CN103994921A - Testing method for elasticity modulus of rock mass weak intercalated layer based on wavelet waveform change rule - Google Patents

Abstract

The invention relates to a testing technology for the elasticity modulus of a rock mass weak intercalated layer and provides a testing method for the elasticity modulus of a weak intercalated layer based on a waveform change rule of wavelets with different frequencies in a process of transmission in the weak intercalated layer. The testing method comprises the following six steps: (1) testing physical and mechanical parameters of rock masses at the two sides of the weak intercalated layer; (2) testing and calculating viscosity coefficients of the rock masses at the two sides of the weak intercalated layer; (3) testing the elasticity modulus and the viscosity coefficient of the weak intercalated layer; (4) establishing a model of transmission of stress waves on the weak intercalated layer; (5) calculating a waveform of an incidence side according to a recorded waveform of a transmission side; and (6) calculating the elasticity modulus and the viscosity coefficient of the weak intercalated layer. The testing method is simple to operate; a testing result comprehensively reflects the influence on a stress wave amplitude spectrum and phase spectrum of the weak intercalated layer.

Description

Characters of Weak Intercalation in Layered Rock Mass elastic modulus method of testing based on wavelet wave form varies rule

Technical field

The present invention relates to Characters of Weak Intercalation in Layered Rock Mass elastic modulus measuring technology, the wave form varies rule of the wavelet based on different frequency in weak intercalated layer communication process, has proposed the method for testing of weak intercalated layer elastic modulus.

Background technology

In the factors of stability that affect the Geotechnical Engineerings such as side slope, tunnel, underground chamber, bad engineering geological condition and rock mass structure condition are main internal causes, rock mass discontinuity particularly weak intercalated layer plays control action to rock mass deformation and rock mass engineering project unstable failure, and deflection and the improvement rock mass engineering project etc. of the mechanics parameter of Obtaining Accurate weak intercalated layer to estimation rock mass engineering project is significant.

The home position testing method of Mechanics Parameters of Rock Mass is divided into dynamic test method and static(al) method of testing.The ultimate principle of static method: apply normal direction load on selected rock mass surface, cell wall or boring wall, and measure the deformation values of its rock mass, then draw out pressure-deformation relation curve, calculate the deformation parameter of rock mass.Conventional static method mainly contains: bearing plate method, boring deformation method, slit method, hydraulic pressure cavern method, list (two) axial compression contracting test method(s) etc.The ultimate principle of dynamic method: by artificial means rock mass is excited to generation stress wave, specify the vibration signal of measuring point with sensor and vibration signals collecting instrument record, ask the deformation parameter of rock mass according to wave theory, Main Basis stress wave propagation velocity of wave calculates the deformation parameter of rock mass at present.

With respect to dynamic method, it is little that static method test result has discreteness, it has been generally acknowledged that more reliable, but be subject to the restriction of loading environment, be difficult to carry out the test of large volume rock sample, and from rock mass engineering project angle, very wish to obtain the mechanics parameter of large volume rock mass, for this reason, static(al) estimation algorithm is proposed, as beded rock mass deformation parameter estimation equation, estimate velocity of longitudinal wave and rock mass average deformation modulus etc. with RMR value estimation Deformation Module of Rock Mass, by Q value.Be summed up, in engineering, mainly contain two kinds of static(al) estimation algorithms: the one, at the scene on the basis of geologic examination, set up suitable rock mass geology mechanical model, utilizing indoor small specimen testing data and geomechanics model to combine estimates, the validity of its estimation result depends on geomechanics model, because being difficult to set up the effective mechanical model of complicated rock mass, limit promoting the use of the method, cause current the method mainly to apply to beded rock mass; The 2nd, on the basis of Evaluation of Rock Mass Quality and lot of experiments data, set up the empirical relationship between Rock Mass Classification index and deformation parameter, for deformation parameter estimation, the advantage of the method is to have considered to affect rock mass mechanics qualitative factor, but still belongs to semiempirical formula at present.

In Practical Project, the rock mass strength parameter being obtained by on-the-spot Rock mass of large dimension mechanical test can reflect rock mass engineering project mechanical characteristic preferably, but be limited to the reasons such as rock mass size in test, time and test funds, on-the-spot and the indoor mechanical test quantity of carrying out in Practical Project is all very limited, therefore only depends on these limited test figures to be difficult to obtain truly reflecting the design parameter of rock mass engineering project characteristic.With respect to static(al) method of testing, dynamic test method has the advantage such as mechanics parameter that quick facility, testing cost are low, can implement large volume test and test tiny rock mass discontinuity, being that static(al) method of testing is indispensable supplements, motive force of development method of testing is significant, but dynamic test method is immature, particularly calculate Mechanics Parameters of Rock Mass according to the vibrational waveform of measuring point immature, it is insufficient that counter stress wave amplitude and phase information are excavated.In rock mass, have the structural plane of a large amount of different scales, directly affect deformation characteristic and the deformation parameter of rock mass, wherein weak intercalated layer is a very important class rock mass discontinuity, and rock mass deformation and destruction are had to material impact.Adopt the deformation parameter of dynamic method test weak intercalated layer, key issue is to grasp the propagation law of stress wave at weak intercalated layer, and proposes suitable computing method.

Summary of the invention

The object of this invention is to provide a kind of Characters of Weak Intercalation in Layered Rock Mass elastic modulus method of testing based on wavelet wave form varies rule.

Technical scheme of the present invention: a kind of Characters of Weak Intercalation in Layered Rock Mass elastic modulus method of testing based on wavelet wave form varies rule, comprises the following steps:

The first step, the physical and mechanical parameter of test weak intercalated layer both sides rock mass:

Adopt the elastic modulus that bores elastic modulus instrument test weak intercalated layer both sides rock mass, adopt density, the Poisson ratio of existing conventional method test weak intercalated layer and both sides rock mass thereof;

Second step, the viscosity coefficient of Measurement and Computation weak intercalated layer both sides rock mass:

When larger for weak intercalated layer both sides lithological change, need select respectively the region of surfacing in weak intercalated layer both sides is test zone; If weak intercalated layer both sides lithological change hour, thinks that both sides Mechanics Parameters of Rock Mass is identical, only need a side therein to select test zone; In test zone, arrange 1 straight line survey line, survey line length is 1.5-4.5m, the selected vibration source point that applies shock load on survey line, selected 2-4 measuring points on survey line; The principle of measuring point numbering is: centered by vibration source point, from the close-by examples to those far off since 1 number consecutively, the 1st measuring point (putting nearest measuring point with vibration source) is 0.3-1.0m with the distance of vibration source point; Be bonded on measuring point with gesso degree of will speed up sensor, apply a shock load at vibration source point, adopt vibration signals collecting instrument to record the vibrational waveform of sensor; The process of calculating weak intercalated layer both sides rock mass viscosity coefficient is: (1) is carried out Fourier transform to the P waveform of the individual sensor record of m (m>1) and obtained its spectral amplitude, the area S that adopts relational expression 1 calculated amplitude spectral curve and frequency coordinate axle to surround _pm; (2) the P waveform of the 1st sensor record is carried out to Fourier transform and obtain its spectral amplitude, the initial value of given rock mass viscosity coefficient, initial value is 0.05-0.2MPa.s, test the elastic modulus, density and the Poisson ratio that obtain in conjunction with the first step, spectral amplitude is calculated to the calculated amplitude spectrum of m measuring point according to relational expression 2, adopt relational expression 1 to calculate the calculated amplitude spectrum of m measuring point and the area S that frequency coordinate axle surrounds _pjm; (3) constantly increase the viscosity coefficient of rock mass, calculate S _pjmwith S _pmthe absolute value of difference, draw the relation curve of absolute value and viscosity coefficient, on curve, find out the minimum value of absolute value, viscosity coefficient corresponding to minimum value is exactly the viscosity coefficient of rock mass;

Relational expression 1

$S_P=\underset{n=0}{\overset{n=\∞}{\mathrm{\Σ}}}{A}_P\left(f_n\right)\mathrm{\Δf}$

S in relational expression 1 _pfor the area that P wave-amplitude spectral curve and frequency coordinate axle surround, n is frequency sampling number, A _p(f _n) for frequency be f _ntime amplitude, Δ f is sample frequency step-length;

Relational expression 2

$A_{\mathrm{Pjm}}\left(f_n\right)=A_{P1}\left(f_n\right)\exp (-\sqrt{\frac{\mathrm{\ρE}{\left(2\mathrm{\π}{f}_n\right)}^2(1+v)(1-2v)}{2(1-v)[E^2+{\left(2\mathrm{\π}{f}_n\right)}^2{\mathrm{\η}}^2]}[{(1+\frac{{\left(2\mathrm{\π}{f}_n\right)}^2{\mathrm{\η}}^2}{E^2})}^{1/2}-1]}\mathrm{Vl})$

A in relational expression 2 _pjm(f _n) for frequency be f _ntime m measuring point calculating P wave-amplitude, A _p1(f _n) for frequency be f _ntime the 1st measuring point P wave-amplitude, f _nfor frequency, ρ is density, and E is elastic modulus, and η is coefficient of viscosity, and ν is Poisson ratio, and Δ l is the distance between the 1st and m measuring point;

The 3rd step, elastic modulus and the viscosity coefficient of test weak intercalated layer:

Along weak intercalated layer trend to be tested, selection can reflect the test section of weak intercalated layer mechanical characteristic, and test section requires surperficial opposed flattened; Arrange 1 survey line through weak intercalated layer, survey line length is 1.0-3.0m, and the angle of survey line and weak intercalated layer trend is 80 °-90 °; Select respectively 1-3 measuring points along survey line in weak intercalated layer both sides, the principle of measuring point numbering is: centered by vibration source point, and from the close-by examples to those far off number consecutively, the distance of first measuring point and vibration source point (impact loading point) is 0.3-0.6m; Two component accelerometer sensor is bonded on measuring point with gesso, one-component moves towards to arrange along weak intercalated layer, and the vertical weak intercalated layer of another component move towards layout; A side that applies shock load is called light incident side, and opposite side is called transmissive side, and vibration source point is 0.5-1.0m with the distance of weak intercalated layer, applies shock load produce stress wave at light incident side, adopts vibration signals collecting instrument to record the vibration signal of measuring point;

The 4th step, set up the propagation model of stress wave at weak intercalated layer:

Stress wave has the feature aspect three in the communication process through weak intercalated layer, (1) conventionally relatively grow at the rock mass that has weak intercalated layer near zone, stress wave is in the communication process of such rock mass, rock mass counter stress wave-amplitude and phase place have obvious impact, should adopt viscoelasticity mechanical model to describe weak intercalated layer and both sides rock mass thereof; (2), when stress wave is through weak intercalated layer, the impact of its thickness counter stress wave phase also be can not ignore; (3), because weak intercalated layer has certain thickness, multiple transmission and the reflex corresponding Reeb propagation of stress wave in weak intercalated layer has material impact.Three features for above-mentioned stress wave through weak intercalated layer, are thought of as viscoelastic body by weak intercalated layer and both sides rock mass thereof, set up the propagation model of stress wave at weak intercalated layer; When P ripple is incident to weak intercalated layer, adopt respectively transmission coefficient and the relational expression 4 calculated stress wave reflection coefficients of relational expression 3 calculated stress ripples; When SV ripple incident weak intercalated layer, adopt respectively transmission coefficient and the relational expression 6 calculated stress wave reflection coefficients of relational expression 5 calculated stress ripples;

Relational expression 3

$T_{\mathrm{PP}}=\frac{2}{\frac{P_{\mathrm{II}}}{P_I}[\frac{({\mathrm{\λ}}_{\mathrm{II}}+2{\mathrm{\μ}}_{\mathrm{II}})P_{\mathrm{II}}+{\mathrm{\ω}}^{2}M}{({\mathrm{\λ}}_I+2{\mathrm{\μ}}_1)P_1}+\frac{({\mathrm{\λ}}_{\mathrm{II}}+2{\mathrm{\μ}}_{\mathrm{II}})P_{\mathrm{II}}-K}{K}]\exp \left(P_{\mathrm{II}}h\right)\exp (-\mathrm{j\ω}\frac{h}{C_{\mathrm{PJ}}})}$

Relational expression 4

$R_{\mathrm{PP}}=\frac{({\mathrm{\λ}}_I+2{\mathrm{\μ}}_I)P_I[({\mathrm{\λ}}_{\mathrm{II}}+2{\mathrm{\μ}}_{\mathrm{II}})P_{\mathrm{II}}-K]+[({\mathrm{\λ}}_{\mathrm{II}}+2{\mathrm{\μ}}_{\mathrm{II}})P_{\mathrm{II}}+{\mathrm{\ω}}^{2}M]K}{[({\mathrm{\λ}}_{\mathrm{II}}+2{\mathrm{\μ}}_{\mathrm{II}})P_{\mathrm{II}}+{\mathrm{\ω}}^{2}M]K+[K-({\mathrm{\λ}}_{\mathrm{II}}+2{\mathrm{\μ}}_{\mathrm{II}})P_{\mathrm{II}}]({\mathrm{\λ}}_I+2{\mathrm{\μ}}_I)P_I}$

