CN114882962A - Large-diameter friction pile material damping measurement and calculation method based on low-strain reflection wave method - Google Patents
Large-diameter friction pile material damping measurement and calculation method based on low-strain reflection wave method Download PDFInfo
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Abstract
The invention discloses a large-diameter friction pile material damping measurement and calculation method based on a low-strain reflection wave method, and particularly relates to the technical field of civil engineering. The method comprises the steps of establishing a plane strain model, establishing a longitudinal vibration control equation aiming at soil on the pile side and the pile bottom of the large-diameter friction pile, establishing the longitudinal vibration control equation aiming at the large-diameter friction pile and the three-dimensional virtual soil pile respectively based on a viscoelastic three-dimensional axisymmetric theory, solving the longitudinal vibration control equation to obtain a pile top speed reflection wave theoretical curve by combining boundary conditions of a pile side soil-large-diameter friction pile-three-dimensional virtual soil pile-pile bottom soil coupling vibration system, and coinciding the pile top speed reflection wave theoretical curve of the specified large-diameter pile with an actually measured pile top speed reflection wave actually measured curve by acquiring pile-soil parameters and the pile top speed reflection wave actually measured curve of the specified large-diameter pile to determine the viscous damping coefficient of a pile body material, so that the problem that the damping of the pile body material in actual engineering is difficult to measure and calculate is solved.
Description
Technical Field
The invention relates to the technical field of civil engineering, in particular to a large-diameter friction pile material damping measurement and calculation method based on a low-strain reflection wave method.
Background
The low strain method is used as a detection method based on shock elastic waves, is a mainstream method for detecting the integrity of a foundation pile at present, obtains an actually-measured acceleration (or speed) response time-course curve by applying low-energy shock load on the pile top, analyzes a time domain and a frequency domain by using a one-dimensional linear fluctuation theory, and judges the integrity of the detected pile.
The pile-soil longitudinal coupling vibration theory is used as a theoretical basis of a low-strain reflection wave method, a plurality of research results are available, the pile body is mostly simplified into a one-dimensional rod piece in the current stage of research, only the wave is considered to be transmitted along the longitudinal direction of the pile body (the axial direction of the pile body), and the wave is not considered to be transmitted along the transverse direction of the pile body, so that the method is only suitable for a relatively long and thin pile foundation, but along with the increase of the complexity of a building, the requirements on the bearing capacity of the pile foundation are higher and higher, the radius of the pile foundation is larger and larger, and the error generated when the pile-soil longitudinal coupling vibration theory is applied to the research of the pile-soil longitudinal coupling vibration problem by adopting the pile foundation one-dimensional fluctuation theory.
In order to better analyze the longitudinal vibration characteristics of a large-diameter pile, a pile foundation three-dimensional elastic wave band theory is adopted, stress waves are three-dimensionally propagated when a pile body is subjected to transient concentrated load in low-strain detection, an axisymmetric wave equation is used for describing, a pile top speed reflection wave curve is obtained by solving, in the practical application process, the pile top speed reflection wave curve obtained by solving the three-dimensional elastic wave theory is shown in a graph 1(a) aiming at the same pile body, a pile top speed reflection wave curve obtained by actually measuring the on-site low-strain reflection method is shown in a graph 1(b), and by comparing the graph 1(a) with the graph 1(b), the amplitude of a pile bottom reflection signal on the pile top speed reflection wave curve calculated based on the three-dimensional elastic wave theory is obviously larger than an actually measured value, and the fluctuation between an initial signal and a pile bottom reflection signal is also larger, the original phenomenon is that the influence of damping of a pile body material is not considered when a pile top speed reflection wave curve is solved based on a three-dimensional elastic wave theory, the damping of the pile body material is known to enable waves to be dissipated in the transmission process, and the influence of the damping of the pile body material is not considered when the existing three-dimensional elastic wave theory is applied to large-diameter pile wave theory analysis.
Therefore, the existing pile foundation low-strain reflection wave method can only be used for detecting the integrity of a pile foundation, the length of a pile and the elastic wave speed of a pile body, and cannot be used for measuring and calculating the damping of a pile body material.
Disclosure of Invention
The invention aims to solve the defects of the prior art and provides a large-diameter friction pile material damping measurement and calculation method based on a low-strain reflection wave method, which comprises the steps of establishing a large-diameter friction pile longitudinal vibration control equation considering pile body material damping, combining boundary conditions of a pile side soil-large-diameter friction pile-three-dimensional virtual soil pile-pile bottom soil coupling vibration system, solving to obtain an analytic solution of a pile top speed reflection wave curve of the large-diameter friction pile, determining a pile top speed reflection wave theoretical curve of the large-diameter friction pile, adjusting viscosity damping coefficients of a pile body material in the pile top speed reflection wave theoretical curve, and coinciding with an actually measured pile top speed reflection wave actually measured curve obtained through actual measurement to determine actual pile body material damping of the large-diameter friction pile, solving the problem of difficulty in measuring and calculation of the pile body material damping, and being beneficial to determination of the pile body material damping in actual engineering, the method lays a foundation for guiding the accuracy of the dynamic design of the large-diameter friction pile and improving the integrity of the low-strain detection pile body.
The invention adopts the following technical scheme:
a large-diameter friction pile material damping measurement and calculation method based on a low-strain reflection wave method specifically comprises the following steps:
s1: constructing a plane strain model, wherein the plane strain model comprises a large-diameter friction pile, a pile bottom soil body, a pile side soil body and a three-dimensional virtual soil pile formed by extending the large-diameter friction pile downwards to the top surface of bedrock, and establishing a longitudinal vibration control equation of the pile side soil body and the pile bottom soil body of the large-diameter friction pile;
s2: based on a viscoelastic three-dimensional axial symmetry theory, establishing a longitudinal vibration control equation respectively aiming at the large-diameter friction pile and the three-dimensional virtual soil pile;
s3: establishing boundary conditions of a pile side soil-large-diameter friction pile-three-dimensional virtual soil pile-pile bottom soil coupling vibration system;
s4: solving a longitudinal vibration control equation of the pile side soil body and the pile bottom soil body of the large-diameter friction pile in the step S1 and a longitudinal vibration control equation of the large-diameter friction pile and the three-dimensional virtual soil pile in the step S2, and calculating to obtain a pile top speed reflection wave theoretical curve of the large-diameter friction pile by combining boundary conditions of a pile side soil-large-diameter friction pile-three-dimensional virtual soil pile-pile bottom soil coupling vibration system in the step S3;
s5, carrying out on-site measurement on the friction pile with the specified large diameter based on a low-strain reflection wave method to obtain a pile-soil parameter and a pile top speed reflection wave actual measurement curve of the friction pile with the specified large diameter;
and S6, substituting the pile-soil parameters extracted on the site into the pile top velocity reflection wave theoretical curve of the large-diameter friction pile in the step S4 to obtain a pile top velocity reflection wave theoretical curve of the specified large-diameter friction pile, and performing fitting analysis on the pile top velocity reflection wave theoretical curve of the specified large-diameter friction pile and the measured pile top velocity reflection wave curve measured in the step S5 to determine the viscosity damping coefficient of the pile body material of the specified large-diameter friction pile.
