CN114882962B - Large-diameter friction pile material damping measuring and calculating method based on low-strain reflection wave method - Google Patents
Large-diameter friction pile material damping measuring and calculating method based on low-strain reflection wave method Download PDFInfo
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Abstract
The invention discloses a method for measuring and calculating damping of a large-diameter friction pile material based on a low-strain reflection wave method, and particularly relates to the technical field of civil engineering. According to the invention, a plane strain model is constructed, a longitudinal vibration control equation is established for soil bodies at the pile side and the pile bottom of the large-diameter friction pile, then a longitudinal vibration control equation is established for the large-diameter friction pile and the three-dimensional virtual soil pile based on a viscoelastic three-dimensional axisymmetric theory, the boundary conditions of a pile side soil-large-diameter friction pile-three-dimensional virtual soil pile-pile bottom soil coupling vibration system are combined, the longitudinal vibration control equation is solved to obtain a pile top velocity reflection wave theoretical curve, pile-soil parameters of the specified large-diameter pile and the pile top velocity reflection wave actual measurement curve are acquired, the pile top velocity reflection wave theoretical curve of the specified large-diameter pile is overlapped with the actual measurement curve of the actual measured pile top velocity reflection wave, and the viscous damping coefficient of pile body materials is determined, so that the problem of pile body material damping measurement difficulty in actual engineering is effectively solved.
Description
Technical Field
The invention relates to the technical field of civil engineering, in particular to a method for measuring and calculating damping of a large-diameter friction pile material based on a low-strain reflection wave method.
Background
The low strain method is used as a detection method based on shock elastic waves, and is currently becoming a mainstream method for detecting the integrity of foundation piles, and the integrity of the detected piles is judged by applying low-energy shock load on the pile tops, obtaining a response time course curve of measured acceleration (or speed), and analyzing a time domain and a frequency domain by using a one-dimensional linear fluctuation theory.
The pile-soil longitudinal coupling vibration theory is only suitable for a relatively slender pile foundation, however, as the complexity of a building increases, the requirements on the bearing capacity of the pile foundation are higher and the radius of the pile foundation is larger, and the pile foundation one-dimensional fluctuation theory is adopted to be applied to the research of pile-soil longitudinal coupling vibration problem to generate larger errors.
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 transmitted when the pile body is subjected to transient concentrated load in low-strain detection, axisymmetric wave equation description is adopted, a pile top speed reflection wave curve is obtained by solving, in the practical application process, for the same pile body, the pile top speed reflection wave curve obtained by solving through the three-dimensional elastic wave theory is shown in a figure 1 (a), the pile top speed reflection wave curve obtained by actual measurement through a low-strain reflection method is shown in a figure 1 (b), by comparing the figure 1 (a) with the figure 1 (b), the pile top speed reflection wave curve calculated through the three-dimensional elastic wave theory is obviously larger than an actual measurement value, fluctuation between an initial signal and the pile bottom reflection signal is also larger, the effect of damping of a pile body material is not considered when the pile top speed reflection wave curve is solved through the three-dimensional elastic wave theory, and the damping of the pile body material is well known to enable waves to be dissipated in the transmission process, and the damping effect of the pile body material is not considered when the three-dimensional elastic wave theory is applied to the pile body is large in the theoretical damping effect.
Therefore, the existing pile foundation low strain reflected wave method can only be used for detecting the integrity of the pile foundation, the pile length and the elastic wave speed of the pile body, and cannot be used for measuring and calculating the damping of the pile body material, the determination of the damping of the pile body material at the present stage is mainly estimated by means of indoor experimental data of concrete materials or experience of experts in the field, the damping of the pile body material of the large-diameter pile cannot be adjusted according to the actual condition of the pile foundation, the error is large, the applicability is poor, and the damping of the pile body material of the large-diameter pile is difficult to accurately obtain on site.
Disclosure of Invention
The invention aims to solve the defects of the prior art, and provides a large-diameter friction pile material damping measuring and calculating method based on a low-strain reflection wave method.
The invention adopts the following technical scheme:
a method for measuring and calculating damping of a large-diameter friction pile material 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 the large-diameter friction pile extending downwards to the top surface of a bedrock, and establishing a longitudinal vibration control equation of the large-diameter friction pile side soil body and the pile bottom soil body;
s2: based on a viscoelastic three-dimensional axisymmetry theory, a longitudinal vibration control equation is established for the large-diameter friction pile and the three-dimensional virtual soil pile respectively;
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 a pile side soil body and a 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 a three-dimensional virtual soil pile in the step S2, and calculating to obtain a pile top velocity 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, performing field measurement on the specified large-diameter friction pile based on a low-strain reflection wave method to obtain pile-soil parameters and pile top speed reflection wave actual measurement curves of the specified large-diameter friction pile;
s6, substituting pile-soil parameters extracted in the acquisition site into the pile top speed reflected wave theoretical curve of the large-diameter friction pile in the step S4 to obtain a pile top speed reflected wave theoretical curve of the specified large-diameter friction pile, and then carrying out fitting analysis on the pile top speed reflected wave theoretical curve of the specified large-diameter friction pile and the pile top speed reflected wave actual measurement curve measured in the step S5 to determine the viscous damping coefficient of the pile body material of the specified large-diameter friction pile.
Preferably, in the step S1, the longitudinal vibration control equation of the pile side soil body and the pile bottom soil body of the large-diameter friction pile is:
wherein t is time; r is a radial coordinate;is the vertical displacement of the soil body; />Is the shear modulus of the soil body; />Is the viscous damping coefficient of the soil body; />Is the density of the soil body; j is the soil type, j=1, 2, j=1 represents the pile side soil of the large-diameter friction pile, and j=2 represents the pile bottom soil of the large-diameter friction pile.