In relational expression 3 and relational expression 4, the subscript I of P, λ and tri-parameters of μ and II are respectively the parameter of light incident side and transmissive side rock mass; T _pPtransmission coefficient during for the incident of P ripple; R _pPreflection coefficient during for the incident of P ripple; J is empty unit; ω is angular frequency; λ and μ are the Lame's constant of weak intercalated layer both sides rock mass, and its calculating is respectively with j, ω, E, ν, η are respectively elastic modulus, Poisson ratio, the viscosity coefficient of empty unit, angular frequency and weak intercalated layer both sides rock mass; P is the parameter relevant with stress wave wave number in the rock mass of weak intercalated layer both sides, and its computing formula is j, ω, ρ, λ and μ are respectively the Lame's constant of empty unit, angular frequency and weak intercalated layer both sides rock mass; C _pJfor P ripple is at the velocity of wave of weak intercalated layer, its computing formula is ρ _j, λ _jand μ _jbe respectively density and the Lame's constant of weak intercalated layer; K is the equivalent stiffness of weak intercalated layer, and its computing formula is j, ω, h, E _jand η _jbe respectively thickness, elastic modulus, the viscosity coefficient of empty unit, angular frequency and weak intercalated layer; M is the quality of weak intercalated layer, and its computing formula is M=ρ _jh, h and ρ _jbe respectively thickness and the density of weak intercalated layer;

Relational expression 5

$T_{\mathrm{SS}}=\frac{2K{u}_I{P_I}^2\exp \left(\mathrm{j\ω}\frac{h}{C_{\mathrm{SJ}}}\right)}{P_{\mathrm{II}}\exp \left(P_{\mathrm{II}}h\right)[k(u_{\mathrm{II}}{P}_{\mathrm{II}}-{\mathrm{\ω}}^{2}M)+u_I{P}_I(K+u_{\mathrm{II}}{P}_{\mathrm{II}})]}$

Relational expression 6

$P_{\mathrm{SS}}=\frac{-u_I{P}_I(K+u_{\mathrm{II}}{P}_{\mathrm{II}})+K(u_{\mathrm{II}}{P}_{\mathrm{II}}-{\mathrm{\ω}}^{2}M)}{K(u_{\mathrm{II}}{P}_{\mathrm{II}}-{\mathrm{\ω}}^{2}M)+u_I{P}_I(K+u_{\mathrm{II}}{P}_{\mathrm{II}})}$

In relational expression 5 and relational expression 6, the subscript I of P and two parameters of μ and II are respectively the parameter of light incident side and transmissive side rock mass; T _sStransmission coefficient during for the incident of SV ripple; R _sSreflection coefficient during for the incident of SV ripple; J is empty unit; ω is angular frequency; H is the thickness of weak intercalated layer; μ is the Lame's constant of weak intercalated layer both sides rock mass, and its calculating is respectively j, ω, E, ν, η are respectively elastic modulus, Poisson ratio, the viscosity coefficient of empty unit, angular frequency and weak intercalated layer both sides rock mass; P is the parameter relevant with stress wave wave number in the rock mass of weak intercalated layer both sides, and its computing formula is P=-j ω (ρ/μ) ^1/2, j, ω, ρ and μ are respectively density, the Lame's constant of empty unit, angular frequency and weak intercalated layer both sides rock mass; C _sJfor SV ripple is at the velocity of wave of weak intercalated layer, its computing formula is j, ω, ρ _j, E _j, ν _j, η _jbe respectively density, elastic modulus, Poisson ratio, the viscosity coefficient of empty unit, angular frequency and weak intercalated layer; K is the equivalent stiffness of weak intercalated layer, and its computing formula is j, ω, h, E _jand η _jbe respectively thickness, elastic modulus, the viscosity coefficient of empty unit, angular frequency and weak intercalated layer; M is the quality of weak intercalated layer, and its computing formula is M=ρ _jh, h and ρ _jbe respectively thickness and the density of weak intercalated layer;

The 5th step, the waveform of calculating light incident side:

According to the waveform of actual measurement transmitted wave waveshape light incident side, comprise following 5 little steps: (1) carries out Fourier transform to actual measurement transmitted wave waveform, obtains surveying the frequency spectrum of transmitted wave waveform---comprise spectral amplitude and phase spectrum; (2) to actual measurement transmitted wave frequency spectrum divided by transmission coefficient, obtain calculating the frequency spectrum of incident wave; (3) frequency spectrum that calculates incident wave is carried out to inverse Fourier transform, obtain calculating incident wave waveform; (4) frequency spectrum that calculates incident wave be multiplied by reflection coefficient and carry out inverse Fourier transform, obtaining calculating reflection wave; (5) superposition calculation incident wave and calculate the waveform of reflection wave, obtains the calculating waveform of light incident side;

The 6th step, elastic modulus and the viscosity coefficient of calculating weak intercalated layer:

Determine elastic modulus and the viscosity coefficient of weak intercalated layer according to the calculating waveform of light incident side and the difference of measured waveform, comprise following 3 little steps: the elastic modulus of (1) given weak intercalated layer and the initial value of viscosity coefficient, elastic modulus initial value is 0.1～0.5GPa, the initial value of viscosity coefficient is 0.1～0.5MPa.s, obtain the calculating waveform of light incident side P ripple according to the computation process of the 5th step, adopt wave form varies coefficient quantization light incident side to calculate P waveform and the difference of surveying P waveform, obtain both difference value ζ _p, claiming that different wave shape value is wave form varies coefficient, the computing formula of wave form varies coefficient is shown in relational expression 7; (2) given and elastic modulus and viscosity coefficient that in this step, (1) little step is identical, and adopt identical method to calculate light incident side to calculate the wave form varies coefficient ζ of SV ripple and actual measurement SV ripple _sV; (3) ask ζ _pand ζ _sVand ζ, change respectively elastic modulus and the viscosity coefficient of weak intercalated layer, recalculate ζ, find out minimum ζ value, the elastic modulus that minimum ζ value is corresponding and viscosity coefficient are exactly elastic modulus and the viscosity coefficient of the weak intercalated layer that obtains of test;

Relational expression 7:

$\mathrm{\ζ}=\frac{1}{\underset{i=1}{\overset{i=+\∞}{\mathrm{\Σ}}}\left|a_{\mathrm{sc}}\left(t_i\right)\right|\mathrm{\Δt}}\left|\underset{i=1}{\overset{i=+\∞}{\mathrm{\Σ}}}\right|a_{\mathrm{js}}\left(t_i\right)|-\underset{i=1}{\overset{i=+\∞}{\mathrm{\Σ}}}|a_{\mathrm{sc}}\left(t_i\right)\left|\right|\mathrm{\Δt}$

In relational expression 7: ζ is the difference value of calculating waveform and measured waveform; I is the sampling number of composition waveform; t _ifor discrete time; Δ t is sampling time step-length; a _scfor the amplitude of measured waveform; a _jsfor calculating the amplitude of waveform.

