CN103792289A - Full-waveform information test method for joint rigidity of rock mass - Google Patents

Abstract

The invention relates to a full-waveform information test method for the joint rigidity of rock mass. The method comprises data test and data analysis. The test comprises the following two steps: (1) testing the physical mechanics parameter of the rock mass within a test region, and (2) testing the normal rigidity and the tangential rigidity of the joint in the field; the data analysis comprises the following five steps: (1) building a time-domain analysis model when wavelet is propagated within the joint, (2) decomposing transmitted wave by the wavelet, (3) computing a wavelet system of incident wave and reflected wave, (4) computing time-domain wave form at an incident side which is in parallel with the joint trend and is vertical to the joint trend, and (5) computing the normal rigidity and the tangential rigidity of the joint. The test method is used for analyzing the rigidity of the joint based on the full-waveform information, a structural surface has the function of controlling the mechanical property of the rock mass, the exact acquisition of the normal rigidity and the tangential rigidity of the joint of the rock mass has important meaning on the design, the construction, the stability evaluation and the rock mass reinforcement of the rock mass engineering, According to the method, the operation is simple and quick, and the test cost is low, and a test result comprehensively reflects the complexity of the mechanical property.

Description

The Full wave shape information method of testing of ROCK MASS JOINT rigidity

Technical field

The present invention relates to ROCK MASS JOINT rigidity test technology, cause on the basis of sub-wave amplitude and Phase Changing at further investigation joint, proposed the method for testing of Full wave shape information calculating ROCK MASS JOINT rigidity in time domain.

Background technology

In very long geologic process, in rock mass, form the structural plane of different scale, these structural planes cause rock mass to have discontinuous, heterogeneous body and anisotropic mechanical characteristic.These yardsticks differ, come in every shape and the crisscross all kinds of structural planes that distribute affect mechanical property and the stability of engineering rock mass consumingly, deformation and failure to rock mass plays control action, and the mechanics parameter of Obtaining Accurate rock mass discontinuity is the important and difficulties in rock mass mechanics.

The method of testing of joint rigidity mainly contains the technological means such as indoor test, on-the-spot test, inverting and engineering geophysics, and these methods have the advantage of self, also has some deficiency simultaneously.(1) indoor test, pass through on-site sampling, or meet the identical or ratio of similitude of some parameter and require to make test specimen, adopt indoor measurement method to obtain the deformation parameter at joint, the method has cost advantage low and simple to operate, but the problem existing is to be difficult to consider the Geological Environmental Factors such as terrestrial stress and underground water, the easy disturbance of sampling process, particularly joint, its thickness is only several millimeters to several centimetres, is difficult to on-site sampling and carries out indoor measurement.(2) on-the-spot test, the test result of the method has feature accurately and reliably, be subject to the restriction of the aspects such as on-the-spot test cycle length and testing cost height, thereby testing site must have stronger representativeness.(3) parametric inversion, the method has the advantage that cost is low, but depend on the accuracy of input parameter, very little to the contribution of rock mass bulk deformation at the front joint of rock mass macroscopic failure, in the time adjusting the deformation mechanics parameter at joint, rock mass bulk deformation is not obvious, thereby in the time carrying out parametric inversion, the reliability of inversion result is subject to larger impact.(4) engineering geophysics, it is low, simple to operate and be convenient to carry out on-the-spot test that the method has testing cost, but data processing difficulty is larger, is mainly at present the method for testing proposing based on velocity of wave and impedance parameter.

As everyone knows, stress wave has different propagation characteristics in dissimilar medium, and wave reflection and refraction also can occur on the different dielectric interface of elastic property.In the time that the factors such as composition, structure and the density of rock soil medium change, also will there is corresponding variation in stress velocity of wave propagation thereupon.Between the elastic constant of rock and velocity of wave, there is in theory quantitative relationship, shatter belt in rock mass and tomography are defects potential on rock mass structure, there is lower velocity of wave response at these positions, velocity of wave can effectively reflect rock mass structure information, defect is larger, the effect of analyzing rock mass structure according to velocity of wave is better, therefore can utilize stress wave velocity of wave to analyze large-scale structure face (shatter belt, tomography etc.) in rock mass.At present, mainly when employing sound, wave amplitude, three parameters of frequency carry out Ultrasonic Detection and detection, the built amount of halting or sxemiquantitative mathematic(al) representation, also obtained very large achievement while using these achievements in research to carry out engineering geophysics.But ROCK MASS JOINT has the feature of the little and mechanical characteristic complexity of yardstick, conventional measuring technology haves much room for improvement.Affect the many factors of stress wave at ROCK MASS JOINT propagation law, as the material composition at joint, grain size distribution, water percentage, void ratio, dry density etc., also be subject in addition the impact of the geologic media such as grand microcosmic group structure, terrestrial stress and underground water of interlayer, thereby be difficult to the ROCK MASS JOINT according to a certain waveform parameter reflection mechanical characteristic complexity.Stress wave is in the communication process of ROCK MASS JOINT, and the induction degree difference of the stress wave of different frequency to joint, changes but its influence degree can be summarized as spectral amplitude and the phase spectrum of stress wave.The spectral amplitude of stress wave and phase spectrum change, the wave form varies of the present stress wave of final body, and when the sound of stress wave, wave amplitude and frequency only disclosed stress wave propagation rule from some aspect, thereby waveform can concentrated expression stress wave propagation rule.More responsive to the reaction of tomography while showing that by theoretical and experimental study wavelet wave form varies ratio is walked, fully reflect the advantage of wave form varies rule aspect Mechanics Parameters of Rock Mass test and rock mass structure detection.

Summary of the invention

The object of the invention is to provide a kind of Full wave shape information method of testing of ROCK MASS JOINT rigidity, structural plane has control action to rock mass mechanics characteristic, and design, construction, estimation of stability and the rock mass reinforcing to rock mass engineering project of the normal stiffness of Obtaining Accurate ROCK MASS JOINT and shear stiffness is significant.

Technical scheme of the present invention: a kind of Full wave shape information method of testing of ROCK MASS JOINT rigidity, comprises testing procedure and data analysis step:

A, testing procedure

The first step: the physical and mechanical parameter of testing experiment region sillar

Elastic modulus, Poisson ratio and density; Select representational sillar at pilot region, be processed into Standard rock sample, with the mechanics parameter of rock test rig test rock, adopt the density of conventional method test sillar.

Second step: test joint normal direction and shear stiffness

Along Joint strike to be tested, selection can reflect the test section of joint mechanical characteristic, and test section requires surperficial opposed flattened; Arrange 2-5 bar survey line at test section, for guaranteeing measuring accuracy, the incident angle of all surveys line is not more than 65 °; Survey line is numbered, and the 1st bar of survey line is vertical with joint, and incident angle is 0 °, increases with survey line numbering, and incident angle increases, and all surveys line intersect at a bit, and this point is vibration source place, applies the application point of shock load; Along every survey line, arrange two two component sensors in both sides, joint, one-component parallel cracks moves towards to arrange, another component vertical joints is moved towards to arrange, hereinafter to be referred as being light incident side the half side of vibration source direction, abbreviation opposite side is transmissive side, and the distance at sensor and joint is 10-30cm, and the sensor of arranging with transmissive side at light incident side is identical with joint distance; The vibration that shock load produces is vibration source, and the distance between vibration source place and joint is 0.5-2.0m, and the microfissure of both sides, joint rock mass is educated all the more, and distance is less; Record after the position coordinates at each sensor, vibration source and joint, shock load produces stress wave, adopts vibrating data collection instrument to record the vibrational waveform of each sensor.