Preferably, in step S1, the control equation of the longitudinal vibration of the pile-side soil body and the pile-bottom soil body of the large-diameter friction pile is as follows:
wherein t is time; r is a radial coordinate;
vertical displacement of soil body;
the shear modulus of the soil body;
the viscosity damping coefficient of the soil body;
density of the soil body; j is a soil type, j is 1 or 2, j is 1 indicating a pile side soil of the large-diameter friction pile, and j is 2 indicating a pile bottom soil of the large-diameter friction pile.
Preferably, in step S1, based on the viscoelastic three-dimensional axisymmetric theory, the pile body material damping of the large-diameter friction pile is integrated, and a control equation of the longitudinal vibration of the large-diameter friction pile is established, as shown in formula (2):
in the formula u P Vertical displacement of the large-diameter friction pile; lambda P Lame constant, G, of large diameter friction pile P Shear modulus of large diameter friction pile, wherein P ＝E P μ P /(1+μ P )(1-2μ P )，G P ＝E P /2(1+μ P )，E P Is the elastic modulus, mu, of a large-diameter friction pile P The Poisson ratio of the large-diameter friction pile is obtained; eta P The viscous damping coefficient of the large-diameter friction pile is obtained; ρ is a unit of a gradient P The density of the large-diameter friction pile; z is a vertical coordinate; r is a radial coordinate; t is time;
establishing a longitudinal vibration control equation of the three-dimensional virtual soil pile based on a viscoelastic three-dimensional axial symmetry theory, wherein the equation is shown in formula (3):
in the formula u TFSP Vertical displacement of the three-dimensional virtual soil pile;
is the lame constant of the three-dimensional virtual soil pile,
is the shear modulus of a three-dimensional virtual soil pile, wherein,
the elastic modulus of the three-dimensional virtual soil pile is shown;
the Poisson ratio of the three-dimensional virtual soil pile is obtained;
the viscosity damping coefficient of the three-dimensional virtual soil pile is obtained;
the density of the three-dimensional virtual soil pile.
Preferably, in step S3, the soil displacement is reduced to zero at radial infinity:
according to the fact that the displacement and the stress of a pile side soil body and a large-diameter friction pile at the pile radius are equal, the displacement and the stress of a pile bottom soil body and a three-dimensional virtual soil pile at the pile radius are equal, and the displacement and the stress are shown in a formula (5) and a formula (6):
in the formula, r 0 The radius of the large-diameter friction pile; tau is P Is the shear modulus of the large-diameter friction pile,
is the shear modulus of the soil body on the pile side,
u TFSP is the shear modulus of the three-dimensional virtual soil pile,
is the shear modulus of the soil body at the bottom of the pile,
the boundary conditions for obtaining the pile top of the large-diameter friction pile are as follows:
σ P | z＝0 ＝-p(t)g(r) (7)
in the formula, σ P Is the normal stress of the large-diameter friction pile,
p (t), g (r) is uniform excitation force generated by an excitation hammer;
the vertical displacement of major diameter friction pile stake core department is finite value, and the boundary condition of major diameter friction pile stake core department is:
u P (z,r,t)| r＝0 limited value (8)
The vertical displacement of the three-dimensional virtual soil pile at the bedrock is zero, and the boundary conditions of the pile bottom of the three-dimensional virtual soil pile are as follows:
u P (z,r,t)| r＝0 limited value (9).
Preferably, the step S4 specifically includes the following steps:
s4.1, solving the displacement of the soil body;
performing Laplace transformation on the formula (1) to obtain:
in the formula (I), the compound is shown in the specification,
is composed of
Omega is the frequency of the excitation circle,
combining boundary conditions of the coupling vibration system of the pile side soil, the large-diameter friction pile, the three-dimensional virtual soil pile and the pile bottom soil in S3, a general solution of a formula (10) is obtained as follows:
in the formula (I), the compound is shown in the specification,
to be a predetermined coefficient, K 0 () A Bessel function is modified for the second class of zero order;
the shear stress of the earth is then expressed as:
in the formula, K 1 () A modified Bessel function of a second type;
s4.2, performing Laplace transformation on the longitudinal vibration control equation of the large-diameter friction pile established in the S2, and decomposing by using a separation variable method to obtain the displacement of the large-diameter friction pile;
performing Laplace transformation on the formula (2) to obtain:
in the formula of U P (z, r, ω) is u P (z, r, t) in a Ralsberg transform;
by a separation variable method, make U P ＝Z P (z)·R P (r), then equation (13) is expressed as:
wherein
Then the following results are obtained:
Z P″ (z)-(α P ) 2 Z P (z)＝0 (15)
obtaining α based on equation (14) P And beta P The relationship between them is:
the general solution of equation (15) and equation (16) is determined as:
R P (r)＝E P K 0 (β P r)+F P I 0 (β P r) (19)
in the formula, C P 、D P 、E P And F P Are all undetermined coefficients;
based on the boundary conditions at the pile core of the large-diameter friction pile, the basic solutions of the displacement, the normal stress and the shear stress of the large-diameter friction pile are respectively obtained as follows:
substituting equations (11), (12), (20), and (22) into equation (5) yields:
equation (23) and equation (24) are taken together:
β P I 1 (β P r 0 )+ζ P I 0 (β P r 0 )＝0 (25)
in the formula, ζ P The parameters of the pile-soil interaction are shown,
β P is the vibration mode characteristic value, beta, of the large-diameter friction pile P For n characteristic values
A vector of components;
solving the displacement solution of the large-diameter friction pile based on the superposition principle as follows:
in the formula (I), the compound is shown in the specification,
and
all the coefficients are to be determined,
by mixing
Substituting into formula (17) to obtain;
s4.3, performing Laplace transformation on the three-dimensional virtual soil pile longitudinal vibration control equation established in the S2, and decomposing by using a separation variable method to obtain the displacement of the three-dimensional virtual soil pile;
performing Laplace transformation on the formula (3) to obtain:
in the formula of U TFSP (z, r, ω) is u TFSP (z, r, t) in a Ralsberg transform;
by a separation variable method, make U TFSP ＝Z TFSP (z)·R TFSP (r), then equation (27) is expressed as:
wherein
Then the following results are obtained:
Z TFSP″ (z)-(α TFSP ) 2 Z TFSP (z)＝0 (29)
obtaining α based on equation (28) TFSP And beta TFSP The relationship between them is:
the general solution of equation (29) and equation (30) is determined as:
R TFSP (r)＝E TFSP K 0 (β TFSP r)+F TFSP I 0 (β TFSP r) (33)
in the formula, C TFSP 、D TFSP 、E TFSP And F TFSP Are all undetermined coefficients;
based on the boundary conditions of the three-dimensional virtual soil pile bottom, the basic solutions of the three-dimensional virtual soil pile displacement, the normal stress and the shear stress are respectively obtained as follows:
substituting equations (11), (12), (34), and (36) into equation (6) yields:
equation (37) and equation (38) are combined to obtain:
β TFSP I 1 (β TFSP r 0 )+ζ TFSP I 0 (β TFSP r 0 )＝0 (39)
in the formula, ζ TFSP Coupling parameters of a pile bottom soil body and a three-dimensional virtual soil pile are obtained,
β TFSP is the vibration mode characteristic value, beta, of the three-dimensional virtual soil pile TFSP For n characteristic values
A vector of components;