Good effect of the present invention:

(1) considered that stress wave changes through spectral amplitude and the phase spectrum of weak intercalated layer, the impact that adopts the corresponding Reeb of wave form varies reflection weak intercalated layer to propagate, test result is accurate more comprehensively.(2) stress wave is in the communication process of weak intercalated layer, multiple transmission is relative with reflex outstanding, adopt equivalent stiffness to describe the mechanical characteristic of weak intercalated layer, in the time setting up the propagation model of stress wave at weak intercalated layer, consider the impact of weak interbed counter stress wave phase, made multiple transmission and reflex obtain rationally effectively simplifying.(3) adopt viscoelastic models to describe rock mass and weak intercalated layer, more meet both mechanical characteristics.

Brief description of the drawings

Fig. 1 is embodiment of the present invention actual measurement transmitted wave waveform.

Fig. 2 is that embodiment of the present invention light incident side calculates waveform.

Fig. 3 is embodiment of the present invention light incident side measured waveform.

Embodiment

The present invention is directed to thickness and be the weak intercalated layer of tens centimetres to tens centimetres, such structural plane has the feature such as easy disturbance and mechanical characteristic complexity, on basis at research stress wave through the wave form varies rule of weak intercalated layer, the Characters of Weak Intercalation in Layered Rock Mass elastic modulus method of testing based on wavelet wave form varies rule is proposed.

Adopt the present invention on the bench slope of certain open cut ore mine, to carry out underground test at home, selected weak interbed is h=0.42m, and both sides rock mass lithology is identical, because of the controlled blasting adopting, be subject to blast disturbance very little, can think that mechanics parameter is identical, implementation process is as follows:

The first step: the physical and mechanical parameter of test weak intercalated layer both sides rock mass.

Adopt the elastic modulus E=13.4GPa of the GY-90 boring elastic modulus instrument test weak intercalated layer both sides rock mass of Wuhan Inst. of Rock and Soil Mechanics, Chinese Academy of Sciences's development, select typical sillar at pilot region, be processed into standard brick rock sample, adopting the density of conventional method test weak intercalated layer both sides rock mass is ρ=2520kg/m ³, Poisson ratio ν=0.18, the density p of weak intercalated layer _j=2470kg/m ³, Poisson ratio ν _j=0.21.

Second step: the viscosity coefficient of Measurement and Computation weak intercalated layer both sides rock mass.

A side at weak intercalated layer is arranged 1 survey line (straight line), survey line length is 2.35m, selected vibration source point (applying the application point of shock load) on survey line, selected 4 measuring points on survey line, the principle of measuring point numbering is: centered by vibration source point, from the close-by examples to those far off since 1 number consecutively, the distance of 4 measuring points and vibration source point is respectively 0.5m, 0.88m, 1.48m, 2.35m.Be bonded on measuring point with gesso degree of will speed up sensor, apply a shock load at vibration source point, adopt vibration signals collecting instrument to record the vibrational waveform of sensor.The parameter of sensor is: charge sensitivity scope is 10.284-14.147pC/ (m.s ^-2); Frequency response: 0.2Hz-5KHz; Sensor connects electric charge filtering integrating amplifier, and electric charge filtering integrating amplifier connects digital collection and signal analyzer, and vibration signal gathers after filtering is processed, and electric charge filtering integrating amplifier is set to low pass 4KHz, and single pass sampling rate is 20KHz.The process of calculating weak intercalated layer both sides rock mass viscosity coefficient is: (1) is carried out Fourier transform to the P waveform of the 2nd sensor record and obtained its spectral amplitude, the area S that adopts relational expression 1 calculated amplitude spectral curve and frequency coordinate axle to surround _p2; (2) the P waveform of the 1st sensor record is carried out to Fourier transform and obtain its spectral amplitude, the initial value of given weak intercalated layer rock mass viscosity coefficient is 0.1MPa.s, tests the elastic modulus E=13.4GPa, the density p=2520kg/m that obtain in conjunction with the first step ³with Poisson ratio ν=0.18, spectral amplitude is calculated to the calculated amplitude spectrum of the 2nd measuring point according to relational expression 2, then adopt relational expression 1 to calculate the calculated amplitude spectrum of the 2nd measuring point and the area S that frequency coordinate axle surrounds _pj2; (3) constantly increase the viscosity coefficient of rock mass, calculate S _pj2with S _p2the absolute value of difference, draw the relation curve of absolute value and viscosity coefficient, on curve, find out the minimum value of absolute value, viscosity coefficient corresponding to minimum value is exactly the viscosity coefficient of rock mass, calculating rock mass viscosity coefficient is 7.5MPs.According to the calculation procedure of the 2nd measuring point, the viscosity coefficient being obtained by the vibrational waveform of the 3rd measuring point and the 4th measuring point is respectively 6.7MPs, 5.8MPs, tries to achieve the viscosity coefficient that average viscosity coefficient η=6.7MPs is weak intercalated layer both sides rock mass.

Relational expression 1

$S_P=\underset{n=0}{\overset{n=\∞}{\mathrm{\Σ}}}{A}_P\left(f_n\right)\mathrm{\Δf}$

S in relational expression 1 _pfor the area that P wave-amplitude spectral curve and frequency coordinate axle surround, n is that frequency adopts number, A _p(f _n) for frequency be f _ntime amplitude, Δ f is sample frequency step-length.

Relational expression 2

$A_{\mathrm{Pjm}}\left(f_n\right)=A_{P1}\left(f_n\right)\exp (-\sqrt{\frac{\mathrm{\ρE}{\left(2\mathrm{\π}{f}_n\right)}^2(1+v)(1-2v)}{2(1-v)[E^2+{\left(2\mathrm{\π}{f}_n\right)}^2{\mathrm{\η}}^2]}[{(1+\frac{{\left(2\mathrm{\π}{f}_n\right)}^2{\mathrm{\η}}^2}{E^2})}^{1/2}-1]}\mathrm{Vl})$

A in relational expression 2 _pjm(f _n) for frequency be f _ntime m measuring point calculating P wave-amplitude, A _p1(f _n) for frequency be f _ntime the 1st measuring point P wave-amplitude, f _nfor frequency, ρ is density, and E is elastic modulus, and η is coefficient of viscosity, and ν is Poisson ratio, and Δ l is the distance between the 1st and m measuring point.

The 3rd step: elastic modulus and the viscosity coefficient of test weak intercalated layer.