B, data analysis step

Set up the time domain propagation model of wavelet at joint, transmitted wave is decomposed into wavelet, uses the time domain propagation model of wavelet at joint, calculate light incident side incident wave and reflection wave, calculating time domain waveform based on light incident side and actual measurement time domain waveform matching condition are determined joint rigidity, and data analysis step is as follows.

The first step: set up the time-domain analysis model that wavelet is propagated at joint

Adopt spring model to describe joint distortion, if structural plane joint two lateral stresses are continuous, displacement discontinuous quantity equals the ratio of stress and joint rigidity, set up the differential equation group of transmission, reflection wave speed time domain waveform and incident wave time domain waveform, when the incident of P ripple, see relational expression 1, when the incident of SV ripple, see relational expression 2, use Waveform Matching back tracking method to obtain analytic solution each, reflection configuration, realize and in time domain, analyzed the impact that propagate corresponding Reeb, joint, calculated the time domain waveform of transmitted wave and reflection wave.

Relational expression 1:

Relational expression 2:

In relational expression 1 and relational expression 2, v _p, v _rP, v _rS, v _tP, v _tSbe respectively incident P ripple, reflected P ripple, reflection SV ripple, transmission P ripple, transmission SV wave propagation velocity time domain waveform; ρ ₁and ρ ₂be respectively the density of light incident side sillar and transmissive side sillar; c _p1, c _s1be respectively P ripple and the SV phase velocity of wave of light incident side sillar; c _p2, c _s2be respectively P ripple and the SV phase velocity of wave of transmissive side sillar; T is the time; φ is incident angle and P wave reflection angle;

for SV wave reflection angle; φ ' is the angle of transmission of P ripple;

for the angle of transmission of SV ripple; K _tfor structural plane shear stiffness; K _nfor structural plane normal stiffness.

Second step: wavelet decomposition transmitted wave

(1) vibrational waveform of decomposition transmissive side obtains transmission P ripple and transmission SV ripple, the sensor record of transmissive side the parallel cracks trend of transmissive side and the vibrational waveform that vertical joints is moved towards, according to the relation of stress wave propagation direction and direction of vibration, decomposed and obtained transmission P ripple and transmission SV ripple by wave field, the formula that wave field decomposes is shown in relational expression 3.

Relational expression 3:

$\left\{\begin{array}{c}{a}_{\mathrm{pi}}\left(t\right)=a_{\mathrm{yi}}\left(t\right)\cos {\mathrm{\θ}}_i+a_{\mathrm{xi}}\left(t\right)\sin {\mathrm{\θ}}_i\\ a_{\mathrm{si}}\left(t\right)=a_{\mathrm{xi}}\left(t\right)\cos {\mathrm{\θ}}_i-a_{\mathrm{yi}}\left(t\right)\sin {\mathrm{\θ}}_i\end{array}\right.$

In relational expression 3, a _piand a (t) _si(t) be respectively the time domain waveform of P ripple and the SV ripple of i sensor position; a _xiand a (t) _yi(t) respectively i x that sensor records and y direction (x and y represent respectively to sit along joint to vertical joints sit to coordinate, time domain waveform as shown in Figure 2), θ _iit is the angle of i sensor place survey line and Article 1 survey line.

(2) set up wavelet storehouse, selection can effectively reflect the wavelet base of stress wave in joint propagation characteristic, introduces the time shift factor and scale factor, sets up wavelet storehouse, the matrix (line number that m is matrix that wavelet storehouse is m × n; N is matrix column number), by the time shift factor and the rational value of scale factor, guarantee that wavelet can cover signal to be decomposed on time domain and frequency domain.It is the vertical wavelet of wavelet capital construction storehouse that the present invention adopts Ricker wavelet, and the time-domain expression of Ricker wavelet is shown in relational expression 4.

Relational expression 4:

$a_R\left(t\right)=(1-{2\mathrm{\π}}^2{f}_M^2{t}^2)\exp (-{\mathrm{\π}}^2{f}_M^2{t}^2)$

In relational expression 4, f _mfor crest frequency, in relational expression 4, introduce time shift factor q and scale factor p, set up Ricker wavelet storehouse, the wavelet function of introducing after the time shift factor and scale factor is shown in relational expression 5.

Relational expression 5:

$u_R\left(t\right)=[1-{2\mathrm{\π}}^2{f}_M^2{\left(\frac{t-q_j}{p_j}\right)}^2]\exp [-{\mathrm{\π}}^2{f}_M^2{\left(\frac{t-q_j}{p_j}\right)}^2]$

(3) be wavelet series by transmission P Wave Decomposition, inner product is done in signal to be decomposed and wavelet storehouse and obtain wavelet coefficient, the wavelet of wavelet coefficient maximum is defined as optimum wavelet, the difference of calculating signal to be decomposed and optimum wavelet obtains residual signal, and residual signal and wavelet storehouse are done to inner product, determines second optimum wavelet, by that analogy, in the time meeting error requirements, finish to find optimum wavelet, determine thus the wavelet series of transmission P ripple.

(4) be wavelet series by transmission SV Wave Decomposition, the method that is wavelet according to transmission P Wave Decomposition, decomposes SV ripple, obtains the wavelet series of transmission SV ripple.

The 3rd step: the wavelet series of calculating incident wave and reflection wave

In data analysis step, second step decomposes the transmission P ripple that obtains and the wavelet series of transmission SV ripple, the time-domain analysis model that the stress wave of setting up according to the first step in data analysis step is propagated at joint, calculates respectively with transmission P marble wave system and is listed as corresponding incident wave wavelet series and reflection wave wavelet series; Calculate respectively incident wave wavelet series and the reflection wave wavelet series corresponding with the wavelet series of transmission SV ripple.

The 4th step: the time domain waveform of calculating light incident side parallel cracks trend and vertical joints trend

Be arranged in light incident side sensor record incident wave and reflection wave, according to the position relation of stress direction of wave travel and spot sensor, by incident P ripple, reflected P ripple, incident SV ripple and reflection SV Wave Decomposition to along Joint strike and vertical joints trend.Vibration source produces P ripple and SV ripple is directly transmitted to i sensor along ray II, and the angle of propagation rays II and y axle is β _i, adopt relational expression 6 to calculate β _i; Vibration source produces P ripple and SV ripple reflects and is transmitted to i sensor again through joint place along ray I, and the angle of propagation rays I and y axle is α _i, adopt relational expression 7 to calculate α _i.

Relational expression 6 is:

${\mathrm{\α}}_i=\arctan \left(\frac{c_i}{h+2b}\right)$

Relational expression 7 is:

${\mathrm{\β}}_i=\arctan \left(\frac{c_i}{h}\right)$

In relational expression 6 and relational expression 7, h is the vertical range of vibration source and light incident side sensor; B is the vertical range of measuring point to joint; c _ifor the distance of i sensor of light incident side and y axle.

I this measuring point of sensor record, at the vibrational waveform of x and y direction, as shown in Figure 2, set up x and the vibrational waveform of y direction and the relation of reflection wave, and its relation is shown in relational expression 8.