solving the displacement solution of the three-dimensional virtual soil pile based on the superposition principle as follows:
in the formula, C TFSP 、D TFSP All the coefficients are to be determined,
s4.4, substituting the formula (21) into the formula (7) and substituting the formula (40) into the formula (9) based on the boundary conditions of the pile top of the large-diameter friction pile and the three-dimensional virtual soil pile bottom to obtain:
wherein P (omega) is Laplace transformation of P (t), and H is the length of the soil layer on the bedrock;
s4.5, based on Bessel function I 0 () Orthogonality of (d) yields:
the orthogonality of equation (45) and equation (46) is used to multiply the equation of equation (43) by
While multiplying the two sides of the equation of formula (44) by
And in the interval [0, r 0 ]Integrating above to obtain:
in the formula (I), the compound is shown in the specification,
combining the displacement and stress continuous conditions on the interface of the large-diameter friction pile and the three-dimensional virtual soil pile to obtain:
in the formula, H P The length of the large-diameter friction pile;
simultaneous formulas (47) - (50) are solved to obtain undetermined coefficients in the displacement solution of the large-diameter friction pile
And
comprises the following steps:
wherein the content of the first and second substances,
solving and determining the frequency domain analytic solution of the displacement and the speed of the large-diameter friction pile as follows:
V P (z,r,ω)＝iωU P (z,r,ω) (56)
s4.6, acquiring pile top displacement and pile top speed reflected waves of the large-diameter friction pile;
based on the frequency domain analytic solution of the displacement and the speed of the large-diameter friction pile, obtaining a time domain semi-analytic solution of the pile top displacement and the speed of the large-diameter friction pile by utilizing inverse discrete Fourier transform, wherein the theoretical curve of the reflection wave of the pile top displacement and the pile top speed of the large-diameter friction pile is as follows:
u P (z,r,t)＝IFT[U P (z,r,ω)] (57)
wherein IFT is inverse Fourier transform;
the theoretical value of the velocity reflected wave of the pile top of the large-diameter friction pile is obtained.
Preferably, in the step S5, the pile-soil parameters include the length H of the soil layer on the bedrock and the shear modulus of the soil body
Viscous damping coefficient of soil mass
And density of the soil body
And radius r of large-diameter friction pile 0 Length H P Elastic modulus E P Poisson ratio mu P And density ρ P 。
Preferably, in step S5, the collecting site is selected to extract pile-soil parameters, and a detection device is selected, where the detection device includes a transient excitation device and a steady excitation device, and a plurality of detection points are symmetrically arranged with the top center of the specified large-diameter friction pile as the pile center according to the pile diameter of the specified large-diameter pile, and a sensor is installed at each detection point, and then the pile center of the specified large-diameter friction pile is used as the excitation point, and a pile top speed reflected wave actual measurement curve of the specified large-diameter friction pile is obtained by using the detection device to measure.
Preferably, detection equipment is selected according to the field condition of the specified large-diameter friction pile and foundation pile dynamic measuring instrument JG/T3055, transient excitation equipment in the detection equipment comprises a force hammer and a hammer pad for exciting wide pulses and narrow pulses, a mechanical sensor is arranged on the force hammer, the steady excitation equipment is set to be an electromagnetic steady excitation exciter, and the frequency sweeping range is 10-2000 Hz.
Preferably, the step S6 specifically includes the following steps:
s6.1, substituting the pile-soil parameters extracted on the site into a formula (58) to obtain a pile top velocity reflection wave theoretical curve of the specified large-diameter friction pile, and coinciding the pile top velocity reflection wave theoretical curve of the specified large-diameter friction pile with the pile top velocity reflection wave actual measurement curve measured in the step S5;
s6.2, calculating the coincidence degree of the theoretical curve of the pile top speed reflection wave of the specified large-diameter friction pile and the actually measured curve of the pile top speed reflection wave, and if the coincidence degree of the theoretical curve of the pile top speed reflection wave of the specified large-diameter friction pile and the actually measured curve of the measured pile top speed reflection wave is lower than 90%, entering the step S6.3; if the coincidence degree of the theoretical curve of the pile top velocity reflection wave of the specified large-diameter friction pile and the measured curve of the measured pile top velocity reflection wave is not lower than 90%, the step S6.4 is carried out;
s6.3, adjusting a viscosity damping coefficient eta in a theoretical curve of the velocity reflection wave of the pile top of the specified large-diameter friction pile P Until the coincidence degree of the theoretical curve of the pile top velocity reflection wave of the specified large-diameter friction pile and the measured curve of the measured pile top velocity reflection wave is not lower than 90%, the step S6.3 is carried out;
s6.4, according to the viscous damping coefficient eta in the theoretical curve of the velocity reflection wave of the pile top of the specified large-diameter friction pile P Determining the viscosity damping coefficient of the pile body material of the specified large-diameter friction pile, wherein the viscosity damping coefficient of the pile body material of the specified large-diameter friction pile is equal to the viscosity damping coefficient eta in the theoretical curve of the velocity reflection wave of the pile top of the specified large-diameter pile foundation P And determining the viscosity damping coefficient of the pile body material of the friction pile with the specified large diameter.
The invention has the following beneficial effects:
the invention provides a large-diameter friction pile material damping measurement and calculation method based on a low-strain reflection wave method, which comprehensively considers the vibration characteristic of a large-diameter friction pile, provides a three-dimensional virtual soil pile suitable for the large-diameter friction pile, constructs the three-dimensional virtual soil pile at the bottom of the large-diameter friction pile, comprehensively considers the influence of the fluctuation effect of the soil mass at the bottom of a large-diameter friction pile body on the vibration characteristic, establishes a longitudinal vibration control equation of the soil mass at the pile side of the large-diameter friction pile and the soil mass at the pile bottom, simultaneously fully considers the damping of a pile body material, establishes the longitudinal vibration control equation aiming at the large-diameter friction pile and the three-dimensional virtual soil pile based on a viscoelastic three-dimensional axial symmetry theory, solves and obtains a pile top velocity reflection wave theoretical curve of the large-diameter friction pile by combining the boundary conditions of a pile side soil-large-diameter friction pile-three-dimensional virtual soil pile-pile bottom soil coupling vibration system, the viscous damping coefficient of the pile body material in the theoretical curve of the velocity reflected wave of the pile top is adjusted and is superposed with the actually measured curve of the velocity reflected wave of the pile top obtained through actual measurement, so that the actual damping of the pile body material of the large-diameter friction pile is accurately determined.