Preferably, in the step S1, based on the viscoelastic three-dimensional axisymmetry theory, pile body material damping of the large-diameter friction pile is integrated, and a longitudinal vibration control equation of the large-diameter friction pile is established, as shown in formula (2):
wherein u is P Vertical displacement of the large-diameter friction pile; lambda (lambda) P Ramez constant for large diameter friction pile, G P Is the shear modulus of a large diameter friction pile, wherein lambda P ＝E P μ P /(1+μ P )(1-2μ P )，G P ＝E P /2(1+μ P )，E P Elastic modulus, mu, of large-diameter friction pile P Poisson ratio of the large-diameter friction pile; η (eta) P The viscous damping coefficient of the large-diameter friction pile; ρ P The density of the friction pile with large diameter; z is a vertical coordinate; r is a radial coordinate; t is time;
based on a viscoelastic three-dimensional axisymmetry theory, a longitudinal vibration control equation of the three-dimensional virtual soil pile is established, as shown in a formula (3):
wherein u is TFSP Vertical displacement of the three-dimensional virtual soil pile;is the Lamex constant of the three-dimensional virtual soil pile, < ->Is the shear modulus of the three-dimensional virtual soil pile, wherein ∈>The elastic modulus of the three-dimensional virtual soil pile; />Poisson ratio of the three-dimensional virtual soil pile; />The viscous damping coefficient of the three-dimensional virtual soil pile; />Is the density of the three-dimensional virtual soil pile.
Preferably, 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 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, and the displacement and the stress are shown in the formula (5) and the formula (6):
wherein r is 0 The radius of the friction pile is the large diameter; τ P For the shear modulus of a large diameter friction pile,is the shear modulus of the soil body at the pile side +.>u TFSP Shear modulus of three-dimensional virtual soil pile +.>Is the shear modulus of the pile bottom soil body, +.>
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 sigma P Is the normal stress of the large-diameter friction pile,p (t) g (r) is uniformly distributed exciting force generated by the exciting hammer;
the vertical displacement of the pile core of the large-diameter friction pile is a limited value, and the boundary condition of the pile core of the large-diameter friction pile is as follows:
u P (z,r,t)| r＝0 =finite 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 =finite value (9).
Preferably, in the step S4, the method specifically includes the following steps:
s4.1, solving soil displacement;
laplace transformation is carried out on the formula (1) to obtain:
in the method, in the process of the invention,is->Is the Law transformation, ω is the excitation circle frequency, +.>
Combining boundary conditions of the pile side soil-large-diameter friction pile-three-dimensional virtual soil pile-pile bottom soil coupling vibration system in the step S3 to obtain general solution of the formula (10):
in the method, in the process of the invention,to be determined as coefficient, K 0 () Correcting a Bessel function for the second class zero order;
the shear stress of the soil mass is expressed as:
wherein K is 1 () Correcting the Bessel function for the second class first order;
s4.2, performing Laplace transformation on the longitudinal vibration control equation of the large-diameter friction pile established in the S2, decomposing by using a separation variable method, and solving the displacement of the large-diameter friction pile;
laplace transformation is carried out on the formula (2) to obtain:
in U P (z, r, ω) is u P A Laplace transformation of (z, r, t);
by adopting a separation variable method, U is led to P ＝Z P (z)·R P (r), then equation (13) is expressed as:
wherein the method comprises the steps ofThe following is obtained:
Z P″ (z)-(α P ) 2 Z P (z)＝0 (15)
obtaining alpha based on formula (14) P And beta P The relation between the two 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)
wherein C is P 、D P 、E P And F P All are undetermined coefficients;
based on boundary conditions at the pile core of the large-diameter friction pile, basic solutions of displacement, normal stress and shear stress of the large-diameter friction pile are respectively obtained:
substituting formulas (11), (12), (20) and (22) into formula (5) yields:
combining equation (23) and equation (24) yields:
β P I 1 (β P r 0 )+ζ P I 0 (β P r 0 )＝0 (25)
in zeta P Is the interaction parameter of the pile soil,β P is a special vibration mode of large-diameter friction pileSign value, beta P For n eigenvalues->A vector of components;
the displacement solution of the large-diameter friction pile is obtained based on the superposition principle:
in the method, in the process of the invention,and->Are all undetermined coefficients, < >>By putting->Substituting the obtained product into a formula (17) for calculation;
s4.3, performing Laplace transformation on the longitudinal vibration control equation of the three-dimensional virtual soil pile established in the S2, decomposing by using a separation variable method, and solving the displacement of the three-dimensional virtual soil pile;
laplace transformation is carried out on the formula (3) to obtain:
in U TFSP (z, r, ω) is u TFSP A Laplace transformation of (z, r, t);
by adopting a separation variable method, U is led to TFSP ＝Z TFSP (z)·R TFSP (r), then equation (27) is expressed as:
wherein the method comprises the steps ofThe following is obtained:
Z TFSP″ (z)-(α TFSP ) 2 Z TFSP (z)＝0 (29)
obtaining alpha based on formula (28) TFSP And beta TFSP The relation between the two 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)
wherein C is TFSP 、D TFSP 、E TFSP And F TFSP All are undetermined coefficients;
based on the boundary conditions of the pile bottom of the three-dimensional virtual soil pile, the basic solutions of the displacement, the normal stress and the shear stress of the three-dimensional virtual soil pile are respectively obtained as follows:
substituting equations (11), (12), (34) and (36) into equation (6) yields:
combining equation (37) and equation (38) yields:
β TFSP I 1 (β TFSP r 0 )+ζ TFSP I 0 (β TFSP r 0 )＝0 (39)
in zeta TFSP The coupling parameters of the pile bottom soil body and the three-dimensional virtual soil pile,β TFSP is the vibration mode characteristic value, beta, of the three-dimensional virtual soil pile TFSP For n eigenvalues->A vector of components;
the displacement solution of the three-dimensional virtual soil pile is obtained based on the superposition principle:
wherein C is TFSP 、D TFSP Are all the coefficients to be determined and are all the coefficients 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 boundary conditions of the pile bottom of the three-dimensional virtual soil pile, so as to obtain the following components:
wherein P (omega) is Lawster transformation of P (t), and H is the length of the upper soil layer of the bedrock;
s4.5 based on Bessel function I 0 () Is obtained by:
multiplying the orthogonality of equation (45) and equation (46) by the two equations of equation (43)Is multiplied by +.about.respectively on both sides of equation (44)>And in interval [0, r 0 ]Integrating to obtain:
in the method, in the process of the invention,
and combining 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 components:
wherein H is P Is the length of the large-diameter friction pile;
simultaneous equations (47) - (50), solving to obtain undetermined coefficients in the large-diameter friction pile displacement solutionAnd->The method comprises the following steps:
wherein,
solving a frequency domain analysis solution for determining the displacement and the speed of the large-diameter friction pile is as follows:
V P (z,r,ω)＝iωU P (z,r,ω) (56)
s4.6, pile top displacement and pile top speed reflection waves of the large-diameter friction pile are obtained;
based on the frequency domain analytic solution of the displacement and the speed of the large-diameter friction pile, the time domain semi-analytic solution of the pile top displacement and the speed of the large-diameter friction pile is obtained by utilizing the inverse discrete Fourier transform, and the pile top displacement and the pile top speed reflection wave theoretical curve of the large-diameter friction pile is obtained by the following steps:
u P (z,r,t)＝IFT[U P (z,r,ω)] (57)
wherein IFT is inverse fourier transform;is the theoretical value of the pile top speed reflected wave of the large-diameter friction pile.
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 bodyViscous damping coefficient of soil body->And density of soil mass->Radius r of large diameter friction pile 0 Length H P Modulus of elasticity E P Poisson's ratio mu P And density ρ P 。
Preferably, in step S5, pile-soil parameters are extracted at the selected collection site, a detection device is selected, the detection device comprises a transient excitation device and a steady excitation device, a plurality of detection points are symmetrically arranged by taking the center of the top surface of the designated large-diameter friction pile as a pile core according to the size of the pile diameter of the designated large-diameter pile, a sensor is installed on each detection point, and then the pile core of the designated large-diameter friction pile is taken as an excitation point, and the pile top velocity reflected wave actual measurement curve of the designated large-diameter friction pile is measured by the detection device.
Preferably, a detection device is selected according to the site condition of a specified large-diameter friction pile and JG/T3055 of a foundation pile dynamic tester, transient excitation equipment in the detection device comprises a force hammer and a hammer pad for exciting wide pulses and narrow pulses, a mechanical sensor is arranged on the force hammer, a steady-state excitation device is an electromagnetic steady-state vibration exciter, and the frequency sweeping range is 10-2000 Hz.
Preferably, in the step S6, the method specifically includes the following steps:
s6.1, substituting pile-soil parameters extracted from an acquisition site into a formula (58) to obtain a pile top speed reflected wave theoretical curve of the specified large-diameter friction pile, and overlapping the pile top speed reflected wave theoretical curve of the specified large-diameter friction pile with the pile top speed reflected wave actual measurement curve measured in the step S5;
s6.2, calculating the superposition degree of a pile top speed reflected wave theoretical curve and a pile top speed reflected wave actual measurement curve of the specified large-diameter friction pile, and if the superposition degree of the pile top speed reflected wave theoretical curve and the measured pile top speed reflected wave actual measurement curve of the specified large-diameter friction pile is lower than 90%, entering into the step S6.3; if the superposition degree of the pile top speed reflected wave theoretical curve of the specified large-diameter friction pile and the measured pile top speed reflected wave actual measurement curve is not lower than 90%, entering a step S6.4;
s6.3, adjusting the viscous damping coefficient eta in the pile top speed reflected wave theoretical curve of the specified large-diameter friction pile P Pile top speed reflected wave theoretical curve for specified large diameter friction pileThe superposition degree of the line and the measured pile top velocity reflected wave actual measurement curve is not lower 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 reflected wave of the pile top of the specified large-diameter friction pile P Determining the viscous damping coefficient of the pile body material of the specified large-diameter friction pile, wherein the viscous damping coefficient of the pile body material of the specified large-diameter friction pile is equal to the viscous damping coefficient eta in the theoretical curve of the speed reflected wave of the pile top of the specified large-diameter pile foundation P Thereby determining the viscous damping coefficient of the pile body material of the designated large-diameter friction pile.
The invention has the following beneficial effects:
the invention provides a method for measuring and calculating the damping of a large-diameter friction pile material based on a low-strain reflection wave method, comprehensively considers the vibration characteristics of a large-diameter friction pile, provides a three-dimensional virtual soil pile suitable for the large-diameter friction pile, constructs a 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 body at the bottom of the large-diameter friction pile body on the vibration characteristics of the large-diameter friction pile body, establishes a longitudinal vibration control equation of the soil body at the pile side and the soil body at the pile bottom of the large-diameter friction pile, simultaneously fully considers the damping of the pile body material, respectively establishes a longitudinal vibration control equation for the large-diameter friction pile and the three-dimensional virtual soil pile based on a viscoelastic three-dimensional axisymmetric theory, combines the boundary conditions of pile side soil-large-diameter friction pile-three-dimensional virtual soil pile-pile bottom soil coupling vibration system, solves to obtain a pile top velocity reflection wave theoretical curve of the large-diameter friction pile, and accurately determines the actual damping of the large-diameter friction pile body material by adjusting the viscosity damping coefficient of the pile top velocity reflection wave theoretical curve and coinciding with the obtained pile top velocity reflection wave actual measurement curve.