Relational expression 8 is:

$\left\{\begin{array}{c}{a}_{\mathrm{xi}}\left(t\right)=a_{P1i}\left(t\right)\sin {\mathrm{\α}}_i+a_{\mathrm{SV}2i}\left(t\right)\cos {\mathrm{\β}}_i+a_{\mathrm{SV}3i}\left(t\right)\cos {\mathrm{\α}}_i+a_{P4i}\left(t\right)\sin {\mathrm{\β}}_i\\ a_{\mathrm{yi}}\left(t\right)=a_{P1i}\left(t\right)\cos {\mathrm{\α}}_i+a_{\mathrm{SV}2i}\left(t\right)\sin {\mathrm{\β}}_i-a_{\mathrm{SV}3i}\left(t\right)\sin {\mathrm{\α}}_i-a_{P4i}\left(t\right)\cos {\mathrm{\β}}_i\end{array}\right.$

In relational expression 8, a _p1iand a (t) _sV3i(t) be respectively P ripple and the SV wave reflection ripple time domain waveform of i sensor position; a _sV2iand a (t) _p4i(t) be respectively P ripple and the SV ripple incident wave time domain waveform of i sensor position; a _xiand a (t) _yi(t) the difference x of i sensor position and the calculating time domain waveform of y direction.

The 5th step: the normal stiffness and the shear stiffness that calculate joint

(1) a given initial normal stiffness in joint, to the computing of the first step to the four steps in the vibrational waveform executing data analytical procedure of the 1st bar of survey line (with the orthogonal survey line of Joint strike), the series that obtains incident P ripple and reflected P ripple is calculated wavelet time domain waveform; The series of stack incident P ripple and reflected P ripple is calculated wavelet time domain waveform, obtains the calculating time domain waveform of light incident side; Adopt waveform norm to quantize to calculate the difference of time domain waveform and light incident side actual measurement time domain waveform, constantly increase joint normal stiffness, recalculate the difference that obtains calculating time domain waveform and actual measurement time domain waveform, in the time that difference meets the demands, determine the normal stiffness at joint.

(2) the initial shear stiffness at a given joint, to the computing of the first step to the four steps in the vibrational waveform executing data analytical procedure of the 1st bar of survey line, the series that obtains incident SV ripple and reflection SV ripple is calculated wavelet time domain waveform; The series of stack incident SV ripple and reflection SV ripple is calculated wavelet time domain waveform, obtains the calculating time domain waveform of light incident side; Adopt waveform norm to quantize to calculate the difference of time domain waveform and light incident side actual measurement time domain waveform, constantly increase joint shear stiffness, recalculate the difference that obtains calculating time domain waveform and actual measurement time domain waveform, in the time that difference meets the demands, determine the shear stiffness at joint.

(3) the 5th step (1), (2) definite normal stiffness and shear stiffness in input data analysis step, to the computing of the first step to the four steps in the vibrational waveform executing data analytical procedure of the 2nd bar of survey line, the series that obtains incident P ripple and reflected P ripple is calculated wavelet time domain waveform; Adopt the calculation procedure identical with P ripple, the series that obtains incident SV ripple and reflection SV ripple is calculated wavelet time domain waveform; Respectively the series of P ripple and SV ripple being calculated to wavelet time domain waveform decomposes to along Joint strike and vertical joints trend, obtain along the calculating time domain waveform of Joint strike and vertical joints trend, quantize respectively along Joint strike and the calculating time domain waveform of vertical joints trend and the difference of measured waveform; Adjust normal stiffness and the shear stiffness at joint, again obtain calculating the difference of time domain waveform and measured waveform, in the time that difference meets the demands, determine normal stiffness and the shear stiffness at joint; Article 3, and other survey line according to the 2nd article of identical method of survey line, calculate corresponding joint rigidity.

(4) gather the joint rigidity calculating according to each survey line vibrational waveform, calculate respectively the mean value of joint normal stiffness and shear stiffness, mean value by the rigidity at survey joint.

Beneficial effect of the present invention: (1) the present invention only need arrange in both sides, joint and manually knock generation stress wave by several sensors, adopts vibrating data collection instrument to record the vibrational waveform of each sensor, and simple to operate, testing cost is low.(2) thickness of ROCK MASS JOINT is little, be generally several millimeters to several centimetres, be difficult to on-site sampling, because of its size little, also insensitive to velocity of wave, the present invention adopts the parameter of wave form varies as reflection joint mechanical characteristic, can concentrated expression spectral amplitude and the variation of phase spectrum, based on the method for Full wave shape information analysis joint rigidity, test result has reflected the complicacy of joint mechanical characteristic more comprehensively.(3) the time domain propagation model at joint according to set up stress wave, uses wave field decomposition technique, and the vibrational waveform of light incident side is decomposed into incident wave and reflection wave, considered the impact of reflection wave on result of calculation, thereby test result is more reasonable.

Certain mine is through the strip mining transformation of decades, form the high gradient slope of hundreds of rice, production great explosion is very large to the stabilizing influence of high gradient slope, and form geologic hazard hidden danger, the stability of the methods analyst high gradient slope that this ore deposit employing numerical evaluation and Monitoring of Slope Deformation combine for this reason, adopt the joint rigidity of the present invention's acquisition as the input parameter of numerical evaluation, result of calculation and Monitoring Data are substantially identical.

Accompanying drawing explanation

Fig. 1 is ROCK MASS JOINT mechanics parameter testing scheme schematic diagram of the present invention.

Fig. 2 is wave field decomposing schematic representation of the present invention.

In figure: 1 vibration source; 2 surveys line; 3 acceleration transducers; 4 ROCK MASS JOINT; The angle of 5 ray II and y axle, uses β _irepresent; The angle of 6 ray I and y axle, uses α _irepresent; 7 ray II; 8 ray I; A 9 i sensor; 10 is the direction of vibration of reflected P ripple; The direction of vibration of 11 incident SV ripples; The direction of vibration of 12 reflection SV ripples; The direction of vibration of 13 incident P ripples; The distance of 14 i of light incident side sensors and y axle, uses c _irepresent; The vertical range at 15 joint two side sensers and joint, represents with b; The vertical range of 16 vibration sources and light incident side sensor, represents with h.

Embodiment

Employing the present invention at home certain opencut has carried out underground test, and data test step, data analysis step and test result are as follows.

A, testing procedure

The first step: the physical and mechanical parameter of testing experiment region sillar, needs the flexible modulus of mechanics parameter, Poisson ratio and the density of testing; Select representational sillar at pilot region, be processed into Standard rock sample, with the mechanics parameter of rock test rig test sillar, adopt the density of conventional method test rock; Determine that by the method for averaging the elastic modulus of test site sillar is 24.06GPa, density is 2543kg/m ³, Poisson ratio is 0.17.

Second step: normal direction and the shear stiffness at test joint, along Joint strike to be tested, selection can reflect the test section of joint mechanical characteristic, test section requires surperficial opposed flattened; Arrange 4 surveys line at test section, as shown in Figure 1, and survey line is numbered, the incident angle of 4 surveys line is respectively 0 °, 20 °, 40 ° and 60 °, and all surveys line intersect at a bit, and this point is vibration source place, applies the application point of shock load; Along every survey line, arrange two two component accelerometer sensors in both sides, joint, with gesso, sensor is bonded in to the surface of pilot region, one-component parallel cracks moves towards to arrange, another component vertical joints is moved towards to arrange, hereinafter to be referred as being light incident side the half side of vibration source direction, abbreviation opposite side is transmissive side, and the sensor of light incident side and transmissive side and the distance at joint are 15cm; The vibration that shock load produces is vibration source, and the distance between vibration source place and joint is 1.0m; Record after the position coordinates at each sensor, vibration source and joint, adopt shock load to produce stress wave, record the vibrational waveform of each sensor; Sensor parameters is: charge sensitivity 10.427～14.091pC/ms ^-2, Hz-KHz 0.2～5kHz, resonance frequency 15kHz; With manually knocking generation vibration signal, vibrational waveform gathers after signal condition instrument carries out filtering processing again, and the parameter of signal condition instrument is set to low pass 3kHz, and total sampling rate is 500kHz; The INV306 vibration acquisition instrument that the vibration acquisition instrument using is produced for Beijing Orient vibration and noise technical institute.