The invention solves the problem of difficult measurement and calculation of the damping of the pile body material, is beneficial to determining the damping of the pile body material in the actual engineering, and lays a foundation for guiding the accuracy of the dynamic design of the large-diameter friction pile and improving the integrity of the low-strain detection pile body.
Drawings
FIG. 1 is a diagram of analysis of the pile top velocity reflection wave curve error; fig. 1(a) is a pile top velocity reflection wave curve calculated based on a three-dimensional elastic wave theory, and fig. 1(b) is a pile top velocity reflection wave curve actually measured based on a low-strain reflection method.
FIG. 2 is a flow chart of the method for measuring and calculating the damping of the large-diameter friction pile material based on the low-strain reflection wave method.
FIG. 3 is a schematic diagram of a planar strain model according to the present invention.
FIG. 4 is a pile tip velocity reflection curve for a given large diameter friction pile; fig. 4(a) is a theoretical curve of the velocity reflected wave of the pile top of the large-diameter friction pile under the condition of different pile body material viscosity damping coefficients, and fig. 4(b) is a comparison graph of the velocity reflected wave curve of the pile top of the specified large-diameter friction pile.
In the figure, r 0 Radius of large-diameter friction pile, r h To exciting the radius of the hammer, H P Length of friction pile of large diameter, H TFSP The length of the three-dimensional virtual soil pile is shown, H is the length of a soil layer on the bedrock, r is a radial coordinate, z is a vertical coordinate, and o is an origin of coordinates.
Detailed Description
The following further illustrates embodiments of the invention, by way of example and with reference to the accompanying drawings, in which:
taking a certain specified large-diameter friction pile as an example, determining the pile body material damping of the large-diameter friction pile by adopting the large-diameter friction pile material damping measuring and calculating method based on the low-strain reflection wave method, as shown in fig. 2, specifically comprises the following steps:
s1: constructing a plane strain model, as shown in fig. 3, including a large-diameter friction pile, a pile bottom soil body, a pile side soil body and a three-dimensional virtual soil pile formed by extending the large-diameter friction pile downwards to the top surface of the bedrock, and establishing a longitudinal vibration control equation of the large-diameter friction pile side soil body and the pile bottom soil body, as shown in formula (1):
wherein t is time; r is a radial coordinate;
vertical displacement of soil body;
the shear modulus of the soil body;
the viscosity damping coefficient of the soil body;
density of the soil body; j is a soil type, j is 1 or 2, j is 1 indicating a pile side soil of the large-diameter friction pile, and j is 2 indicating a pile bottom soil of the large-diameter friction pile.
S2: based on a viscoelastic three-dimensional axial symmetry theory, establishing a longitudinal vibration control equation for the large-diameter friction pile and the three-dimensional virtual soil pile respectively, wherein the pile body material damping of the large-diameter friction pile is comprehensively considered in the longitudinal vibration control equation of the large-diameter friction pile, and the longitudinal vibration control equation of the large-diameter friction pile is established, and is shown in formula (2):
in the formula u P Vertical displacement of the large-diameter friction pile; lambda [ alpha ] P Lame constant, G, of large diameter friction pile P Shear modulus of large diameter friction pile, wherein P ＝E P μ P /(1+μ P )(1-2μ P )，G P ＝E P /2(1+μ P )，E P Is the elastic modulus, mu, of a large-diameter friction pile P The Poisson ratio of the large-diameter friction pile is obtained; eta P The viscous damping coefficient of the large-diameter friction pile is obtained; rho P The density of the large-diameter friction pile; z is a vertical coordinate; r is a radial coordinate; t is time;
a longitudinal vibration control equation of the three-dimensional virtual soil pile based on a viscoelastic three-dimensional axisymmetric theory is shown in formula (3):
in the formula u TFSP Vertical displacement of the three-dimensional virtual soil pile;
is the lame constant of the three-dimensional virtual soil pile,
is the shear modulus of a three-dimensional virtual soil pile, wherein,
the elastic modulus of the three-dimensional virtual soil pile is shown;
the Poisson ratio of the three-dimensional virtual soil pile is obtained;
the viscosity damping coefficient of the three-dimensional virtual soil pile is obtained;
the density of the three-dimensional virtual soil pile.
S3: establishing boundary conditions of a pile side soil-large-diameter friction pile-three-dimensional virtual soil pile-pile bottom soil coupling vibration system, wherein the boundary conditions specifically comprise the following steps:
the displacement of the soil body is reduced to zero at radial infinite distance:
the displacement and the stress of the pile side soil body and the large-diameter friction pile at the pile radius are equal:
the displacement and the stress of the pile bottom soil body and the three-dimensional virtual soil pile at the pile radius are equal:
in the formula, r 0 Is the pile radius; tau is P Is the shear modulus of the large-diameter friction pile,
is the shear modulus of the soil body on the pile side,
u TFSP is the shear modulus of the three-dimensional virtual soil pile,
is the shear modulus of the soil body at the bottom of the pile,
the boundary conditions of the pile top of the large-diameter friction pile are as follows:
σ P | z＝0 ＝-p(t)g(r) (7)
in the formula, σ P Is the normal stress of the large-diameter friction pile,
p (t), g (r) is the uniform exciting force generated by the exciting hammer.
The vertical displacement of major diameter friction pile stake core department is finite value, and the boundary condition of major diameter friction pile stake core department is:
u P (z,r,t)| r＝0 limited value (8)
The vertical displacement of the three-dimensional virtual soil pile at the bedrock is zero, and the boundary conditions of the pile bottom of the three-dimensional virtual soil pile are as follows:
u P (z,r,t)| r＝0 limited value (9).