The invention solves the problem of difficult measurement and calculation of pile body material damping, is beneficial to the determination of pile body material damping in actual engineering, and lays a foundation for guiding the accuracy of large-diameter friction pile power design and improving the integrity of low-strain detection pile bodies.
Drawings
FIG. 1 is a pile-top velocity reflected wave curve error analysis chart; 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 a method for measuring and calculating the damping of a large-diameter friction pile material based on a low-strain reflection wave method.
FIG. 3 is a schematic view of a planar strain model according to the present invention.
FIG. 4 is a pile-top velocity reflection wave curve for a given large diameter friction pile; fig. 4 (a) is a theoretical curve of pile top velocity reflected waves of a large-diameter friction pile under the condition of viscous damping coefficients of different pile body materials, and fig. 4 (b) is a comparison graph of pile top velocity reflected wave curves of specified large-diameter friction piles.
In the figure, r 0 Radius r of large diameter friction pile h To the radius of the exciting hammer, H P For the length of the large-diameter friction pile, H TFSP The three-dimensional virtual soil pile is the length of a three-dimensional virtual soil pile, H is the length of a soil layer on a bedrock, r is a radial coordinate, z is a vertical coordinate, and o is a coordinate origin.
Detailed Description
The following is a further description of embodiments of the invention, taken in conjunction with the accompanying drawings and a study area:
taking a specific large-diameter friction pile as an example, the pile body material damping of the large-diameter friction pile is determined by adopting the large-diameter friction pile material damping measuring and calculating method based on the low-strain reflection wave method, which is shown in fig. 2, and specifically comprises the following steps:
s1: the method comprises the steps of constructing a plane strain model, as shown in fig. 3, 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 the fact that the large-diameter friction pile extends downwards to a bedrock top surface, 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 a formula (1):
wherein t is timeA compartment; r is a radial coordinate;is the vertical displacement of the soil body; />Is the shear modulus of the soil body; />Is the viscous damping coefficient of the soil body; />Is the density of the soil body; j is the soil type, j=1, 2, j=1 represents the pile side soil of the large-diameter friction pile, and j=2 represents the pile bottom soil of the large-diameter friction pile.
S2: based on a viscoelastic three-dimensional axisymmetry theory, a longitudinal vibration control equation is established for the large-diameter friction pile and the three-dimensional virtual soil pile respectively, wherein 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 as shown in a formula (2):
wherein u is P Vertical displacement of the large-diameter friction pile; lambda (lambda) P Ramez constant for large diameter friction pile, G P Is the shear modulus of a large diameter friction pile, wherein lambda P ＝E P μ P /(1+μ P )(1-2μ P )，G P ＝E P /2(1+μ P )，E P Elastic modulus, mu, of large-diameter friction pile P Poisson ratio of the large-diameter friction pile; η (eta) P The viscous damping coefficient of the large-diameter friction pile; ρ P The density of the friction pile with large diameter; z is a vertical coordinate; r is a radial coordinate; t is time;
the longitudinal vibration control equation of the three-dimensional virtual soil pile based on the viscoelastic three-dimensional axisymmetry theory is established, and is shown as a formula (3):
wherein u is TFSP Vertical displacement of the three-dimensional virtual soil pile;is the Lamex constant of the three-dimensional virtual soil pile, < ->Is the shear modulus of the three-dimensional virtual soil pile, wherein ∈>The elastic modulus of the three-dimensional virtual soil pile; />Poisson ratio of the three-dimensional virtual soil pile; />The viscous damping coefficient of the three-dimensional virtual soil pile; />Is 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 soil displacement is reduced to zero at radial infinity:
the displacement and stress of the pile side soil body and the large-diameter friction pile at the pile radius are equal:
the displacement and stress of the pile bottom soil body and the three-dimensional virtual soil pile at the pile radius are equal:
wherein r is 0 Is the pile radius; τ P For the shear modulus of a large diameter friction pile,is the shear modulus of the soil body at the pile side +.>u TFSP Shear modulus of three-dimensional virtual soil pile +.> Is the shear modulus of the pile bottom soil body, +.>
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 sigma P Is the normal stress of the large-diameter friction pile,and p (t) g (r) is uniformly distributed exciting force generated by the exciting hammer.
The vertical displacement of the pile core of the large-diameter friction pile is a limited value, and the boundary condition of the pile core of the large-diameter friction pile is as follows:
u P (z,r,t)| r＝0 =finite 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 =finite value (9).