B, data analysis step

The first step: set up the time-domain analysis model that wavelet is propagated at joint

Adopt spring model to describe joint distortion, if structural plane joint two lateral stresses are continuous, displacement discontinuous quantity equals the ratio of stress and joint rigidity, set up the differential equation group of transmission, reflection wave speed time domain waveform and incident wave time domain waveform, when the incident of P ripple, see relational expression 1, when the incident of SV ripple, see relational expression 2.Use Waveform Matching back tracking method to obtain analytic solution each, reflection configuration, realized and in time domain, analyzed the impact that propagate corresponding Reeb, joint, calculate the time domain waveform of transmission and reflection.

Relational expression 1:

Relational expression 2:

In relational expression 1 and relational expression 2, v _p, v _rP, v _rS, v _tP, v _tSbe respectively incident P ripple, reflected P ripple, reflection SV ripple, transmission P ripple, transmission SV wave propagation velocity time domain waveform; ρ ₁and ρ ₂be respectively the density of light incident side sillar and transmissive side sillar; c _p1, c _s1be respectively P ripple and the SV phase velocity of wave of light incident side sillar; c _p2, c _s2be respectively P ripple and the SV phase velocity of wave of transmissive side sillar; T is the time; φ is incident angle and P wave reflection angle; for SV wave reflection angle; φ ' is the angle of transmission of P ripple;

for the angle of transmission of SV ripple; K _tfor structural plane shear stiffness; K _nfor structural plane normal stiffness.

Second step: wavelet decomposition transmitted wave

(1) vibrational waveform of decomposition transmissive side obtains transmission P ripple and transmission SV ripple, the sensor record of transmissive side the parallel cracks trend of transmissive side and the vibrational waveform that vertical joints is moved towards, according to the relation of stress wave propagation direction and direction of vibration, decomposed and obtained transmission P ripple and transmission SV ripple by wave field, the formula that wave field decomposes is shown in relational expression 3.

Relational expression 3:

$\left\{\begin{array}{c}{a}_{\mathrm{pi}}\left(t\right)=a_{\mathrm{yi}}\left(t\right)\cos {\mathrm{\θ}}_i+a_{\mathrm{xi}}\left(t\right)\sin {\mathrm{\θ}}_i\\ a_{\mathrm{si}}\left(t\right)=a_{\mathrm{xi}}\left(t\right)\cos {\mathrm{\θ}}_i-a_{\mathrm{yi}}\left(t\right)\sin {\mathrm{\θ}}_i\end{array}\right.$

In relational expression 3, a _piand a (t) _si(t) be respectively the time domain waveform of P ripple and the SV ripple of i sensor position; a _xiand a (t) _yi(t) respectively i x that sensor records and y direction (x and y represent respectively to sit along joint to vertical joints sit to coordinate, time domain waveform as shown in Figure 2), θ _iit is the angle of i sensor place survey line and Article 1 survey line.

(2) set up wavelet storehouse, adopting Ricker wavelet is the vertical wavelet of wavelet capital construction storehouse, and the time-domain expression of Ricker wavelet is shown in relational expression 4.

Relational expression 4:

$a_R\left(t\right)=(1-{2\mathrm{\π}}^2{f}_M^2{t}^2)\exp (-{\mathrm{\π}}^2{f}_M^2{t}^2)$

In relational expression 4, f _mfor crest frequency, in relational expression 4, introduce time shift factor q and scale factor p, set up Ricker wavelet storehouse, the matrix in wavelet storehouse 45 × 45, by the obtaining value method of rational p and q, guarantee that wavelet can cover signal to be decomposed on time domain and frequency domain, the wavelet function of introducing after the time shift factor and scale factor is shown in relational expression 5.

Relational expression 5:

$u_R\left(t\right)=[1-{2\mathrm{\π}}^2{f}_M^2{\left(\frac{t-q_j}{p_j}\right)}^2]\exp [-{\mathrm{\π}}^2{f}_M^2{\left(\frac{t-q_j}{p_j}\right)}^2]$

(3) be wavelet series by transmission P Wave Decomposition, inner product is done in signal to be decomposed and wavelet storehouse and obtain wavelet coefficient, the wavelet of wavelet coefficient maximum is defined as optimum wavelet, the difference of calculating signal to be decomposed and optimum wavelet obtains residual signal, residual signal and wavelet storehouse are done to inner product, determine second optimum wavelet, by that analogy, when the ratio of the area that the area surrounding when residual signal and time shaft and initialize signal and time shaft surround is less than 0.2%, finish to find optimum wavelet, determine thus the wavelet of 30 transmission P ripples.

(4) be wavelet series by transmission SV Wave Decomposition, the method that is wavelet according to transmission P Wave Decomposition, decomposes SV ripple, obtains the wavelet of 30 transmission SV ripples.

The 3rd step: the wavelet series of calculating incident wave and reflection wave

In data analysis step, second step decomposes the transmission P ripple that obtains and the wavelet series of transmission SV ripple, given joint initial stiffness is 1.0GPa/m, the time-domain analysis model of propagating at joint according to stress wave that the first step is set up in data analysis step, calculates respectively corresponding incident wave wavelet series and the reflection wave wavelet series of wavelet series of transmission P ripple; Calculate respectively corresponding incident wave wavelet series and the reflection wave wavelet series of wavelet series of transmission SV ripple.

The 4th step: the time domain waveform of calculating light incident side parallel cracks trend and vertical joints trend

Vibration source produces P ripple and SV ripple is directly transmitted to i sensor along ray II, and the angle of propagation rays II and y axle is β _i, adopt relational expression 6 to calculate β _i; Vibration source produces P ripple and SV ripple reflects and is transmitted to i sensor again through joint place along ray I, and the angle of propagation rays I and y axle is α _i, adopt relational expression 7 to calculate α _i.

Relational expression 6 is:

${\mathrm{\α}}_i=\arctan \left(\frac{c_i}{h+2b}\right)$

Relational expression 7 is:

${\mathrm{\β}}_i=\arctan \left(\frac{c_i}{h}\right)$

In relational expression 6 and relational expression 7, h is the vertical range of vibration source and light incident side sensor; B is the vertical range of measuring point to joint; c _ifor the distance of i sensor of light incident side and y axle.

I this measuring point of sensor record, at the vibrational waveform of x and y direction, as shown in Figure 2, set up x and the vibrational waveform of y direction and the relation of reflection wave, and its relation is shown in relational expression 8.