Along weak intercalated layer trend to be tested, selection can reflect the test section of weak intercalated layer mechanical characteristic, and test section requires surperficial opposed flattened.Arrange 1 survey line through interlayer, survey line length is 1.2m, and the angle of survey line and weak intercalated layer trend is 85 °.Select respectively 1 measuring point in weak intercalated layer both sides along survey line, apply shock load side and be called light incident side, opposite side is called transmissive side, measuring point 1 is positioned at light incident side, measuring point 2 is positioned at transmissive side, and measuring point 1, weak intercalated layer left margin (near vibration source) and measuring point 2 are respectively 0.44m, 0.58m and 1.2m with the distance of vibration source point (applying the application point of shock load).Two component accelerometer sensor is bonded on measuring point with gesso, one-component moves towards to arrange along weak intercalated layer, and the vertical weak intercalated layer of another component move towards layout.The parameter of sensor is: charge sensitivity scope is 10.284-14.147pC/ (m.s ^-2); Frequency response: 0.2Hz-5KHz; Sensor connects electric charge filtering integrating amplifier, and electric charge filtering integrating amplifier connects digital collection and signal analyzer, and vibration signal gathers after filtering is processed, and electric charge filtering integrating amplifier is set to low pass 4KHz, and sampling rate is 20KHz.Apply and increase load generation stress wave, adopt vibration signals collecting instrument to record the vibrational waveform of each measuring point.

The 4th step: set up the propagation model of stress wave at weak intercalated layer.

Stress wave has the feature aspect three in the communication process through weak intercalated layer, (1) conventionally relatively grow at the rock mass that has weak intercalated layer near zone, stress wave is in the communication process of such rock mass, rock mass counter stress wave-amplitude and phase place have obvious impact, should adopt viscoelasticity mechanical model to describe weak intercalated layer and both sides rock mass thereof; (2), when stress wave is through weak intercalated layer, the impact of its thickness counter stress wave phase also be can not ignore; (3), because weak intercalated layer has certain thickness, stress wave contains important impact in multiple transmission and the reflex corresponding Reeb propagation of weak intercalated layer.Three features for above-mentioned stress wave through weak intercalated layer, are thought of as viscoelastic body by weak intercalated layer and both sides rock mass thereof, set up the propagation model of stress wave at weak intercalated layer.When P ripple is incident to weak intercalated layer, adopt respectively transmission coefficient and the relational expression 4 calculated stress wave reflection coefficients of relational expression 3 calculated stress ripples; When SV ripple incident weak intercalated layer, adopt respectively transmission coefficient and the relational expression 6 calculated stress wave reflection coefficients of relational expression 5 calculated stress ripples.

Relational expression 3

$T_{\mathrm{PP}}=\frac{2}{\frac{P_{\mathrm{II}}}{P_I}[\frac{({\mathrm{\λ}}_{\mathrm{II}}+2{\mathrm{\μ}}_{\mathrm{II}})P_{\mathrm{II}}+{\mathrm{\ω}}^{2}M}{({\mathrm{\λ}}_I+2{\mathrm{\μ}}_1)P_1}+\frac{({\mathrm{\λ}}_{\mathrm{II}}+2{\mathrm{\μ}}_{\mathrm{II}})P_{\mathrm{II}}-K}{K}]\exp \left(P_{\mathrm{II}}h\right)\exp (-\mathrm{j\ω}\frac{h}{C_{\mathrm{PJ}}})}$

Relational expression 4

$R_{\mathrm{PP}}=\frac{({\mathrm{\λ}}_I+2{\mathrm{\μ}}_I)P_I[({\mathrm{\λ}}_{\mathrm{II}}+2{\mathrm{\μ}}_{\mathrm{II}})P_{\mathrm{II}}-K]+[({\mathrm{\λ}}_{\mathrm{II}}+2{\mathrm{\μ}}_{\mathrm{II}})P_{\mathrm{II}}+{\mathrm{\ω}}^{2}M]K}{[({\mathrm{\λ}}_{\mathrm{II}}+2{\mathrm{\μ}}_{\mathrm{II}})P_{\mathrm{II}}+{\mathrm{\ω}}^{2}M]K+[K-({\mathrm{\λ}}_{\mathrm{II}}+2{\mathrm{\μ}}_{\mathrm{II}})P_{\mathrm{II}}]({\mathrm{\λ}}_I+2{\mathrm{\μ}}_I)P_I}$

In relational expression 3 and relational expression 4, the subscript I of P, λ and tri-parameters of μ and II are respectively the parameter of light incident side and transmissive side rock mass; T _pPtransmission coefficient during for the incident of P ripple; R _pPreflection coefficient during for the incident of P ripple; J is empty unit; ω is angular frequency; λ and μ are the Lame's constant of weak intercalated layer both sides rock mass, and its calculating is respectively with j, ω, E, ν, η are respectively elastic modulus, Poisson ratio, the viscosity coefficient of empty unit, angular frequency and weak intercalated layer both sides rock mass; P is the parameter relevant with stress wave wave number in the rock mass of weak intercalated layer both sides, and its computing formula is j, ω, ρ, λ and μ are respectively the Lame's constant of empty unit, angular frequency and weak intercalated layer both sides rock mass; C _pJfor P ripple is at the velocity of wave of weak intercalated layer, its computing formula is ρ _j, λ _jand μ _jbe respectively density and the Lame's constant of weak intercalated layer; K is the equivalent stiffness of weak intercalated layer, and its computing formula is j, ω, h, E _jand η _jbe respectively thickness, elastic modulus, the viscosity coefficient of empty unit, angular frequency and weak intercalated layer; M is the quality of weak intercalated layer, and its computing formula is M=ρ _jh, h and ρ _jbe respectively thickness and the density of weak intercalated layer.

Relational expression 5

$T_{\mathrm{SS}}=\frac{2K{u}_I{P_I}^2\exp \left(\mathrm{j\ω}\frac{h}{C_{\mathrm{SJ}}}\right)}{P_{\mathrm{II}}\exp \left(P_{\mathrm{II}}h\right)[k(u_{\mathrm{II}}{P}_{\mathrm{II}}-{\mathrm{\ω}}^{2}M)+u_I{P}_I(K+u_{\mathrm{II}}{P}_{\mathrm{II}})]}$

Relational expression 6

$P_{\mathrm{SS}}=\frac{-u_I{P}_I(K+u_{\mathrm{II}}{P}_{\mathrm{II}})+K(u_{\mathrm{II}}{P}_{\mathrm{II}}-{\mathrm{\ω}}^{2}M)}{K(u_{\mathrm{II}}{P}_{\mathrm{II}}-{\mathrm{\ω}}^{2}M)+u_I{P}_I(K+u_{\mathrm{II}}{P}_{\mathrm{II}})}$