S4: solving a longitudinal vibration control equation of a pile side soil body and a 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 a three-dimensional virtual soil pile in the step S2, and calculating to obtain a pile top velocity 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 soil displacement;
laplace transformation is carried out on the formula (1) to obtain:
in the method, in the process of the invention,is->Is the Law transformation, ω is the excitation circle frequency, +.>/>
Combining boundary conditions of the pile side soil-large-diameter friction pile-three-dimensional virtual soil pile-pile bottom soil coupling vibration system in the step S3 to obtain general solution of the formula (10):
in the method, in the process of the invention,to be determined as coefficient, K 0 () Correction of Bessel functions for zero order of the second classA number;
the shear stress of the soil mass is expressed as:
wherein K is 1 () Correcting the Bessel function for the second class first order;
s4.2, performing Laplace transformation on the longitudinal vibration control equation of the large-diameter friction pile established in the S2, decomposing by using a separation variable method, and solving the displacement of the large-diameter friction pile;
laplace transformation is carried out on the formula (2) to obtain:
in U P (z, r, ω) is u P A Laplace transformation of (z, r, t);
by adopting a separation variable method, U is led to P ＝Z P (z)·R P (r), then equation (13) is expressed as:
wherein the method comprises the steps ofThe following is obtained:
Z P″ (z)-(α P ) 2 Z P (z)＝0 (15)
obtaining alpha based on formula (14) P And beta P The relation between the two 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)
wherein C is P 、D P 、E P And F P All are undetermined coefficients;
based on boundary conditions at the pile core of the large-diameter friction pile, basic solutions of displacement, normal stress and shear stress of the large-diameter friction pile are respectively obtained:
substituting formulas (11), (12), (20) and (22) into formula (5) yields:
combining equation (23) and equation (24) yields:
β P I 1 (β P r 0 )+ζ P I 0 (β P r 0 )＝0 (25)
in zeta P Is the interaction parameter of the pile soil,β P is the vibration mode characteristic value of the large-diameter friction pile, beta P For n eigenvalues->Vectors of composition->Can be obtained by utilizing a MATLAB self-contained function findzero;
the displacement solution of the large-diameter friction pile is obtained based on the superposition principle:
in the method, in the process of the invention,and->Are all undetermined coefficients, < >>By putting->Substituting the obtained product into a formula (17) for calculation;
s4.3, performing Laplace transformation on the longitudinal vibration control equation of the three-dimensional virtual soil pile established in the S2, decomposing by using a separation variable method, and solving the displacement of the three-dimensional virtual soil pile;
laplace transformation is carried out on the formula (3) to obtain:
in U TFSP (z, r, ω) is u TFSP A Laplace transformation of (z, r, t);
by adopting a separation variable method, U is led to TFSP ＝Z TFSP (z)·R TFSP (r), then equation (27) is expressed as:
wherein the method comprises the steps ofThe following is obtained:
Z TFSP″ (z)-(α TFSP ) 2 Z TFSP (z)＝0 (29)
obtaining alpha based on formula (28) TFSP And beta TFSP The relation between the two 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)
wherein C is TFSP 、D TFSP 、E TFSP And F TFSP All are undetermined coefficients;
based on the boundary conditions of the pile bottom of the three-dimensional virtual soil pile, the basic solutions of the displacement, the normal stress and the shear stress of the three-dimensional virtual soil pile are respectively obtained as follows:
/>
substituting equations (11), (12), (34) and (36) into equation (6) yields:
combining equation (37) and equation (38) yields:
β TFSP I 1 (β TFSP r 0 )+ζ TFSP I 0 (β TFSP r 0 )＝0 (39)
in zeta TFSP The coupling parameters of the pile bottom soil body and the three-dimensional virtual soil pile,β TFSP is the vibration mode characteristic value, beta, of the three-dimensional virtual soil pile TFSP For n eigenvalues->Vectors of composition-> Can utilize MATLAB self-containedObtaining a function findfero;
the displacement solution of the three-dimensional virtual soil pile is obtained based on the superposition principle:
wherein C is TFSP 、D TFSP Are all the coefficients to be determined and are all the coefficients 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 boundary conditions of the pile bottom of the three-dimensional virtual soil pile, so as to obtain the following components:
wherein P (omega) is Lawster transformation of P (t), and H is the length of the upper soil layer of the bedrock;
s4.5 based on Bessel function I 0 () Is obtained by:
multiplying the orthogonality of equation (45) and equation (46) by the two equations of equation (43)Is multiplied by +.about.respectively on both sides of equation (44)>And in interval [0, r 0 ]Integrating to obtain:
in the method, in the process of the invention,
and combining 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 components:
wherein H is P Is the length of the large-diameter friction pile;
simultaneous equations (47) - (50), solving to obtain undetermined coefficients in the large-diameter friction pile displacement solutionAnd->The method comprises the following steps:
wherein,
solving a frequency domain analysis solution for determining the displacement and the speed of the large-diameter friction pile is as follows:
V P (z,r,ω)＝iωU P (z,r,ω) (56)
s4.6, pile top displacement and pile top speed reflection waves of the large-diameter friction pile are obtained;
based on the frequency domain analytic solution of the displacement and the speed of the large-diameter friction pile, the time domain semi-analytic solution of the pile top displacement and the speed of the large-diameter friction pile is obtained by utilizing the inverse discrete Fourier transform, and the pile top displacement and the pile top speed reflection wave theoretical curve of the large-diameter friction pile is obtained by the following steps:
u P (z,r,t)＝IFT[U P (z,r,ω)] (57)
wherein IFT is inverse fourier transform;is the theoretical value of the pile top speed reflected wave of the large-diameter friction pile.
S5, performing field measurement on the appointed large-diameter friction pile 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 a bedrock and the shear modulus of a soil bodyViscous damping coefficient of soil body->And density of soil mass->Radius r of large diameter friction pile 0 Length H P Modulus of elasticity E P Poisson's ratio mu P And density ρ P 。
And selecting detection equipment according to the field condition of the specified large-diameter friction pile and JG/T3055 of the foundation pile dynamic tester, and measuring the 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, the transient excitation equipment comprises a force hammer and a hammer pad for exciting wide pulses and narrow pulses, the force hammer is provided with a mechanical sensor, the steady-state excitation equipment is an electromagnetic steady-state vibration exciter, the excitation force of the electromagnetic steady-state vibration exciter can be adjusted, and the sweep frequency 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 center of the top surface of the specified large-diameter friction pile as a pile core, the distance between each detection point and the pile core is 2/3 of the pile diameter length, sensors are respectively arranged at the detection points, the pile core of the specified large-diameter friction pile is taken as an excitation point, and a pile top speed reflected wave actual measurement curve of the specified large-diameter friction pile is obtained by measuring by using detection equipment.