S4: solving a longitudinal vibration control equation of the pile side soil body and the pile bottom soil body of the large-diameter friction pile in the step S1 and a longitudinal vibration control equation of the large-diameter friction pile and the three-dimensional virtual soil pile in the step S2, and calculating to obtain a pile top speed reflection wave theoretical curve of the large-diameter friction pile by combining boundary conditions of a pile side soil-large-diameter friction pile-three-dimensional virtual soil pile-pile bottom soil coupling vibration system in the step S3, wherein the step S4 specifically comprises the following steps:
s4.1, solving the displacement of the soil body;
performing Laplace transformation on the formula (1) to obtain:
in the formula (I), the compound is shown in the specification,
is composed of
Omega is the frequency of the excitation circle,
combining the boundary conditions of the pile side soil-large diameter friction pile-three-dimensional virtual soil pile-pile bottom soil coupling vibration system in the S3, the general solution of the formula (10) is obtained as follows:
in the formula (I), the compound is shown in the specification,
to be a predetermined coefficient, K 0 () A Bessel function is modified for the second class of zero order;
the shear stress of the soil body is then expressed as:
in the formula, K 1 () A modified Bessel function of a second type;
s4.2, performing Laplace transformation on the longitudinal vibration control equation of the large-diameter friction pile established in the S2, and decomposing by using a separation variable method to obtain the displacement of the large-diameter friction pile;
performing Laplace transformation on the formula (2) to obtain:
in the formula of U P (z, r, ω) is u P (z, r, t) in a Ralsberg transform;
by a separation variable method, make U P ＝Z P (z)·R P (r), then equation (13) is expressed as:
wherein
Then the following results are obtained:
Z P″ (z)-(α P ) 2 Z P (z)＝0 (15)
obtaining α based on equation (14) P And beta P The relationship between them is:
the general solution of equation (15) and equation (16) is determined as:
R P (r)＝E P K 0 (β P r)+F P I 0 (β P r) (19)
in the formula, C P 、D P 、E P And F P Are all undetermined coefficients;
based on the boundary conditions at the pile core of the large-diameter friction pile, the basic solutions of the displacement, the normal stress and the shear stress of the large-diameter friction pile are respectively obtained as follows:
substituting equations (11), (12), (20), and (22) into equation (5) yields:
equation (23) and equation (24) are taken together:
β P I 1 (β P r 0 )+ζ P I 0 (β P r 0 )＝0 (25)
in the formula, ζ P The parameters of the pile-soil interaction are shown,
β P is the vibration mode characteristic value, beta, of the large-diameter friction pile P For n characteristic values
The vector of the composition is then calculated,
the function findzero can be obtained by using MATLAB;
solving the displacement solution of the large-diameter friction pile based on the superposition principle as follows:
in the formula (I), the compound is shown in the specification,
and
all the coefficients are to be determined,
by mixing
Substituting into formula (17) to obtain;
s4.3, performing Laplace transformation on the three-dimensional virtual soil pile longitudinal vibration control equation established in the S2, and decomposing by using a separation variable method to obtain the displacement of the three-dimensional virtual soil pile;
performing Laplace transformation on the formula (3) to obtain:
in the formula of U TFSP (z, r, ω) is u TFSP (z, r, t) in a Ralsberg transform;
by a separation variable method, make U TFSP ＝Z TFSP (z)·R TFSP (r), then equation (27) is expressed as:
wherein
Then the following results are obtained:
Z TFSP″ (z)-(α TFSP ) 2 Z TFSP (z)＝0 (29)
obtaining α based on equation (28) TFSP And beta TFSP The relationship between them is:
the general solutions of equation (29) and equation (30) are determined as:
R TFSP (r)＝E TFSP K 0 (β TFSP r)+F TFSP I 0 (β TFSP r) (33)
in the formula, C TFSP 、D TFSP 、E TFSP And F TFSP Are all undetermined coefficients;
based on the boundary conditions of the three-dimensional virtual soil pile bottom, the basic solutions of the three-dimensional virtual soil pile displacement, the normal stress and the shear stress are respectively obtained as follows:
substituting equations (11), (12), (34), and (36) into equation (6) yields:
equation (37) and equation (38) are combined to obtain:
β TFSP I 1 (β TFSP r 0 )+ζ TFSP I 0 (β TFSP r 0 )＝0 (39)
in the formula, ζ TFSP Coupling parameters of a pile bottom soil body and a three-dimensional virtual soil pile are obtained,
β TFSP is the vibration mode characteristic value, beta, of the three-dimensional virtual soil pile TFSP For n characteristic values
The vector of the composition is then calculated,
the function findzero can be obtained by using MATLAB;
solving the displacement solution of the three-dimensional virtual soil pile based on the superposition principle as follows:
in the formula, C TFSP 、D TFSP All the coefficients are to be determined,
s4.4, substituting the formula (21) into the formula (7) and substituting the formula (40) into the formula (9) based on the boundary conditions of the pile top of the large-diameter friction pile and the three-dimensional virtual soil pile bottom to obtain:
wherein P (omega) is Laplace transformation of P (t), and H is the length of the soil layer on the bedrock;
s4.5, based on Bessel function I 0 () Orthogonality of (d) yields:
the orthogonality of equation (45) and equation (46) is used to multiply the equation of equation (43) by
While multiplying the two sides of the equation of formula (44) by
And in the interval [0, r 0 ]Integrating above to obtain:
in the formula (I), the compound is shown in the specification,
combining the displacement and stress continuous conditions on the interface of the large-diameter friction pile and the three-dimensional virtual soil pile to obtain:
in the formula, H P The length of the large-diameter friction pile;
simultaneous formulas (47) - (50) are solved to obtain undetermined coefficients in the displacement solution of the large-diameter friction pile
And
comprises the following steps:
wherein the content of the first and second substances,
solving and determining the frequency domain analytic solution of the displacement and the speed of the large-diameter friction pile as follows:
V P (z,r,ω)＝iωU P (z,r,ω) (56)
s4.6, acquiring pile top displacement and pile top speed reflected waves of the large-diameter friction pile;
based on the frequency domain analytic solution of the displacement and the speed of the large-diameter friction pile, obtaining a time domain semi-analytic solution of the pile top displacement and the speed of the large-diameter friction pile by utilizing inverse discrete Fourier transform, wherein the theoretical curve of the reflection wave of the pile top displacement and the pile top speed of the large-diameter friction pile is as follows:
u P (z,r,t)＝IFT[U P (z,r,ω)] (57)
wherein IFT is inverse Fourier transform;
the theoretical value of the velocity reflected wave of the pile top of the large-diameter friction pile is obtained.
S5, carrying out field measurement on the friction pile with the designated large diameter based on a low-strain reflection wave method, and selecting and collecting field extraction pile-soil parameters, wherein the pile-soil parameters comprise the length H of a soil layer on the bedrock and the shear modulus of a soil body
Viscous damping coefficient of soil body
And density of the soil body
And radius r of large-diameter friction pile 0 Length H P Elastic modulus E P Poisson ratio mu P And density ρ P 。
And selecting detection equipment according to the field condition of the specified large-diameter friction pile and a foundation pile dynamic tester JG/T3055, and measuring a pile top speed reflected wave actual measurement curve of the specified large-diameter friction pile by using the detection equipment, wherein the detection equipment comprises transient excitation equipment and steady-state excitation equipment in the embodiment, the transient excitation equipment comprises a force hammer and a hammer pad for exciting wide pulses and narrow pulses, a mechanical sensor is arranged on the force hammer, the steady-state excitation equipment is set as an electromagnetic steady-state vibration exciter, the excitation force of the electromagnetic steady-state vibration exciter can be adjusted, and the frequency sweep range is 10-2000 Hz.