In relational expression 5 and relational expression 6, P and μ subscript I and II are respectively the parameter of light incident side and transmissive side rock mass; T _sStransmission coefficient during for the incident of SV ripple; R _sSreflection coefficient during for the incident of SV ripple; J is empty unit; ω is angular frequency; H is the thickness of weak intercalated layer; μ is the Lame's constant of weak intercalated layer both sides rock mass, and its calculating is respectively j, ω, E, ν, η are respectively elastic modulus, Poisson ratio, the viscosity coefficient of empty unit, angular frequency and weak intercalated layer both sides rock mass; P is the parameter relevant with stress wave wave number in the rock mass of weak intercalated layer both sides, and its computing formula is P=-j ω (ρ/μ) ^1/2, j, ω, ρ and μ are respectively density, the Lame's constant of empty unit, angular frequency and weak intercalated layer both sides rock mass; C _sJfor SV ripple is at the velocity of wave of weak intercalated layer, its computing formula is j, ω, ρ _j, E _j, ν _j, η _jbe respectively density, elastic modulus, Poisson ratio, the viscosity coefficient of empty unit, angular frequency and weak intercalated layer; K is the equivalent stiffness of weak intercalated layer, and its computing formula is j, ω, h, E _jand η _jbe respectively thickness, elastic modulus, the viscosity coefficient of empty unit, angular frequency and weak intercalated layer; M is the quality of weak intercalated layer, and its computing formula is M=ρ _jh, h and ρ _jbe respectively thickness and the density of weak intercalated layer.

The 5th step: the waveform that calculates light incident side.

According to the waveform of actual measurement transmitted wave waveshape light incident side, comprise following 5 little steps, taking P ripple as example, SV is identical with the calculation procedure of P ripple.(1) the actual measurement P waveform of transmissive side as shown in Figure 1, carries out Fourier transform to actual measurement transmitted wave waveform, obtains surveying the frequency spectrum of transmitted wave waveform---comprise spectral amplitude and phase spectrum; (2) to actual measurement transmitted wave frequency spectrum divided by transmission coefficient, obtain calculating the frequency spectrum of incident wave; (3) frequency spectrum that calculates incident wave is carried out to inverse Fourier transform, obtain calculating incident wave waveform; (4) frequency spectrum that calculates incident wave be multiplied by reflection coefficient and carry out inverse Fourier transform, obtaining calculating reflection wave; (5) waveform of superposition calculation incident wave and calculating reflection wave, obtain the calculating waveform of light incident side, when the elastic modulus of weak intercalated layer is 0.85GPa and viscosity coefficient while being 23.0MPs, as shown in Figure 2, the measured waveform of light incident side is as shown in 3 for the calculating waveform of light incident side.

The 6th step: the elastic modulus and the viscosity coefficient that calculate weak intercalated layer.

P ripple is transmitted in vibration along line direction (vertical weak intercalated layer direction), and SV ripple is transmitted in the vibration of cross line direction (parallel weak intercalated layer direction).Determine elastic modulus and the viscosity coefficient of weak intercalated layer according to the calculating waveform of light incident side and the difference of measured waveform, comprise following 3 little steps: the initial value of the elastic modulus of (1) given weak intercalated layer is 0.2GPa, initial value 0.2MPa.s with viscosity coefficient, obtain the calculating waveform of light incident side P ripple according to the computation process of the 5th step, adopt wave form varies coefficient quantization light incident side to calculate P waveform and the difference of surveying P waveform, obtain both difference value ζ _p, difference value is called wave form varies coefficient, and the computing formula of wave form varies coefficient is shown in relational expression 7; (2) initial value of the elastic modulus of given weak intercalated layer is 0.2GPa, and the initial value 0.2MPa.s of viscosity coefficient, and the employing computing method identical with P ripple, obtains the wave form varies coefficient ζ that light incident side calculates SV ripple and surveys SV ripple _sV; (3) ask ζ _pand ζ _sVand ζ, change respectively elastic modulus and the viscosity coefficient of weak intercalated layer, recalculate ζ, find out minimum ζ value, the elastic modulus that minimum ζ value is corresponding and viscosity coefficient are exactly elastic modulus and the viscosity coefficient of the weak intercalated layer that obtains of test.

Relational expression 7

$\mathrm{\ζ}=\frac{1}{\underset{i=1}{\overset{i=+\∞}{\mathrm{\Σ}}}\left|a_{\mathrm{sc}}\left(t_i\right)\right|\mathrm{\Δt}}\left|\underset{i=1}{\overset{i=+\∞}{\mathrm{\Σ}}}\right|a_{\mathrm{js}}\left(t_i\right)|-\underset{i=1}{\overset{i=+\∞}{\mathrm{\Σ}}}|a_{\mathrm{sc}}\left(t_i\right)\left|\right|\mathrm{\Δt}$

In relational expression 7, ζ is the difference value of calculating waveform and measured waveform; I is the sampling number of composition waveform; t _ifor discrete time; Δ t is sampling time step-length; a _scfor the amplitude of measured waveform; a _jsfor calculating the amplitude of waveform.

According to above-mentioned calculating, the viscosity coefficient η of wave form varies coefficient minimum value _j=24.5MPs and elastic modulus are E _j=0.9GPa.

Effect: be the validity of checking employing test result of the present invention, adopt boring elastic modulus instrument to carry out the test of bullet mould at weak intercalated layer, test result is 0.74GPa, and test result of the present invention is more approaching with adopting, and shows that the present invention is effective.

Claims (1)

1. the Characters of Weak Intercalation in Layered Rock Mass elastic modulus method of testing based on wavelet wave form varies rule, comprises the following steps:

The first step, the physical and mechanical parameter of test weak intercalated layer both sides rock mass:

Adopt the elastic modulus that bores elastic modulus instrument test weak intercalated layer both sides rock mass, adopt density, the Poisson ratio of existing conventional method test weak intercalated layer and both sides rock mass thereof;

Second step, the viscosity coefficient of Measurement and Computation weak intercalated layer both sides rock mass:

When larger for weak intercalated layer both sides lithological change, need select respectively the region of surfacing in weak intercalated layer both sides is test zone; If weak intercalated layer both sides lithological change hour, thinks that both sides Mechanics Parameters of Rock Mass is identical, only need a side therein to select test zone; In test zone, arrange 1 straight line survey line, survey line length is 1.5-4.5m, the selected vibration source point that applies shock load on survey line, selected 2-4 measuring points on survey line; The principle of measuring point numbering is: centered by vibration source point, from the close-by examples to those far off since 1 number consecutively, the 1st distance of putting nearest measuring point and vibration source point with vibration source is 0.3-1.0m; Be bonded on measuring point with gesso degree of will speed up sensor, apply a shock load at vibration source point, adopt vibration signals collecting instrument to record the vibrational waveform of sensor; The process of calculating weak intercalated layer both sides rock mass viscosity coefficient is: (1) is carried out Fourier transform to the P waveform of m sensor record and obtained its spectral amplitude, m>1, the area S that adopts relational expression 1 calculated amplitude spectral curve and frequency coordinate axle to surround _pm; (2) the P waveform of the 1st sensor record is carried out to Fourier transform and obtain its spectral amplitude, the initial value of given rock mass viscosity coefficient, initial value is 0.05-0.2MPa.s, test the elastic modulus, density and the Poisson ratio that obtain in conjunction with the first step, spectral amplitude is calculated to the calculated amplitude spectrum of m measuring point according to relational expression 2, adopt relational expression 1 to calculate the calculated amplitude spectrum of m measuring point and the area S that frequency coordinate axle surrounds _pjm; (3) constantly increase the viscosity coefficient of rock mass, calculate S _pjmwith S _pmthe absolute value of difference, draw the relation curve of absolute value and viscosity coefficient, on curve, find out the minimum value of absolute value, viscosity coefficient corresponding to minimum value is exactly the viscosity coefficient of rock mass;

Relational expression 1

$S_P=\underset{n=0}{\overset{n=\∞}{\mathrm{\Σ}}}{A}_P\left(f_n\right)\mathrm{\Δf}$

S in relational expression 1 _pfor the area that P wave-amplitude spectral curve and frequency coordinate axle surround, n is frequency sampling number, A _p(f _n) for frequency be f _ntime amplitude, Δ f is sample frequency step-length;

Relational expression 2

$A_{\mathrm{Pjm}}\left(f_n\right)=A_{P1}\left(f_n\right)\exp (-\sqrt{\frac{\mathrm{\ρE}{\left(2\mathrm{\π}{f}_n\right)}^2(1+v)(1-2v)}{2(1-v)[E^2+{\left(2\mathrm{\π}{f}_n\right)}^2{\mathrm{\η}}^2]}[{(1+\frac{{\left(2\mathrm{\π}{f}_n\right)}^2{\mathrm{\η}}^2}{E^2})}^{1/2}-1]}\mathrm{Vl})$

A in relational expression 2 _pjm(f _n) for frequency be f _ntime m measuring point calculating P wave-amplitude, A _p1(f _n) for frequency be f _ntime the 1st measuring point P wave-amplitude, f _nfor frequency, ρ is density, and E is elastic modulus, and η is coefficient of viscosity, and ν is Poisson ratio, and Δ l is the distance between the 1st and m measuring point;

The 3rd step, elastic modulus and the viscosity coefficient of test weak intercalated layer:

Along weak intercalated layer trend to be tested, selection can reflect the test section of weak intercalated layer mechanical characteristic, and test section requires surperficial opposed flattened; Arrange 1 survey line through weak intercalated layer, survey line length is 1.0-3.0m, and the angle of survey line and weak intercalated layer trend is 80 °-90 °; Select respectively 1-3 measuring points along survey line in weak intercalated layer both sides, the principle of measuring point numbering is: centered by vibration source point, and from the close-by examples to those far off number consecutively, the distance of first measuring point and shock load vibration source point is 0.3-0.6m; Two component accelerometer sensor is bonded on measuring point with gesso, one-component moves towards to arrange along weak intercalated layer, and the vertical weak intercalated layer of another component move towards layout; A side that applies shock load is called light incident side, and opposite side is called transmissive side, and vibration source point is 0.5-1.0m with the distance of weak intercalated layer, applies shock load produce stress wave at light incident side, adopts vibration signals collecting instrument to record the vibration signal of measuring point;

The 4th step, set up the propagation model of stress wave at weak intercalated layer:

Stress wave has the feature aspect three in the communication process through weak intercalated layer, (1) conventionally relatively grow at the rock mass that has weak intercalated layer near zone, stress wave is in the communication process of such rock mass, rock mass counter stress wave-amplitude and phase place have obvious impact, should adopt viscoelasticity mechanical model to describe weak intercalated layer and both sides rock mass thereof; (2), when stress wave is through weak intercalated layer, the impact of its thickness counter stress wave phase also be can not ignore; (3), because weak intercalated layer has certain thickness, multiple transmission and the reflex corresponding Reeb propagation of stress wave in weak intercalated layer has material impact; Three features for above-mentioned stress wave through weak intercalated layer, are thought of as viscoelastic body by weak intercalated layer and both sides rock mass thereof, set up the propagation model of stress wave at weak intercalated layer; When P ripple is incident to weak intercalated layer, adopt respectively transmission coefficient and the relational expression 4 calculated stress wave reflection coefficients of relational expression 3 calculated stress ripples; When SV ripple incident weak intercalated layer, adopt respectively transmission coefficient and the relational expression 6 calculated stress wave reflection coefficients of relational expression 5 calculated stress ripples;

Relational expression 3

$T_{\mathrm{PP}}=\frac{2}{\frac{P_{\mathrm{II}}}{P_I}[\frac{({\mathrm{\λ}}_{\mathrm{II}}+2{\mathrm{\μ}}_{\mathrm{II}})P_{\mathrm{II}}+{\mathrm{\ω}}^{2}M}{({\mathrm{\λ}}_I+2{\mathrm{\μ}}_1)P_1}+\frac{({\mathrm{\λ}}_{\mathrm{II}}+2{\mathrm{\μ}}_{\mathrm{II}})P_{\mathrm{II}}-K}{K}]\exp \left(P_{\mathrm{II}}h\right)\exp (-\mathrm{j\ω}\frac{h}{C_{\mathrm{PJ}}})}$

Relational expression 4

$R_{\mathrm{PP}}=\frac{({\mathrm{\λ}}_I+2{\mathrm{\μ}}_I)P_I[({\mathrm{\λ}}_{\mathrm{II}}+2{\mathrm{\μ}}_{\mathrm{II}})P_{\mathrm{II}}-K]+[({\mathrm{\λ}}_{\mathrm{II}}+2{\mathrm{\μ}}_{\mathrm{II}})P_{\mathrm{II}}+{\mathrm{\ω}}^{2}M]K}{[({\mathrm{\λ}}_{\mathrm{II}}+2{\mathrm{\μ}}_{\mathrm{II}})P_{\mathrm{II}}+{\mathrm{\ω}}^{2}M]K+[K-({\mathrm{\λ}}_{\mathrm{II}}+2{\mathrm{\μ}}_{\mathrm{II}})P_{\mathrm{II}}]({\mathrm{\λ}}_I+2{\mathrm{\μ}}_I)P_I}$