Relational expression 8 is:

$\left\{\begin{array}{c}{a}_{\mathrm{xi}}\left(t\right)=a_{P1i}\left(t\right)\sin {\mathrm{\α}}_i+a_{\mathrm{SV}2i}\left(t\right)\cos {\mathrm{\β}}_i+a_{\mathrm{SV}3i}\left(t\right)\cos {\mathrm{\α}}_i+a_{P4i}\left(t\right)\sin {\mathrm{\β}}_i\\ a_{\mathrm{yi}}\left(t\right)=a_{P1i}\left(t\right)\cos {\mathrm{\α}}_i+a_{\mathrm{SV}2i}\left(t\right)\sin {\mathrm{\β}}_i-a_{\mathrm{SV}3i}\left(t\right)\sin {\mathrm{\α}}_i-a_{P4i}\left(t\right)\cos {\mathrm{\β}}_i\end{array}\right.$

In relational expression 8, a _p1iand a (t) _sV3i(t) be respectively P ripple and the SV wave reflection ripple time domain waveform of i sensor position; a _sV2iand a (t) _p4i(t) be respectively P ripple and the SV ripple incident wave time domain waveform of i sensor position; a _xiand a (t) _yi(t) the difference x of i sensor position and the calculating time domain waveform of y direction.

The 5th step: the normal stiffness and the shear stiffness that calculate joint

(1) the initial normal stiffness 1.0GPa/m at given joint, to the computing of the first step to the four steps in the vibrational waveform executing data analytical procedure of the 1st bar of survey line (with the orthogonal survey line of Joint strike), the series that obtains incident P ripple and reflected P ripple is calculated wavelet time domain waveform; The series of stack incident P ripple and reflected P ripple is calculated wavelet time domain waveform, obtains the calculating time domain waveform of light incident side P ripple; Adopt waveform norm to quantize to calculate the difference of time domain waveform and light incident side actual measurement time domain waveform, constantly increase joint normal stiffness, recalculate and obtain calculating time domain waveform and the difference of surveying time domain waveform, in the time that difference is less than 0.3%, determine the normal stiffness 28.2GPa/m at joint;

(2) the initial shear stiffness 1.0GPa/m at given joint, to the computing of the first step to the four steps in the vibrational waveform executing data analytical procedure of the 1st bar of survey line, the series that obtains incident SV ripple and reflection SV ripple is calculated wavelet time domain waveform; The series of stack incident SV ripple and reflection SV ripple is calculated wavelet time domain waveform, obtains the calculating time domain waveform of light incident side SV ripple; Adopt waveform norm to quantize to calculate the difference of time domain waveform and light incident side actual measurement time domain waveform, constantly increase joint shear stiffness, recalculate the difference that obtains calculating transmission waveform and measured waveform, in the time that difference is less than 0.3%, determine the shear stiffness 17.6GPa/m at joint;

(3) the 5th step (1), (2) definite normal stiffness and shear stiffness in input data analysis step, to the computing of the first step to the four steps in the vibrational waveform executing data analytical procedure of the 2nd bar of survey line, the series that obtains incident P ripple and reflected P ripple is calculated wavelet time domain waveform; Adopt the calculation procedure identical with P ripple, the series that obtains incident SV ripple and reflection SV ripple is calculated wavelet time domain waveform; Respectively the series of P ripple and SV ripple being calculated to wavelet time domain waveform decomposes to along Joint strike and vertical joints trend, obtain along the calculating time domain waveform of Joint strike and vertical joints trend, quantize respectively along Joint strike and the calculating time domain waveform of vertical joints trend and the difference of measured waveform; Adjust normal stiffness and the shear stiffness at joint, again obtain calculating the difference of time domain waveform and measured waveform, in the time that difference is less than 0.3%, determine normal stiffness and the shear stiffness at joint; Article 3, and other survey line according to the 2nd article of identical method of survey line, calculate corresponding joint rigidity; Be respectively 28.2GPa/m, 22.0GPa/m, 14.7GPa/m, 20.5GPa/m, 19.1GPa/m by 5 definite normal stiffnesses of survey line, shear stiffness is respectively 17.6GPa/m, 14.5GPa/m, 21.4GPa/m, 12.5GPa/m, 11.3GPa/m;

(4) gather the joint rigidity calculating according to each survey line vibrational waveform, calculate respectively the mean value of joint normal stiffness and shear stiffness, mean value by the rigidity at survey joint; Mean rigidity normal direction is 20.9GPa/m, and average shear stiffness is 15.5GPa/m.

Adopt the joint rigidity of the present invention's acquisition as the input parameter of numerical evaluation, result of calculation and this ore deposit adopt the STABILITY MONITORING data of Monitoring of Slope Deformation methods analyst high gradient slope substantially identical.

Claims (2)

1. a Full wave shape information method of testing for ROCK MASS JOINT rigidity, is characterized in that: comprise testing procedure and data analysis step:

A, testing procedure

The first step: the physical and mechanical parameter of testing experiment region sillar

Elastic modulus, Poisson ratio and density; Select representational sillar at pilot region, be processed into Standard rock sample, with the mechanics parameter of rock test rig test rock, adopt the density of conventional method test sillar;

Second step: test joint normal direction and shear stiffness

Along Joint strike to be tested, selection can reflect the test section of joint mechanical characteristic, and test section requires surperficial opposed flattened; Arrange 2-5 bar survey line at test section, for guaranteeing measuring accuracy, the incident angle of all surveys line is not more than 65 °; Survey line is numbered, and the 1st bar of survey line is vertical with joint, and incident angle is 0 °, increases with survey line numbering, and incident angle increases, and all surveys line intersect at a bit, and this point is vibration source place, applies the application point of shock load; Along every survey line, arrange two two component sensors in both sides, joint, one-component parallel cracks moves towards to arrange, another component vertical joints is moved towards to arrange, hereinafter to be referred as being light incident side the half side of vibration source direction, abbreviation opposite side is transmissive side, and the distance at sensor and joint is 10-30cm, and the sensor of arranging with transmissive side at light incident side is identical with joint distance; The vibration that shock load produces is vibration source, and the distance between vibration source place and joint is 0.5-2.0m, and the microfissure of both sides, joint rock mass is educated all the more, and distance is less; Record after the position coordinates at each sensor, vibration source and joint, shock load produces stress wave, adopts vibrating data collection instrument to record the vibrational waveform of each sensor;

B, data analysis step

Set up the time domain propagation model of wavelet at joint, transmitted wave is decomposed into wavelet, uses the time domain propagation model of wavelet at joint, calculate light incident side incident wave and reflection wave, calculating time domain waveform based on light incident side and actual measurement time domain waveform matching condition are determined joint rigidity, and data analysis step is as follows:

The first step: set up the time-domain analysis model that wavelet is propagated at joint

Adopt spring model to describe joint distortion, if structural plane joint two lateral stresses are continuous, displacement discontinuous quantity equals the ratio of stress and joint rigidity, set up the differential equation group of transmission, reflection wave speed time domain waveform and incident wave time domain waveform, when the incident of P ripple, see relational expression 1, when the incident of SV ripple, see relational expression 2, use Waveform Matching back tracking method to obtain analytic solution each, reflection configuration, realize and in time domain, analyzed the impact that propagate corresponding Reeb, joint, calculated the time domain waveform of transmitted wave and reflection wave;

Relational expression 1:

Relational expression 2:

In relational expression 1 and relational expression 2, v _p, v _rP, v _rS, v _tP, v _tSbe respectively incident P ripple, reflected P ripple, reflection SV ripple, transmission P ripple, transmission SV wave propagation velocity time domain waveform; ρ ₁and ρ ₂be respectively the density of light incident side sillar and transmissive side sillar; c _p1, c _s1be respectively P ripple and the SV phase velocity of wave of light incident side sillar; c _p2, c _s2be respectively P ripple and the SV phase velocity of wave of transmissive side sillar; T is the time; φ is incident angle and P wave reflection angle;

for SV wave reflection angle; φ ' is the angle of transmission of P ripple;

for the angle of transmission of SV ripple; K _tfor structural plane shear stiffness; K _nfor structural plane normal stiffness;