According to the pile diameter of the specified large-diameter pile, 2-4 detection points are symmetrically arranged by taking the top surface center of the specified large-diameter friction pile as a pile center, the distance between each detection point and the pile center is 2/3 of the length of the pile diameter, a sensor is respectively arranged at each detection point, the pile center of the specified large-diameter friction pile is taken as an excitation point, and a detection device is used for measuring to obtain a pile top speed reflected wave actual measurement curve of the specified large-diameter friction pile.
S6, substituting the pile-soil parameters extracted on the site into the pile top speed reflection wave theoretical curve of the large-diameter friction pile in the step S4 to obtain a pile top speed reflection wave theoretical curve of the specified large-diameter friction pile, fitting and analyzing the pile top speed reflection wave theoretical curve of the specified large-diameter friction pile and the measured pile top speed reflection wave curve measured in the step S5 to determine the viscosity damping coefficient of the pile body material of the specified large-diameter friction pile, and the step S6 specifically comprises the following steps:
s6.1, substituting the pile-soil parameters extracted on the site into a formula (58) to obtain a pile top velocity reflection wave theoretical curve of the specified large-diameter friction pile, and coinciding the pile top velocity reflection wave theoretical curve of the specified large-diameter friction pile with the pile top velocity reflection wave actual measurement curve measured in the step S5;
s6.2, calculating the coincidence degree of the theoretical curve of the pile top speed reflection wave of the specified large-diameter friction pile and the actually measured curve of the pile top speed reflection wave, and if the coincidence degree of the theoretical curve of the pile top speed reflection wave of the specified large-diameter friction pile and the actually measured curve of the measured pile top speed reflection wave is lower than 90%, entering the step S6.3; if the coincidence degree of the theoretical curve of the pile top velocity reflection wave of the specified large-diameter friction pile and the measured curve of the measured pile top velocity reflection wave is not lower than 90%, the step S6.4 is carried out;
s6.3, adjusting a viscosity damping coefficient eta in a theoretical curve of the velocity reflection wave of the pile top of the specified large-diameter friction pile P Until the coincidence degree of the theoretical curve of the pile top velocity reflection wave of the specified large-diameter friction pile and the measured curve of the measured pile top velocity reflection wave is not lower than 90%, the step S6.3 is carried out;
s6.4, substituting pile-soil parameters intoThe mapping relation between the theoretical curve of the velocity reflection wave of the pile top of the large-diameter friction pile and the damping of the pile body material can be obtained in the formula (58), namely
As shown in fig. 4, fig. 4(a) is a theoretical curve of velocity reflection wave of pile top corresponding to different viscosity damping coefficients of pile body material, which can be obtained from fig. 4(a), and as the damping of the pile body material increases, the amplitude of the reflected signal at the bottom of the pile decreases, therefore, according to the viscosity damping coefficient η in the theoretical curve of velocity reflection wave of pile top of the friction pile with specified large diameter P Determining the viscosity damping coefficient of the pile body material of the specified large-diameter friction pile, namely when the coincidence degree of the pile top speed reflection wave theoretical curve of the specified large-diameter friction pile and the measured pile top speed reflection wave actual measurement curve is not less than 90%, the viscosity damping coefficient of the pile body material of the specified large-diameter friction pile is equal to the viscosity damping coefficient eta in the pile top speed reflection wave theoretical curve of the specified large-diameter pile foundation P In this embodiment, by comparing the theoretical curve of the velocity reflected wave of the pile top of the specified large-diameter friction pile with the actually measured curve of the velocity reflected wave of the pile top, as shown in fig. 4(b), it is determined that the viscosity damping coefficient of the material of the pile body of the specified large-diameter friction pile in this embodiment is η P ＝1×10 5 Nm -2 s。
It is to be understood that the above description is not intended to limit the present invention, and the present invention is not limited to the above examples, and those skilled in the art may make modifications, alterations, additions or substitutions within the spirit and scope of the present invention.
Claims (9)
1. A large-diameter friction pile material damping measurement and calculation method based on a low-strain reflection wave method is characterized by comprising the following steps:
s1: constructing a plane strain model, wherein the plane strain model comprises a large-diameter friction pile, a pile bottom soil body, a pile side soil body and a three-dimensional virtual soil pile formed by extending the large-diameter friction pile downwards to the top surface of bedrock, and establishing a longitudinal vibration control equation of the pile side soil body and the pile bottom soil body of the large-diameter friction pile;
s2: based on a viscoelastic three-dimensional axial symmetry theory, establishing a longitudinal vibration control equation respectively aiming at the large-diameter friction pile and the three-dimensional virtual soil pile;
s3: establishing boundary conditions of a pile side soil-large-diameter friction pile-three-dimensional virtual soil pile-pile bottom soil coupling vibration system;
s4: solving a longitudinal vibration control equation of the pile side soil body and the pile bottom soil body of the large-diameter friction pile in the step S1 and a longitudinal vibration control equation of the large-diameter friction pile and the three-dimensional virtual soil pile in the step S2, and calculating to obtain a pile top speed reflection wave theoretical curve of the large-diameter friction pile by combining boundary conditions of a pile side soil-large-diameter friction pile-three-dimensional virtual soil pile-pile bottom soil coupling vibration system in the step S3;
s5, carrying out on-site measurement on the friction pile with the specified large diameter based on a low-strain reflection wave method to obtain a pile-soil parameter and a pile top speed reflection wave actual measurement curve of the friction pile with the specified large diameter;
and S6, substituting the pile-soil parameters extracted on the site into the pile top velocity reflection wave theoretical curve of the large-diameter friction pile in the step S4 to obtain a pile top velocity reflection wave theoretical curve of the specified large-diameter friction pile, and performing fitting analysis on the pile top velocity reflection wave theoretical curve of the specified large-diameter friction pile and the measured pile top velocity reflection wave curve measured in the step S5 to determine the viscosity damping coefficient of the pile body material of the specified large-diameter friction pile.
2. The method for measuring and calculating damping of large-diameter friction pile material based on low-strain reflection wave method as claimed in claim 1, wherein in step S1, the control equation of longitudinal vibration of the pile side soil body and the pile bottom soil body of the large-diameter friction pile is as follows:
wherein t is time; r is a radial coordinate;
vertical displacement of soil body;
the shear modulus of the soil body;
the viscosity damping coefficient of the soil body;
density of the soil body; j is a soil type, j is 1 or 2, j is 1 indicating a pile side soil of the large-diameter friction pile, and j is 2 indicating a pile bottom soil of the large-diameter friction pile.
