boundary condition equation (5) is:
U SS (r,ω)＝A SS K 0 (q SS r) (14)
U ES (r,ω)＝A ES K 0 (q ES r) (15)
in which A SS And A ES To be determined as coefficient, K 0 () The bessel function is modified for the second zero order,
the soil shear stress is expressed as:
k in the formula 1 () Correcting the Bessel function for the second class first order;
step 2, carrying out Laplacian transformation on the vibration control equation of the half-buried large-diameter friction pile, and decomposing the equation by utilizing a separation variable method
Performing laplace transform on formula (3):
in the method, in the process of the invention,is->Is a pull-type transformation of (2);
by adopting a separation variable method, the method enablesEquation (18) can be written as:
wherein the method comprises the steps ofAnd->Then it is possible to obtain:
as can be seen from the formula (19),and->The following relationship is satisfied:
the general solution of equations (20) and (21) is:
wherein the method comprises the steps ofIs a coefficient to be determined;
considering boundary condition (10), the basic solution of pile body displacement, positive stress and shear stress is as follows:
step 3, solving displacement of exposed section of semi-embedded large-diameter friction pile
When j=2, the boundary condition expression (6) is considered to be available:
due toIt is possible to obtain:
solving (28) to obtainN eigenvalues of>Will->Substitution (22) available->
Thus, according to the superposition principle, the displacement and the positive stress of the exposed section of the semi-embedded large-diameter friction pile can be expressed as:
in the middle ofAnd->Is a series of pending coefficients.
Step 4, solving displacement of embedded section of semi-embedded large-diameter friction pile
When j=2, the boundary condition expression (7) is considered, and the expressions (14), (24), (16), and (26) are substituted to be available:
the combined type (31) and (32) can be obtained:
in the middle of N eigenvalues>Can be obtained by solving the transcendental equation (33), will +.>Substitution (22) available->
According to the superposition principle, the displacement and the normal stress of the embedded section of the semi-embedded large-diameter friction pile can be expressed as follows:
in the middle ofAnd->Is a series of undetermined coefficients;
step 5, solving the displacement of the three-dimensional virtual soil pile
Performing laplace variation on the formula (4):
u in FP Is u FP Is a pull-type transformation of (2);
by adopting a separation variable method, U is led to FP ＝Z FP (z)·R FP (r), equation (36) can be written as:
wherein the method comprises the steps ofAnd->Then it is possible to obtain:
the general solution of equation (38) is:
wherein C is FP ,D FP ,E FP ,F FP Is a coefficient to be determined;
the displacement of the center of the three-dimensional virtual soil pile is limited, and the displacement, the normal stress and the shear stress of the pile body of the three-dimensional virtual soil pile can be basically solved as follows:
further consider the boundary condition equation (8), and substituting equations (15), (17), (41), (43) into the equation:
the combined type (44) and (45) can be obtained:
β FP I 1 (β FP r 0 )+ζ FP I 0 (β FP r 0 )＝0 (46)
in the middle ofβ FP N eigenvalues>Can be obtained by solving the transcendental equation (46), will +.>Substitution (39) is available->
According to the superposition principle, the displacement and the positive stress of the three-dimensional virtual soil pile can be expressed as follows:
in the middle ofAnd->Is a series of undetermined coefficients;
step 6, introducing boundary conditions of pile tops of half-embedded large-diameter friction piles and pile bottoms of three-dimensional virtual soil piles
Substituting the formulas (30) and (47) into the boundary condition formulas (9) and (11) can obtain:
wherein P (ω) is the Laplace transform of P (t);
step 7, consider orthogonality of Bessel function
Bessel function I 0 () Has the following orthogonality:
multiplying simultaneously on both sides of equations (49) and (50) by the orthogonality of equations (51) and (52), respectivelyAndand in interval [0, r 0 ]The integral is carried out on the two components to obtain the following components:
in the middle of
Step 8, introducing displacement and stress continuous conditions on the interfaces of the exposed section and the embedded section of the half-embedded large-diameter friction pile and the embedded section and the three-dimensional virtual soil pile
Step 9, simultaneously solving each undetermined coefficient
The six equations, six unknowns, of the combined type (53) - (58) can be solved to obtain two undetermined coefficients related to the exposed section of the semi-embedded large-diameter friction pile:
in the middle of
Step 10, pile top frequency domain analysis solution of semi-embedded large-diameter friction pile
The displacement and speed frequency domain analysis solution of the semi-embedded large-diameter friction pile can be obtained through the solution, and is as follows:
V P (z,r,ω)＝iωU P (z,r,ω) (62)
step 11, semi-time domain semi-resolution solution of pile top of semi-embedded large-diameter friction pile
The semi-resolution solution of the pile top displacement and the speed time domain response of the semi-embedded large-diameter friction pile can be obtained by using inverse discrete Fourier transform:
u P (z,r,t)＝IFT[U P (z,r,ω)] (63)
where IFT is the inverse fourier transform, which can be implemented by MATLAB,the theoretical solution of the pile top speed reflection wave curve is obtained.
6. The high-precision method for detecting the integrity of the semi-buried large-diameter friction pile by using the low strain method according to claim 5, wherein in the step S5, a MATLAB programming program is used for carrying out numerical calculation analysis on a formula (64) to obtain a numerical calculation example of a pile top velocity reflection wave curve theoretical solution based on a pile body three-dimensional viscoelastic fluctuation theory, and the distribution rule of high-frequency interference components on the pile top of the large-diameter pile is analyzed based on the numerical calculation example.
7. The high accuracy method for detecting the integrity of a half-buried large diameter friction pile according to claim 6, wherein the amplitudes of the high frequency interference components at the radial 0.5 radius and 0.8 radius positions of the pile top are opposite, and the high frequency interference components are eliminated by adding the pile top velocity reflection wave curves at the radial 0.5 radius and 0.8 radius positions.
8. The high-precision method for detecting the integrity of the semi-embedded large-diameter friction pile by using the low-strain method according to claim 1, wherein the step S6 is characterized in that when the integrity of the semi-embedded large-diameter pile is detected on site, the used exciting hammer is any one of transient exciting equipment and steady exciting equipment; the transient excitation equipment comprises a force hammer and a hammer pad, wherein the force hammer and the hammer pad can excite wide pulses and narrow pulses, and the force hammer can be provided with a force sensor; the steady-state excitation equipment is an electromagnetic steady-state vibration exciter, the excitation force of the steady-state vibration exciter is adjustable, and the sweep frequency range is 10 Hz-2000 Hz.
9. The high-precision method for detecting the integrity of the half-embedded large-diameter friction pile by using the low-strain method according to claim 1, wherein when the S6 is used for detecting the integrity of the half-embedded large-diameter pile in situ, an excitation point is selected at the center of the pile, the velocity reflection wave curves of the pile top of the half-embedded large-diameter pile at the positions of 0.5 radius and 0.8 radius from the center of the pile are actually measured, and the velocity reflection wave curves of the pile top of the half-embedded large-diameter pile at the positions of 0.5 radius and 0.8 radius are overlapped to obtain a final discrimination curve of the integrity of the half-embedded large-diameter pile.
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