Second step: wavelet decomposition transmitted wave

(1) vibrational waveform of decomposition transmissive side obtains transmission P ripple and transmission SV ripple, the sensor record of transmissive side the parallel cracks trend of transmissive side and the vibrational waveform that vertical joints is moved towards, according to the relation of stress wave propagation direction and direction of vibration, decomposed and obtained transmission P ripple and transmission SV ripple by wave field, the formula that wave field decomposes is shown in relational expression 3;

Relational expression 3:

$\left\{\begin{array}{c}{a}_{\mathrm{pi}}\left(t\right)=a_{\mathrm{yi}}\left(t\right)\cos {\mathrm{\θ}}_i+a_{\mathrm{xi}}\left(t\right)\sin {\mathrm{\θ}}_i\\ a_{\mathrm{si}}\left(t\right)=a_{\mathrm{xi}}\left(t\right)\cos {\mathrm{\θ}}_i-a_{\mathrm{yi}}\left(t\right)\sin {\mathrm{\θ}}_i\end{array}\right.$

In relational expression 3, a _piand a (t) _si(t) be respectively the time domain waveform of P ripple and the SV ripple of i sensor position; a _xiand a (t) _yi(t) time domain waveform of i x that sensor records and y direction respectively, wherein x and y represent respectively to sit along joint to vertical joints sit to coordinate, θ _iit is the angle of i sensor place survey line and Article 1 survey line;

(2) set up wavelet storehouse, selection can effectively reflect the wavelet base of stress wave in joint propagation characteristic, introduces the time shift factor and scale factor, sets up wavelet storehouse, the matrix that wavelet storehouse is m × n, the line number that wherein m is matrix; N is matrix column number, by the time shift factor and the rational value of scale factor, guarantees that wavelet can cover signal to be decomposed on time domain and frequency domain; It is the vertical wavelet of wavelet capital construction storehouse that the present invention adopts Ricker wavelet, and the time-domain expression of Ricker wavelet is shown in relational expression 4;

Relational expression 4:

$a_R\left(t\right)=(1-{2\mathrm{\π}}^2{f}_M^2{t}^2)\exp (-{\mathrm{\π}}^2{f}_M^2{t}^2)$

In relational expression 4, f _mfor crest frequency, in relational expression 4, introduce time shift factor q and scale factor p, set up Ricker wavelet storehouse, the wavelet function of introducing after the time shift factor and scale factor is shown in relational expression 5;

Relational expression 5:

$u_R\left(t\right)=[1-{2\mathrm{\π}}^2{f}_M^2{\left(\frac{t-q_j}{p_j}\right)}^2]\exp [-{\mathrm{\π}}^2{f}_M^2{\left(\frac{t-q_j}{p_j}\right)}^2]$

(3) be wavelet series by transmission P Wave Decomposition, inner product is done in signal to be decomposed and wavelet storehouse and obtain wavelet coefficient, the wavelet of wavelet coefficient maximum is defined as optimum wavelet, the difference of calculating signal to be decomposed and optimum wavelet obtains residual signal, and residual signal and wavelet storehouse are done to inner product, determines second optimum wavelet, by that analogy, in the time meeting error requirements, finish to find optimum wavelet, determine thus the wavelet series of transmission P ripple;

(4) be wavelet series by transmission SV Wave Decomposition, the method that is wavelet according to transmission P Wave Decomposition, decomposes SV ripple, obtains the wavelet series of transmission SV ripple;

The 3rd step: the wavelet series of calculating incident wave and reflection wave

In data analysis step, second step decomposes the transmission P ripple that obtains and the wavelet series of transmission SV ripple, the time-domain analysis model that the stress wave of setting up according to the first step in data analysis step is propagated at joint, calculates respectively with transmission P marble wave system and is listed as corresponding incident wave wavelet series and reflection wave wavelet series; Calculate respectively incident wave wavelet series and the reflection wave wavelet series corresponding with the wavelet series of transmission SV ripple;

The 4th step: the time domain waveform of calculating light incident side parallel cracks trend and vertical joints trend

Be arranged in light incident side sensor record incident wave and reflection wave, according to the position relation of stress direction of wave travel and spot sensor, by incident P ripple, reflected P ripple, incident SV ripple and reflection SV Wave Decomposition to along Joint strike and vertical joints trend; Vibration source produces P ripple and SV ripple is directly transmitted to i sensor along ray II, and the angle of propagation rays II and y axle is β _i, adopt relational expression 6 to calculate β _i; Vibration source produces P ripple and SV ripple reflects and is transmitted to i sensor again through joint place along ray I, and the angle of propagation rays I and y axle is α _i, adopt relational expression 7 to calculate α _i;

Relational expression 6 is:

${\mathrm{\α}}_i=\arctan \left(\frac{c_i}{h+2b}\right)$

Relational expression 7 is:

${\mathrm{\β}}_i=\arctan \left(\frac{c_i}{h}\right)$

In relational expression 6 and relational expression 7, h is the vertical range of vibration source and light incident side sensor; B is the vertical range of measuring point to joint; c _ifor the distance of i sensor of light incident side and y axle;

I this measuring point of sensor record, at the vibrational waveform of x and y direction, set up x and the vibrational waveform of y direction and the relation of reflection wave, and its relation is shown in relational expression 8;

Relational expression 8 is:

$\left\{\begin{array}{c}{a}_{\mathrm{xi}}\left(t\right)=a_{P1i}\left(t\right)\sin {\mathrm{\α}}_i+a_{\mathrm{SV}2i}\left(t\right)\cos {\mathrm{\β}}_i+a_{\mathrm{SV}3i}\left(t\right)\cos {\mathrm{\α}}_i+a_{P4i}\left(t\right)\sin {\mathrm{\β}}_i\\ a_{\mathrm{yi}}\left(t\right)=a_{P1i}\left(t\right)\cos {\mathrm{\α}}_i+a_{\mathrm{SV}2i}\left(t\right)\sin {\mathrm{\β}}_i-a_{\mathrm{SV}3i}\left(t\right)\sin {\mathrm{\α}}_i-a_{P4i}\left(t\right)\cos {\mathrm{\β}}_i\end{array}\right.$

In relational expression 8, a _p1iand a (t) _sV3i(t) be respectively P ripple and the SV wave reflection ripple time domain waveform of i sensor position; a _sV2iand a (t) _p4i(t) be respectively P ripple and the SV ripple incident wave time domain waveform of i sensor position; a _xiand a (t) _yi(t) the difference x of i sensor position and the calculating time domain waveform of y direction;

The 5th step: the normal stiffness and the shear stiffness that calculate joint

(1) a given initial normal stiffness in joint, to the computing of the first step to the four steps in the vibrational waveform executing data analytical procedure of the 1st bar of survey line, the series that obtains incident P ripple and reflected P ripple is calculated wavelet time domain waveform; The series of stack incident P ripple and reflected P ripple is calculated wavelet time domain waveform, obtains the calculating time domain waveform of light incident side; Adopt waveform norm to quantize to calculate the difference of time domain waveform and light incident side actual measurement time domain waveform, constantly increase joint normal stiffness, recalculate the difference that obtains calculating time domain waveform and actual measurement time domain waveform, in the time that difference meets the demands, determine the normal stiffness at joint;