3. The method for measuring and calculating damping of large-diameter friction pile material based on low-strain reflection wave method as claimed in claim 2, wherein in step S1, based on viscoelastic three-dimensional axisymmetric theory, the damping of pile body material of large-diameter friction pile is synthesized, and a control equation of longitudinal vibration of large-diameter friction pile is established, as shown in formula (2):
in the formula u P Vertical displacement of the large-diameter friction pile; lambda P Lame constant, G, of large diameter friction pile P Shear modulus of large diameter friction pile, wherein P ＝E P μ P /(1+μ P )(1-2μ P )，G P ＝E P /2(1+μ P )，E P Is the elastic modulus, mu, of a large-diameter friction pile P The Poisson ratio of the large-diameter friction pile is obtained; eta P The viscous damping coefficient of the large-diameter friction pile is obtained; rho P The density of the large-diameter friction pile; z is a vertical coordinate; r is a radial coordinate; t is time;
establishing a longitudinal vibration control equation of the three-dimensional virtual soil pile based on a viscoelastic three-dimensional axial symmetry theory, wherein the equation is shown in formula (3):
in the formula u TFSP Vertical displacement of the three-dimensional virtual soil pile;
is the lame constant of the three-dimensional virtual soil pile,
is the shear modulus of a three-dimensional virtual soil pile, wherein,
the elastic modulus of the three-dimensional virtual soil pile is shown;
the Poisson ratio of the three-dimensional virtual soil pile is obtained;
the viscosity damping coefficient of the three-dimensional virtual soil pile is obtained;
the density of the three-dimensional virtual soil pile.
4. The method for measuring and calculating the damping of the large-diameter friction pile material based on the low-strain reflection wave method as claimed in claim 3, wherein in the step S3, the soil displacement is reduced to zero at radial infinity:
according to the fact that the displacement and the stress of a pile side soil body and a large-diameter friction pile at the pile radius are equal, the displacement and the stress of a pile bottom soil body and a three-dimensional virtual soil pile at the pile radius are equal, and the displacement and the stress are shown in a formula (5) and a formula (6):
in the formula, r 0 Is the pile radius; tau is P Is the shear modulus of the large-diameter friction pile,
is the shear modulus of the soil body on the pile side,
u TFSP is the shear modulus of the three-dimensional virtual soil pile,
is the shear modulus of the soil body at the bottom of the pile,
the boundary conditions for obtaining the pile top of the large-diameter friction pile are as follows:
σ P | z＝0 ＝-p(t)g(r) (7)
in the formula, σ P Is the normal stress of the large-diameter friction pile,
p (t), g (r) is uniform exciting force generated by an exciting hammer;
the vertical displacement of major diameter friction pile stake core department is finite value, and the boundary condition of major diameter friction pile stake core department is:
u P (z,r,t)| r＝0 limited value (8)
The vertical displacement of the three-dimensional virtual soil pile at the bedrock is zero, and the boundary conditions of the pile bottom of the three-dimensional virtual soil pile are as follows:
u P (z,r,t)| r＝0 limited value (9).
5. The method for measuring and calculating damping of a large-diameter friction pile material based on the low-strain reflection wave method as claimed in claim 4, wherein the step S4 specifically includes the following steps:
s4.1, solving the displacement of the soil body;
performing Laplace transformation on the formula (1) to obtain:
in the formula (I), the compound is shown in the specification,
is composed of
Omega is the frequency of the excitation circle,
combining the boundary conditions of the pile side soil-large diameter friction pile-three-dimensional virtual soil pile-pile bottom soil coupling vibration system in the S3, the general solution of the formula (10) is obtained as follows:
in the formula (I), the compound is shown in the specification,
to be a predetermined coefficient, K 0 () A Bessel function is modified for the second class of zero order;
the shear stress of the soil body is then expressed as:
in the formula, K 1 () A modified Bessel function of a second type;
s4.2, performing Laplace transformation on the longitudinal vibration control equation of the large-diameter friction pile established in the S2, and decomposing by using a separation variable method to obtain the displacement of the large-diameter friction pile;
performing Laplace transformation on the formula (2) to obtain:
in the formula of U P (z, r, ω) is u P (z, r, t) in a Ralsberg transform;
by a separation variable method, make U P ＝Z P (z)·R P (r), then equation (13) is expressed as:
wherein
Then the following results are obtained:
Z P″ (z)-(α P ) 2 Z P (z)＝0 (15)
obtaining α based on equation (14) P And beta P The relationship between them is:
the general solution of equation (15) and equation (16) is determined as:
R P (r)＝E P K 0 (β P r)+F P I 0 (β P r) (19)
in the formula, C P 、D P 、E P And F P Are all undetermined coefficients;
based on the boundary conditions at the pile core of the large-diameter friction pile, the basic solutions of the displacement, the normal stress and the shear stress of the large-diameter friction pile are respectively obtained as follows:
substituting equations (11), (12), (20), and (22) into equation (5) yields:
equation (23) and equation (24) are taken together:
β P I 1 (β P r 0 )+ζ P I 0 (β P r 0 )＝0 (25)
in the formula, ζ P Is the interaction parameter of the pile soil,
β P is the vibration mode characteristic value, beta, of the large-diameter friction pile P For n characteristic values
A vector of components;
solving the displacement solution of the large-diameter friction pile based on the superposition principle as follows:
in the formula (I), the compound is shown in the specification,
and
all the coefficients are to be determined,
by mixing
Substituting into formula (17) to obtain;
s4.3, performing Laplace transformation on the three-dimensional virtual soil pile longitudinal vibration control equation established in the S2, and decomposing by using a separation variable method to obtain the displacement of the three-dimensional virtual soil pile;
performing Laplace transformation on the formula (3) to obtain:
in the formula of U TFSP (z, r, ω) is u TFSP (z, r, t) in a Ralsberg transform;
making U by adopting a separation variable method TFSP ＝Z TFSP (z)·R TFSP (r), then equation (27) is expressed as:
wherein
Then the following results are obtained:
Z TFSP″ (z)-(α TFSP ) 2 Z TFSP (z)＝0 (29)
obtaining α based on equation (28) TFSP And beta TFSP The relationship between them is:
the general solutions of equation (29) and equation (30) are determined as:
R TFSP (r)＝E TFSP K 0 (β TFSP r)+F TFSP I 0 (β TFSP r) (33)
in the formula, C TFSP 、D TFSP 、E TFSP And F TFSP Are all undetermined coefficients;
based on the boundary conditions of the three-dimensional virtual soil pile bottom, the basic solutions of the three-dimensional virtual soil pile displacement, the normal stress and the shear stress are respectively obtained as follows:
substituting equations (11), (12), (34), and (36) into equation (6) yields:
equation (37) and equation (38) are combined to obtain:
β TFSP I 1 (β TFSP r 0 )+ζ TFSP I 0 (β TFSP r 0 )＝0 (39)
in the formula, ζ TFSP Coupling parameters of a pile bottom soil body and a three-dimensional virtual soil pile are obtained,
β TFSP is the vibration mode characteristic value, beta, of the three-dimensional virtual soil pile TFSP For n characteristic values
A vector of components;
solving the displacement solution of the three-dimensional virtual soil pile based on the superposition principle as follows:
in the formula, C TFSP 、D TFSP All the coefficients are to be determined,