S6, substituting pile-soil parameters extracted in an acquisition site into the pile top speed reflected wave theoretical curve of the large-diameter friction pile in the step S4 to obtain a pile top speed reflected wave theoretical curve of the specified large-diameter friction pile, performing fitting analysis on the pile top speed reflected wave theoretical curve of the specified large-diameter friction pile and the pile top speed reflected wave actual measurement curve measured in the step S5 to determine the viscous damping coefficient of the pile body material of the specified large-diameter friction pile, wherein the step S6 specifically comprises the following steps:
s6.1, substituting pile-soil parameters extracted from an acquisition site into a formula (58) to obtain a pile top speed reflected wave theoretical curve of the specified large-diameter friction pile, and overlapping the pile top speed reflected wave theoretical curve of the specified large-diameter friction pile with the pile top speed reflected wave actual measurement curve measured in the step S5;
s6.2, calculating the superposition degree of a pile top speed reflected wave theoretical curve and a pile top speed reflected wave actual measurement curve of the specified large-diameter friction pile, and if the superposition degree of the pile top speed reflected wave theoretical curve and the measured pile top speed reflected wave actual measurement curve of the specified large-diameter friction pile is lower than 90%, entering into the step S6.3; if the superposition degree of the pile top speed reflected wave theoretical curve of the specified large-diameter friction pile and the measured pile top speed reflected wave actual measurement curve is not lower than 90%, entering a step S6.4;
s6.3, adjusting the viscous damping coefficient eta in the pile top speed reflected wave theoretical curve of the specified large-diameter friction pile P Until the superposition degree of the pile top speed reflected wave theoretical curve of the specified large-diameter friction pile and the measured pile top speed reflected wave actual measurement curve is not lower than 90%, and entering into a step S6.3;
s6.4, substituting pile-soil parameters into the formula (58) can obtain the mapping relation between the pile top velocity reflected wave theoretical curve of the large-diameter friction pile and pile body material damping, namelyAs shown in fig. 4, fig. 4 (a) is a theoretical curve of pile-top velocity reflected waves corresponding to viscous damping coefficients of different pile-body materials, and as can be obtained from fig. 4 (a), the amplitude of the pile-bottom reflected signal decreases with the increase of the damping of the pile-body material, so that the viscous damping coefficient η in the theoretical curve of pile-top velocity reflected waves of a friction pile with a specified large diameter is calculated P Determining the viscous damping coefficient of the pile body material of the specified large-diameter friction pile, namely when the superposition degree of the pile top velocity reflected wave theoretical curve of the specified large-diameter friction pile and the measured pile top velocity reflected wave actual measurement curve is not lower than 90%, wherein the viscous damping coefficient of the pile body material of the specified large-diameter friction pile is equal to the viscous damping coefficient eta in the pile top velocity reflected wave theoretical curve of the specified large-diameter pile P In this embodiment, by comparing the theoretical curve of the pile-top velocity reflected wave of the specified large-diameter friction pile with the actual measurement curve of the pile-top velocity reflected wave, as shown in fig. 4 (b), it is determined that the viscous damping coefficient of the pile body material of the specified large-diameter friction pile in this embodiment is η P ＝1×10 5 Nm -2 s。
It should be understood that the above description is not intended to limit the invention to the particular embodiments disclosed, but to limit the invention to the particular embodiments disclosed, and that the invention is not limited to the particular embodiments disclosed, but is intended to cover modifications, adaptations, additions and alternatives falling within the spirit and scope of the invention.
Claims (9)
1. A method for measuring and calculating damping of a large-diameter friction pile material based on a low-strain reflection wave method is characterized by comprising the following steps of:
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 the large-diameter friction pile extending downwards to the top surface of a bedrock, and establishing a longitudinal vibration control equation of the large-diameter friction pile side soil body and the pile bottom soil body;
s2: based on a viscoelastic three-dimensional axisymmetry theory, a longitudinal vibration control equation is established for the large-diameter friction pile and the three-dimensional virtual soil pile respectively;
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 a pile side soil body and a 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 a three-dimensional virtual soil pile in the step S2, and calculating to obtain a pile top velocity 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, performing field measurement on the specified large-diameter friction pile based on a low-strain reflection wave method to obtain pile-soil parameters and pile top speed reflection wave actual measurement curves of the specified large-diameter friction pile;
s6, substituting pile-soil parameters extracted in the acquisition site into the pile top speed reflected wave theoretical curve of the large-diameter friction pile in the step S4 to obtain a pile top speed reflected wave theoretical curve of the specified large-diameter friction pile, and then carrying out fitting analysis on the pile top speed reflected wave theoretical curve of the specified large-diameter friction pile and the pile top speed reflected wave actual measurement curve measured in the step S5 to determine the viscous damping coefficient of the pile body material of the specified large-diameter friction pile.
2. The method for measuring and calculating the damping of the large-diameter friction pile material based on the low-strain reflection wave method according to claim 1, wherein in the step S1, a longitudinal vibration control equation of a pile side soil body and a pile bottom soil body of the large-diameter friction pile is as follows:
wherein t is time; r is a radial coordinate;is the vertical displacement of the soil body; />Is the shear modulus of the soil body; />Is the viscous damping coefficient of the soil body; />Is the density of the soil body; j is the soil mass type, j=1, 2, j=1 tableThe pile side soil mass of the large-diameter friction pile is shown, and j=2 represents the pile bottom soil mass of the large-diameter friction pile.