(2) the initial shear stiffness at a given joint, to the computing of the first step to the four steps in the vibrational waveform executing data analytical procedure of the 1st bar of survey line, the series that obtains incident SV ripple and reflection SV ripple is calculated wavelet time domain waveform; The series of stack incident SV ripple and reflection SV ripple is calculated wavelet time domain waveform, obtains the calculating time domain waveform of light incident side; Adopt waveform norm to quantize to calculate the difference of time domain waveform and light incident side actual measurement time domain waveform, constantly increase joint shear stiffness, recalculate the difference that obtains calculating time domain waveform and actual measurement time domain waveform, in the time that difference meets the demands, determine the shear stiffness at joint;

(3) the 5th step (1), (2) definite normal stiffness and shear stiffness in input data analysis step, to the computing of the first step to the four steps in the vibrational waveform executing data analytical procedure of the 2nd bar of survey line, the series that obtains incident P ripple and reflected P ripple is calculated wavelet time domain waveform; Adopt the calculation procedure identical with P ripple, the series that obtains incident SV ripple and reflection SV ripple is calculated wavelet time domain waveform; Respectively the series of P ripple and SV ripple being calculated to wavelet time domain waveform decomposes to along Joint strike and vertical joints trend, obtain along the calculating time domain waveform of Joint strike and vertical joints trend, quantize respectively along Joint strike and the calculating time domain waveform of vertical joints trend and the difference of measured waveform; Adjust normal stiffness and the shear stiffness at joint, again obtain calculating the difference of time domain waveform and measured waveform, in the time that difference meets the demands, determine normal stiffness and the shear stiffness at joint; Article 3, and other survey line according to the 2nd article of identical method of survey line, calculate corresponding joint rigidity;

(4) gather the joint rigidity calculating according to each survey line vibrational waveform, calculate respectively the mean value of joint normal stiffness and shear stiffness, mean value by the rigidity at survey joint.

2. the Full wave shape information method of testing of a kind of ROCK MASS JOINT rigidity according to claim 1, is characterized in that: best testing procedure and data analysis step are as follows:

A, testing procedure

The first step: the physical and mechanical parameter of testing experiment region sillar, needs the flexible modulus of mechanics parameter, Poisson ratio and the density of testing; Select representational sillar at pilot region, be processed into Standard rock sample, with the mechanics parameter of rock test rig test sillar, adopt the density of conventional method test rock; Determine that by the method for averaging the elastic modulus of test site sillar is 24.06GPa, density is 2543kg/m ³, Poisson ratio is 0.17;

Second step: normal direction and the shear stiffness at test joint, along Joint strike to be tested, selection can reflect the test section of joint mechanical characteristic, test section requires surperficial opposed flattened; Arrange 4 surveys line at test section, and survey line is numbered, the incident angle of 4 surveys line is respectively 0 °, 20 °, 40 ° and 60 °, and all surveys line intersect at a bit, and this point is vibration source place, applies the application point of shock load; Along every survey line, arrange two two component accelerometer sensors in both sides, joint, with gesso, sensor is bonded in to the surface of pilot region, one-component parallel cracks moves towards to arrange, another component vertical joints is moved towards to arrange, hereinafter to be referred as being light incident side the half side of vibration source direction, abbreviation opposite side is transmissive side, and the sensor of light incident side and transmissive side and the distance at joint are 15cm; The vibration that shock load produces is vibration source, and the distance between vibration source place and joint is 1.0m; Record after the position coordinates at each sensor, vibration source and joint, adopt shock load to produce stress wave, record the vibrational waveform of each sensor; Sensor parameters is: charge sensitivity 10.427～14.091pC/ms ^-2, Hz-KHz 0.2～5kHz, resonance frequency 15kHz; With manually knocking generation vibration signal, vibrational waveform gathers after signal condition instrument carries out filtering processing again, and the parameter of signal condition instrument is set to low pass 3kHz, and total sampling rate is 500kHz; The INV306 vibration acquisition instrument that the vibration acquisition instrument using is produced for Beijing Orient vibration and noise technical institute;

B, data analysis step

The first step: set up the time-domain analysis model that wavelet is propagated at joint

Adopt spring model to describe joint distortion, if structural plane joint two lateral stresses are continuous, displacement discontinuous quantity equals the ratio of stress and joint rigidity, set up the differential equation group of transmission, reflection wave speed time domain waveform and incident wave time domain waveform, when the incident of P ripple, see relational expression 1, when the incident of SV ripple, see relational expression 2; Use Waveform Matching back tracking method to obtain analytic solution each, reflection configuration, realized and in time domain, analyzed the impact that propagate corresponding Reeb, joint, calculate the time domain waveform of transmission and reflection;

Relational expression 1:

Relational expression 2:

In relational expression 1 and relational expression 2, v _p, v _rP, v _rS, v _tP, v _tSbe respectively incident P ripple, reflected P ripple, reflection SV ripple, transmission P ripple, transmission SV wave propagation velocity time domain waveform; ρ ₁and ρ ₂be respectively the density of light incident side sillar and transmissive side sillar; c _p1, c _s1be respectively P ripple and the SV phase velocity of wave of light incident side sillar; c _p2, c _s2be respectively P ripple and the SV phase velocity of wave of transmissive side sillar; T is the time; φ is incident angle and P wave reflection angle;

for SV wave reflection angle; φ ' is the angle of transmission of P ripple;

for the angle of transmission of SV ripple; K _tfor structural plane shear stiffness; K _nfor structural plane normal stiffness;

Second step: wavelet decomposition transmitted wave

(1) vibrational waveform of decomposition transmissive side obtains transmission P ripple and transmission SV ripple, the sensor record of transmissive side the parallel cracks trend of transmissive side and the vibrational waveform that vertical joints is moved towards, according to the relation of stress wave propagation direction and direction of vibration, decomposed and obtained transmission P ripple and transmission SV ripple by wave field, the formula that wave field decomposes is shown in relational expression 3;

Relational expression 3:

$\left\{\begin{array}{c}{a}_{\mathrm{pi}}\left(t\right)=a_{\mathrm{yi}}\left(t\right)\cos {\mathrm{\θ}}_i+a_{\mathrm{xi}}\left(t\right)\sin {\mathrm{\θ}}_i\\ a_{\mathrm{si}}\left(t\right)=a_{\mathrm{xi}}\left(t\right)\cos {\mathrm{\θ}}_i-a_{\mathrm{yi}}\left(t\right)\sin {\mathrm{\θ}}_i\end{array}\right.$

In relational expression 3, a _piand a (t) _si(t) be respectively the time domain waveform of P ripple and the SV ripple of i sensor position; a _xiand a (t) _yi(t) time domain waveform of i x that sensor records and y direction respectively, wherein x and y represent respectively to sit along joint to vertical joints sit to coordinate, θ _iit is the angle of i sensor place survey line and Article 1 survey line;

(2) set up wavelet storehouse, adopting Ricker wavelet is the vertical wavelet of wavelet capital construction storehouse, and the time-domain expression of Ricker wavelet is shown in relational expression 4;

Relational expression 4:

$a_R\left(t\right)=(1-{2\mathrm{\π}}^2{f}_M^2{t}^2)\exp (-{\mathrm{\π}}^2{f}_M^2{t}^2)$