s4.4, substituting the formula (21) into the formula (7) and substituting the formula (40) into the formula (9) based on the boundary conditions of the pile top of the large-diameter friction pile and the three-dimensional virtual soil pile bottom to obtain:
wherein P (omega) is Laplace transformation of P (t), and H is the length of the soil layer on the bedrock;
s4.5, based on Bessel function I 0 () Orthogonality of (a) to obtain：
The orthogonality of equation (45) and equation (46) is used to multiply the equation of equation (43) by
While multiplying the two sides of the equation of formula (44) by
And in the interval [0, r 0 ]Integrating above to obtain:
in the formula (I), the compound is shown in the specification,
combining the displacement and stress continuous conditions on the interface of the large-diameter friction pile and the three-dimensional virtual soil pile to obtain the following results:
in the formula, H P The length of the large-diameter friction pile;
simultaneous formulas (47) - (50) are solved to obtain undetermined coefficients in the displacement solution of the large-diameter friction pile
And
comprises the following steps:
wherein the content of the first and second substances,
solving and determining the frequency domain analytic solution of the displacement and the speed of the large-diameter friction pile as follows:
V P (z,r,ω)＝iωU P (z,r,ω) (56)
s4.6, acquiring pile top displacement and pile top speed reflected waves of the large-diameter friction pile;
based on the frequency domain analytic solution of the displacement and the speed of the large-diameter friction pile, obtaining a time domain semi-analytic solution of the pile top displacement and the speed of the large-diameter friction pile by utilizing inverse discrete Fourier transform, wherein the theoretical curve of the reflection wave of the pile top displacement and the pile top speed of the large-diameter friction pile is as follows:
u P (z,r,t)＝IFT[U P (z,r,ω)] (57)
wherein IFT is inverse Fourier transform;
the theoretical value of the velocity reflected wave of the pile top of the large-diameter friction pile is obtained.
6. The method for measuring and calculating damping of large-diameter friction pile material based on low-strain reflection wave method as claimed in claim 1, wherein in step S5, the pile-soil parameters include length H of soil layer on bedrock and shear modulus of soil body
Viscous damping coefficient of soil mass
And density of the soil body
And radius r of large-diameter friction pile 0 Length H P Elastic modulus E P Poisson ratio mu P And density ρ P 。
7. The method for measuring and calculating damping of large-diameter friction pile material based on low-strain reflection wave method as claimed in claim 1, wherein in step S5, the collection field is selected to extract pile-soil parameters, the detection device is selected, the detection device comprises a transient excitation device and a steady-state excitation device, a plurality of detection points are symmetrically arranged by using the center of the top surface of the designated large-diameter friction pile as the pile center according to the size of the pile diameter of the designated large-diameter pile, a sensor is installed on each detection point, then the pile center of the designated large-diameter friction pile is used as the excitation point, and the detection device is used to measure and obtain the measured curve of the pile top velocity reflection wave of the designated large-diameter friction pile.
8. The method for measuring and calculating the damping of the large-diameter friction pile material based on the low-strain reflection wave method is characterized in that detection equipment is selected according to the field condition of the specified large-diameter friction pile and foundation pile dynamic measuring instrument JG/T3055, transient excitation equipment in the detection equipment comprises a force hammer and a hammer pad for exciting wide pulses and narrow pulses, a mechanical sensor is arranged on the force hammer, the steady excitation equipment is an electromagnetic steady excitation device, and the frequency sweep range is 10-2000 Hz.
9. The method for measuring and calculating damping of a large-diameter friction pile material based on the low-strain reflection wave method as claimed in claim 5, wherein the step S6 specifically includes the following steps:
s6.1, substituting the pile-soil parameters extracted on the site into a formula (58) to obtain a pile top velocity reflection wave theoretical curve of the specified large-diameter friction pile, and coinciding the pile top velocity reflection wave theoretical curve of the specified large-diameter friction pile with the pile top velocity reflection wave actual measurement curve measured in the step S5;
s6.2, calculating the coincidence degree of the theoretical curve of the pile top speed reflection wave of the specified large-diameter friction pile and the actually measured curve of the pile top speed reflection wave, and if the coincidence degree of the theoretical curve of the pile top speed reflection wave of the specified large-diameter friction pile and the actually measured curve of the measured pile top speed reflection wave is lower than 90%, entering the step S6.3; if the coincidence degree of the theoretical curve of the pile top velocity reflection wave of the specified large-diameter friction pile and the measured curve of the measured pile top velocity reflection wave is not lower than 90%, the step S6.4 is carried out;
s6.3, adjusting the viscosity damping coefficient eta in the theoretical curve of the velocity reflection wave of the pile top of the specified large-diameter friction pile P Up to the pile top speed of the specified large-diameter friction pileThe coincidence degree of the wave-shooting theoretical curve and the measured pile top speed reflection wave actual measurement curve is not less than 90%, and the step S6.3 is carried out;
s6.4, according to the viscous damping coefficient eta in the theoretical curve of the velocity reflection wave of the pile top of the specified large-diameter friction pile P Determining the viscosity damping coefficient of the pile body material of the specified large-diameter friction pile, wherein the viscosity damping coefficient of the pile body material of the specified large-diameter friction pile is equal to the viscosity damping coefficient eta in the theoretical curve of the velocity reflection wave of the pile top of the specified large-diameter pile foundation P And determining the viscosity damping coefficient of the pile body material of the friction pile with the specified large diameter.
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| CN113373990A (en) * | 2021-06-21 | 2021-09-10 | 福建工程学院 | Method for determining optimal placement position of sensor in low strain detection of pile foundation |
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2022
- 2022-06-02 CN CN202210623702.XA patent/CN114882962B/en active Active
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| US20070006652A1 (en) * | 2005-07-06 | 2007-01-11 | Abnaki Systems, Inc. | Load measuring sensor and method |
| US20080011091A1 (en) * | 2006-06-27 | 2008-01-17 | Abnaki Systems, Inc. | Method for measuring loading and temperature in structures and materials by measuring changes in natural frequencies |
| CN111549833A (en) * | 2020-05-11 | 2020-08-18 | 安徽建大交通科技有限公司 | Foundation pile detection method and system and storage medium |
| CN113373990A (en) * | 2021-06-21 | 2021-09-10 | 福建工程学院 | Method for determining optimal placement position of sensor in low strain detection of pile foundation |
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| 肖?;王奎华;王孟波;: "基于桩侧虚土桩模型的桩-桩芯土竖向动力响应", 浙江大学学报(工学版), no. 08, 15 August 2020 (2020-08-15) * |
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