3. The method for measuring and calculating the damping of the large-diameter friction pile material based on the low-strain reflection wave method according to claim 2, wherein in the step S1, based on the viscoelastic three-dimensional axisymmetry theory, the pile body material damping of the large-diameter friction pile is synthesized, and a longitudinal vibration control equation of the large-diameter friction pile is established, as shown in the formula (2):
wherein u is P Vertical displacement of the large-diameter friction pile; lambda (lambda) P Ramez constant for large diameter friction pile, G P Is the shear modulus of a large diameter friction pile, wherein lambda P ＝E P μ P /(1+μ P )(1-2μ P )，G P ＝E P /2(1+μ P )，E P Elastic modulus, mu, of large-diameter friction pile P Poisson ratio of the large-diameter friction pile; η (eta) P The viscous damping coefficient of the large-diameter friction pile; ρ P The density of the friction pile with large diameter; z is a vertical coordinate; r is a radial coordinate; t is time;
based on a viscoelastic three-dimensional axisymmetry theory, a longitudinal vibration control equation of the three-dimensional virtual soil pile is established, as shown in a formula (3):
wherein u is TFSP Vertical displacement of the three-dimensional virtual soil pile;is the Lamex constant of the three-dimensional virtual soil pile, < ->Is the shear modulus of the three-dimensional virtual soil pile, wherein ∈> The elastic modulus of the three-dimensional virtual soil pile; />Poisson ratio of the three-dimensional virtual soil pile; />The viscous damping coefficient of the three-dimensional virtual soil pile; />Is 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 according to 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 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, and the displacement and the stress are shown in the formula (5) and the formula (6):
wherein r is 0 Is the pile radius; τ P For the shear modulus of a large diameter friction pile, is the shear modulus of the soil body at the pile side +.>u TFSP Shear modulus of three-dimensional virtual soil pile +.> Is the shear modulus of the pile bottom soil body, +.>
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 sigma P Is the normal stress of the large-diameter friction pile,p (t) g (r) is uniformly distributed exciting force generated by the exciting hammer;
the vertical displacement of the pile core of the large-diameter friction pile is a limited value, and the boundary condition of the pile core of the large-diameter friction pile is as follows:
u P (z,r,t)| r＝0 =finite 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 =finite value (9).
5. The method for measuring and calculating the damping of the large-diameter friction pile material based on the low-strain reflection wave method according to claim 4, wherein in the step S4, the method specifically comprises the following steps:
s4.1, solving soil displacement;
laplace transformation is carried out on the formula (1) to obtain:
in the method, in the process of the invention,is->Is the Law transformation, ω is the excitation circle frequency, +.>
Combining boundary conditions of the pile side soil-large-diameter friction pile-three-dimensional virtual soil pile-pile bottom soil coupling vibration system in the step S3 to obtain general solution of the formula (10):
in the method, in the process of the invention,to be determined as coefficient, K 0 () Correcting a Bessel function for the second class zero order;
the shear stress of the soil mass is expressed as:
wherein K is 1 () Correcting the Bessel function for the second class first order;
s4.2, performing Laplace transformation on the longitudinal vibration control equation of the large-diameter friction pile established in the S2, decomposing by using a separation variable method, and solving the displacement of the large-diameter friction pile;
laplace transformation is carried out on the formula (2) to obtain:
in U P (z, r, ω) is u P A Laplace transformation of (z, r, t);
by adopting a separation variable method, U is led to P ＝Z P (z)·R P (r), then equation (13) is expressed as:
wherein the method comprises the steps ofThe following is obtained:
Z P″ (z)-(α P ) 2 Z P (z)＝0 (15)
obtaining alpha based on formula (14) P And beta P The relation between the two 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)
wherein C is P 、D P 、E P And F P All are undetermined coefficients;
based on boundary conditions at the pile core of the large-diameter friction pile, basic solutions of displacement, normal stress and shear stress of the large-diameter friction pile are respectively obtained:
substituting formulas (11), (12), (20) and (22) into formula (5) yields:
combining equation (23) and equation (24) yields:
β P I 1 (β P r 0 )+ζ P I 0 (β P r 0 )＝0 (25)
in zeta P Is the interaction parameter of the pile soil,β P is the vibration mode characteristic value of the large-diameter friction pile, beta P For n eigenvalues->A vector of components;
the displacement solution of the large-diameter friction pile is obtained based on the superposition principle:
in the method, in the process of the invention,and->Are all undetermined coefficients, < >>By putting->Substituting the obtained product into a formula (17) for calculation;
s4.3, performing Laplace transformation on the longitudinal vibration control equation of the three-dimensional virtual soil pile established in the S2, decomposing by using a separation variable method, and solving the displacement of the three-dimensional virtual soil pile;
laplace transformation is carried out on the formula (3) to obtain:
in U TFSP (z, r, ω) is u TFSP Lawster's variation of (z, r, t)Changing;
by adopting a separation variable method, U is led to TFSP ＝Z TFSP (z)·R TFSP (r), then equation (27) is expressed as:
wherein the method comprises the steps ofThe following is obtained:
Z TFSP″ (z)-(α TFSP ) 2 Z TFSP (z)＝0 (29)
obtaining alpha based on formula (28) TFSP And beta TFSP The relation between the two 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)
wherein C is TFSP 、D TFSP 、E TFSP And F TFSP All are undetermined coefficients;
based on the boundary conditions of the pile bottom of the three-dimensional virtual soil pile, the basic solutions of the displacement, the normal stress and the shear stress of the three-dimensional virtual soil pile are respectively obtained as follows:
substituting equations (11), (12), (34) and (36) into equation (6) yields:
combining equation (37) and equation (38) yields:
β TFSP I 1 (β TFSP r 0 )+ζ TFSP I 0 (β TFSP r 0 )＝0 (39)