In relational expression 4, f _mfor crest frequency, in relational expression 4, introduce time shift factor q and scale factor p, set up Ricker wavelet storehouse, the matrix in wavelet storehouse 45 × 45, by the obtaining value method of rational p and q, guarantee that wavelet can cover signal to be decomposed on time domain and frequency domain, the wavelet function of introducing after the time shift factor and scale factor is shown in relational expression 5;

Relational expression 5:

$u_R\left(t\right)=[1-{2\mathrm{\π}}^2{f}_M^2{\left(\frac{t-q_j}{p_j}\right)}^2]\exp [-{\mathrm{\π}}^2{f}_M^2{\left(\frac{t-q_j}{p_j}\right)}^2]$

(3) be wavelet series by transmission P Wave Decomposition, inner product is done in signal to be decomposed and wavelet storehouse and obtain wavelet coefficient, the wavelet of wavelet coefficient maximum is defined as optimum wavelet, the difference of calculating signal to be decomposed and optimum wavelet obtains residual signal, residual signal and wavelet storehouse are done to inner product, determine second optimum wavelet, by that analogy, when the ratio of the area that the area surrounding when residual signal and time shaft and initialize signal and time shaft surround is less than 0.2%, finish to find optimum wavelet, determine thus the wavelet of 30 transmission P ripples;

(4) be wavelet series by transmission SV Wave Decomposition, the method that is wavelet according to transmission P Wave Decomposition, decomposes SV ripple, obtains the wavelet of 30 transmission SV ripples;

The 3rd step: the wavelet series of calculating incident wave and reflection wave

In data analysis step, second step decomposes the transmission P ripple that obtains and the wavelet series of transmission SV ripple, given joint initial stiffness is 1.0GPa/m, the time-domain analysis model of propagating at joint according to stress wave that the first step is set up in data analysis step, calculates respectively corresponding incident wave wavelet series and the reflection wave wavelet series of wavelet series of transmission P ripple; Calculate respectively corresponding incident wave wavelet series and the reflection wave wavelet series of wavelet series of transmission SV ripple;

The 4th step: the time domain waveform of calculating light incident side parallel cracks trend and vertical joints trend

Vibration source produces P ripple and SV ripple is directly transmitted to i sensor along ray II, and the angle of propagation rays II and y axle is β _i, adopt relational expression 6 to calculate β _i; Vibration source produces P ripple and SV ripple reflects and is transmitted to i sensor again through joint place along ray I, and the angle of propagation rays I and y axle is α _i, adopt relational expression 7 to calculate α _i;

Relational expression 6 is:

${\mathrm{\α}}_i=\arctan \left(\frac{c_i}{h+2b}\right)$

Relational expression 7 is:

${\mathrm{\β}}_i=\arctan \left(\frac{c_i}{h}\right)$

In relational expression 6 and relational expression 7, h is the vertical range of vibration source and light incident side sensor; B is the vertical range of measuring point to joint; c _ifor the distance of i sensor of light incident side and y axle;

I this measuring point of sensor record, at the vibrational waveform of x and y direction, set up x and the vibrational waveform of y direction and the relation of reflection wave, and its relation is shown in relational expression 8;

Relational expression 8 is:

$\left\{\begin{array}{c}{a}_{\mathrm{xi}}\left(t\right)=a_{P1i}\left(t\right)\sin {\mathrm{\α}}_i+a_{\mathrm{SV}2i}\left(t\right)\cos {\mathrm{\β}}_i+a_{\mathrm{SV}3i}\left(t\right)\cos {\mathrm{\α}}_i+a_{P4i}\left(t\right)\sin {\mathrm{\β}}_i\\ a_{\mathrm{yi}}\left(t\right)=a_{P1i}\left(t\right)\cos {\mathrm{\α}}_i+a_{\mathrm{SV}2i}\left(t\right)\sin {\mathrm{\β}}_i-a_{\mathrm{SV}3i}\left(t\right)\sin {\mathrm{\α}}_i-a_{P4i}\left(t\right)\cos {\mathrm{\β}}_i\end{array}\right.$

In relational expression 8, a _p1iand a (t) _sV3i(t) be respectively P ripple and the SV wave reflection ripple time domain waveform of i sensor position; a _sV2iand a (t) _p4i(t) be respectively P ripple and the SV ripple incident wave time domain waveform of i sensor position; a _xiand a (t) _yi(t) the difference x of i sensor position and the calculating time domain waveform of y direction;

The 5th step: the normal stiffness and the shear stiffness that calculate joint

(1) the initial normal stiffness 1.0GPa/m at given joint, to the computing of the first step to the four steps in the vibrational waveform executing data analytical procedure of the 1st bar of survey line, the series that obtains incident P ripple and reflected P ripple is calculated wavelet time domain waveform; The series of stack incident P ripple and reflected P ripple is calculated wavelet time domain waveform, obtains the calculating time domain waveform of light incident side P ripple; Adopt waveform norm to quantize to calculate the difference of time domain waveform and light incident side actual measurement time domain waveform, constantly increase joint normal stiffness, recalculate and obtain calculating time domain waveform and the difference of surveying time domain waveform, in the time that difference is less than 0.3%, determine the normal stiffness 28.2GPa/m at joint;

(2) the initial shear stiffness 1.0GPa/m at given joint, to the computing of the first step to the four steps in the vibrational waveform executing data analytical procedure of the 1st bar of survey line, the series that obtains incident SV ripple and reflection SV ripple is calculated wavelet time domain waveform; The series of stack incident SV ripple and reflection SV ripple is calculated wavelet time domain waveform, obtains the calculating time domain waveform of light incident side SV ripple; Adopt waveform norm to quantize to calculate the difference of time domain waveform and light incident side actual measurement time domain waveform, constantly increase joint shear stiffness, recalculate the difference that obtains calculating transmission waveform and measured waveform, in the time that difference is less than 0.3%, determine the shear stiffness 17.6GPa/m at joint;

(3) the 5th step (1), (2) definite normal stiffness and shear stiffness in input data analysis step, to the computing of the first step to the four steps in the vibrational waveform executing data analytical procedure of the 2nd bar of survey line, the series that obtains incident P ripple and reflected P ripple is calculated wavelet time domain waveform; Adopt the calculation procedure identical with P ripple, the series that obtains incident SV ripple and reflection SV ripple is calculated wavelet time domain waveform; Respectively the series of P ripple and SV ripple being calculated to wavelet time domain waveform decomposes to along Joint strike and vertical joints trend, obtain along the calculating time domain waveform of Joint strike and vertical joints trend, quantize respectively along Joint strike and the calculating time domain waveform of vertical joints trend and the difference of measured waveform; Adjust normal stiffness and the shear stiffness at joint, again obtain calculating the difference of time domain waveform and measured waveform, in the time that difference is less than 0.3%, determine normal stiffness and the shear stiffness at joint; Article 3, and other survey line according to the 2nd article of identical method of survey line, calculate corresponding joint rigidity; Be respectively 28.2GPa/m, 22.0GPa/m, 14.7GPa/m, 20.5GPa/m, 19.1GPa/m by 5 definite normal stiffnesses of survey line, shear stiffness is respectively 17.6GPa/m, 14.5GPa/m, 21.4GPa/m, 12.5GPa/m, 11.3GPa/m;

(4) gather the joint rigidity calculating according to each survey line vibrational waveform, calculate respectively the mean value of joint normal stiffness and shear stiffness, mean value by the rigidity at survey joint; Mean rigidity normal direction is 20.9GPa/m, and average shear stiffness is 15.5GPa/m.