In relational expression 3 and relational expression 4, the subscript I of P, λ and tri-parameters of μ and II are respectively the parameter of light incident side and transmissive side rock mass; T _pPtransmission coefficient during for the incident of P ripple; R _pPreflection coefficient during for the incident of P ripple; J is empty unit; ω is angular frequency; λ and μ are the Lame's constant of weak intercalated layer both sides rock mass, and its calculating is respectively with j, ω, E, ν, η are respectively elastic modulus, Poisson ratio, the viscosity coefficient of empty unit, angular frequency and weak intercalated layer both sides rock mass; P is the parameter relevant with stress wave wave number in the rock mass of weak intercalated layer both sides, and its computing formula is j, ω, ρ, λ and μ are respectively the Lame's constant of empty unit, angular frequency and weak intercalated layer both sides rock mass; C _pJfor P ripple is at the velocity of wave of weak intercalated layer, its computing formula is ρ _j, λ _jand μ _jbe respectively density and the Lame's constant of weak intercalated layer; K is the equivalent stiffness of weak intercalated layer, and its computing formula is j, ω, h, E _jand η _jbe respectively thickness, elastic modulus, the viscosity coefficient of empty unit, angular frequency and weak intercalated layer; M is the quality of weak intercalated layer, and its computing formula is M=ρ _jh, h and ρ _jbe respectively thickness and the density of weak intercalated layer;

Relational expression 5

$T_{\mathrm{SS}}=\frac{2K{u}_I{P_I}^2\exp \left(\mathrm{j\ω}\frac{h}{C_{\mathrm{SJ}}}\right)}{P_{\mathrm{II}}\exp \left(P_{\mathrm{II}}h\right)[k(u_{\mathrm{II}}{P}_{\mathrm{II}}-{\mathrm{\ω}}^{2}M)+u_I{P}_I(K+u_{\mathrm{II}}{P}_{\mathrm{II}})]}$

Relational expression 6

$P_{\mathrm{SS}}=\frac{-u_I{P}_I(K+u_{\mathrm{II}}{P}_{\mathrm{II}})+K(u_{\mathrm{II}}{P}_{\mathrm{II}}-{\mathrm{\ω}}^{2}M)}{K(u_{\mathrm{II}}{P}_{\mathrm{II}}-{\mathrm{\ω}}^{2}M)+u_I{P}_I(K+u_{\mathrm{II}}{P}_{\mathrm{II}})}$

In relational expression 5 and relational expression 6, the subscript I of P and two parameters of μ and II are respectively the parameter of light incident side and transmissive side rock mass; T _sStransmission coefficient during for the incident of SV ripple; R _sSreflection coefficient during for the incident of SV ripple; J is empty unit; ω is angular frequency; H is the thickness of weak intercalated layer; μ is the Lame's constant of weak intercalated layer both sides rock mass, and its calculating is respectively j, ω, E, ν, η are respectively elastic modulus, Poisson ratio, the viscosity coefficient of empty unit, angular frequency and weak intercalated layer both sides rock mass; P is the parameter relevant with stress wave wave number in the rock mass of weak intercalated layer both sides, and its computing formula is P=-j ω (ρ/μ) ^1/2, j, ω, ρ and μ are respectively density, the Lame's constant of empty unit, angular frequency and weak intercalated layer both sides rock mass; C _sJfor SV ripple is at the velocity of wave of weak intercalated layer, its computing formula is j, ω, ρ _j, E _j, ν _j, η _jbe respectively density, elastic modulus, Poisson ratio, the viscosity coefficient of empty unit, angular frequency and weak intercalated layer; K is the equivalent stiffness of weak intercalated layer, and its computing formula is j, ω, h, E _jand η _jbe respectively thickness, elastic modulus, the viscosity coefficient of empty unit, angular frequency and weak intercalated layer; M is the quality of weak intercalated layer, and its computing formula is M=ρ _jh, h and ρ _jbe respectively thickness and the density of weak intercalated layer;

The 5th step, the waveform of calculating light incident side:

According to the waveform of actual measurement transmitted wave waveshape light incident side, comprise following 5 little steps: (1) carries out Fourier transform to actual measurement transmitted wave waveform, obtains surveying the frequency spectrum of transmitted wave waveform---comprise spectral amplitude and phase spectrum; (2) to actual measurement transmitted wave frequency spectrum divided by transmission coefficient, obtain calculating the frequency spectrum of incident wave; (3) frequency spectrum that calculates incident wave is carried out to inverse Fourier transform, obtain calculating incident wave waveform; (4) frequency spectrum that calculates incident wave be multiplied by reflection coefficient and carry out inverse Fourier transform, obtaining calculating reflection wave; (5) superposition calculation incident wave and calculate the waveform of reflection wave, obtains the calculating waveform of light incident side;

The 6th step, elastic modulus and the viscosity coefficient of calculating weak intercalated layer:

Determine elastic modulus and the viscosity coefficient of weak intercalated layer according to the calculating waveform of light incident side and the difference of measured waveform, comprise following 3 little steps: the elastic modulus of (1) given weak intercalated layer and the initial value of viscosity coefficient, elastic modulus initial value is 0.1～0.5GPa, the initial value of viscosity coefficient is 0.1～0.5MPa.s, obtain the calculating waveform of light incident side P ripple according to the computation process of the 5th step, adopt wave form varies coefficient quantization light incident side to calculate P waveform and the difference of surveying P waveform, obtain both difference value ζ _p, claiming that different wave shape value is wave form varies coefficient, the computing formula of wave form varies coefficient is shown in relational expression 7; (2) given and elastic modulus and viscosity coefficient that in this step, (1) little step is identical, and adopt identical method to calculate light incident side to calculate the wave form varies coefficient ζ of SV ripple and actual measurement SV ripple _sV; (3) ask ζ _pand ζ _sVand ζ, change respectively elastic modulus and the viscosity coefficient of weak intercalated layer, recalculate ζ, find out minimum ζ value, the elastic modulus that minimum ζ value is corresponding and viscosity coefficient are exactly elastic modulus and the viscosity coefficient of the weak intercalated layer that obtains of test;

Relational expression 7:

$\mathrm{\ζ}=\frac{1}{\underset{i=1}{\overset{i=+\∞}{\mathrm{\Σ}}}\left|a_{\mathrm{sc}}\left(t_i\right)\right|\mathrm{\Δt}}\left|\underset{i=1}{\overset{i=+\∞}{\mathrm{\Σ}}}\right|a_{\mathrm{js}}\left(t_i\right)|-\underset{i=1}{\overset{i=+\∞}{\mathrm{\Σ}}}|a_{\mathrm{sc}}\left(t_i\right)\left|\right|\mathrm{\Δt}$

In relational expression 7: ζ is the difference value of calculating waveform and measured waveform; I is the sampling number of composition waveform; t _ifor discrete time; Δ t is sampling time step-length; a _scfor the amplitude of measured waveform; a _jsfor calculating the amplitude of waveform.