in zeta TFSP The coupling parameters of the pile bottom soil body and the three-dimensional virtual soil pile,β TFSP is the vibration mode characteristic value, beta, of the three-dimensional virtual soil pile TFSP For n eigenvalues->A vector of components;
the displacement solution of the three-dimensional virtual soil pile is obtained based on the superposition principle:
wherein C is TFSP 、D TFSP Are all the coefficients to be determined and are all the coefficients 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 boundary conditions of the pile bottom of the three-dimensional virtual soil pile, so as to obtain the following components:
wherein P (omega) is Lawster transformation of P (t), and H is the length of the upper soil layer of the bedrock;
s4.5 based on Bessel function I 0 () Is obtained by:
using equation (45) and the equationThe orthogonality of equation (46) is multiplied by the equation of equation (43) on both sidesIs multiplied by +.about.respectively on both sides of equation (44)>And in interval [0, r 0 ]Integrating to obtain:
in the method, in the process of the invention,
and combining 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 components:
wherein H is P Is the length of the large-diameter friction pile;
simultaneous equations (47) - (50), solving to obtain undetermined coefficients in the large-diameter friction pile displacement solutionAnd->The method comprises the following steps:
wherein,
solving a frequency domain analysis solution for determining the displacement and the speed of the large-diameter friction pile is as follows:
V P (z,r,ω)＝iωU P (z,r,ω) (56)
s4.6, pile top displacement and pile top speed reflection waves of the large-diameter friction pile are obtained;
based on the frequency domain analytic solution of the displacement and the speed of the large-diameter friction pile, the time domain semi-analytic solution of the pile top displacement and the speed of the large-diameter friction pile is obtained by utilizing the inverse discrete Fourier transform, and the pile top displacement and the pile top speed reflection wave theoretical curve of the large-diameter friction pile is obtained by the following steps:
u P (z,r,t)＝IFT[U P (z,r,ω)] (57)
wherein IFT is inverse fourier transform;is the theoretical value of the pile top speed reflected wave of the large-diameter friction pile.
6. The method for measuring and calculating the damping of a large-diameter friction pile material based on the low-strain reflection wave method according to claim 1, wherein 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 bodyViscous damping coefficient of soil body->And density of soil mass->Radius r of large diameter friction pile 0 Length H P Modulus of elasticity E P Poisson's ratio mu P And density ρ P 。
7. The method for measuring and calculating the damping of the large-diameter friction pile material based on the low-strain reflection wave method according to claim 1, wherein in the step S5, pile-soil parameters are extracted at a selected acquisition site, detection equipment is selected, the detection equipment comprises transient excitation equipment and steady-state excitation equipment, a plurality of detection points are symmetrically arranged by taking the center of the top surface of a specified large-diameter friction pile as a pile center according to the pile diameter of the specified large-diameter pile, sensors are installed on the detection points, and the pile center of the specified large-diameter friction pile is taken as an excitation point, so that a pile top speed reflection wave actual measurement curve of the specified large-diameter friction pile is obtained by measurement of the detection equipment.
8. The method for measuring and calculating the damping of the large-diameter friction pile material based on the low-strain reflection wave method, which is disclosed in claim 7, is characterized in that detection equipment is selected according to the site condition of a specified large-diameter friction pile and JG/T3055 of foundation pile dynamic tester, 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, a steady-state excitation equipment is set as an electromagnetic steady-state vibration exciter, and the frequency sweeping range is 10-2000 Hz.
9. The method for measuring and calculating the damping of the large-diameter friction pile material based on the low-strain reflection wave method according to claim 5, wherein in the step S6, the method specifically comprises the following steps:
s6.1, substituting pile-soil parameters extracted from an acquisition site into a formula (58) to obtain a pile top speed reflected wave theoretical curve of the specified large-diameter friction pile, and overlapping the pile top speed reflected wave theoretical curve of the specified large-diameter friction pile with the pile top speed reflected wave actual measurement curve measured in the step S5;
s6.2, calculating the superposition degree of a pile top speed reflected wave theoretical curve and a pile top speed reflected wave actual measurement curve of the specified large-diameter friction pile, and if the superposition degree of the pile top speed reflected wave theoretical curve and the measured pile top speed reflected wave actual measurement curve of the specified large-diameter friction pile is lower than 90%, entering into the step S6.3; if the superposition degree of the pile top speed reflected wave theoretical curve of the specified large-diameter friction pile and the measured pile top speed reflected wave actual measurement curve is not lower than 90%, entering a step S6.4;
s6.3, adjusting the viscous damping coefficient eta in the pile top speed reflected wave theoretical curve of the specified large-diameter friction pile P Until the superposition degree of the pile top speed reflected wave theoretical curve of the specified large-diameter friction pile and the measured pile top speed reflected wave actual measurement curve is not lower than 90%, and entering into a step S6.3;
s6.4, according to the viscous damping coefficient eta in the theoretical curve of the velocity reflected wave of the pile top of the specified large-diameter friction pile P Determining the viscous damping coefficient of the pile body material of the specified large-diameter friction pile, wherein the viscous damping coefficient of the pile body material of the specified large-diameter friction pile is equal to the viscosity of the theoretical curve of the reflected wave of the pile top speed of the specified large-diameter pile foundationCoefficient of sexual damping eta P Thereby determining the viscous damping coefficient of the pile body material of the designated large-diameter friction pile.
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