CN110243278B - Distributed measurement method for rock-soil displacement - Google Patents
Distributed measurement method for rock-soil displacement Download PDFInfo
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- CN110243278B CN110243278B CN201910619103.9A CN201910619103A CN110243278B CN 110243278 B CN110243278 B CN 110243278B CN 201910619103 A CN201910619103 A CN 201910619103A CN 110243278 B CN110243278 B CN 110243278B
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B7/00—Measuring arrangements characterised by the use of electric or magnetic techniques
- G01B7/16—Measuring arrangements characterised by the use of electric or magnetic techniques for measuring the deformation in a solid, e.g. by resistance strain gauge
- G01B7/18—Measuring arrangements characterised by the use of electric or magnetic techniques for measuring the deformation in a solid, e.g. by resistance strain gauge using change in resistance
Abstract
The invention discloses a distributed measurement method for rock-soil displacement. Measuring the transmission time of a signal in an unstretched spiral transmission line with a known length by using a time domain reflection technology to obtain the transmission speed of the signal in the spiral transmission line and the characteristic impedance of the signal in an unstretched state; measuring the characteristic impedance in a working state according to a given characteristic impedance transformation threshold until the change of the measured characteristic impedance is larger than the threshold, judging that stretching occurs, measuring the time when the characteristic impedance changes and the time when the characteristic impedance recovers to a normal value, and calculating the length of a stretching area; and according to the measured maximum characteristic impedance in the stretching area, introducing a fitting function to obtain the stretching amount, obtaining the number of turns of the spiral transmission line in the stretching area, and finally obtaining the total stretching amount. The invention has the beneficial effects that: the method realizes the measurement of the large stretching amount of the rock soil, and provides an accurate and easily-realized measurement and monitoring method for greatly reducing the damage of address catastrophe to human beings.
Description
Technical Field
The invention relates to the technical field related to geological disaster monitoring and prediction, in particular to a distributed measurement method for rock and soil displacement.
Background
Although the monitoring of the hidden danger points of the disasters has been researched all over the world, the geological disaster prediction is still a big problem for people, and the casualties caused by the geological disaster still occur frequently. The annual address disaster yearbook published in China for statistics can obtain that the annual geological disaster occurrence frequency of China is high, and the investment for geological disaster prevention and control is increased year by year in recent years. Monitoring, early warning and prevention of geological disasters are still important work. In order to effectively control the occurrence of geological disasters, better monitor disaster hidden danger points and timely prevent various geological disasters, a monitoring means based on fusion of various physical quantities such as surface deformation quantity, underground deformation quantity, soil moisture content, slope inclination angle, rainfall intensity and the like is provided for various complicated terrain geology, and the soil deformation quantity is one of important physical quantities. Geological disasters can be classified according to causes, geological environments, geomorphic features, casualty degrees and the like, and the classification method is more. In the monitoring method of various geological disasters, the measurement of the deformation displacement of the earth surface and the underground is a main monitoring mode, and in the landslide measurement, the monitoring of the deformation displacement of the earth surface and the underground is also a most direct and most effective means for acquiring the deformation characteristics of a landslide range, a landslide surface position, a landslide direction and the like, and accurate data information can be provided for landslide control.
The sensing technologies mainly used for monitoring the deformation displacement of the rock soil currently include a remote sensing technology, a navigation satellite positioning technology, a total station observation technology, a stay wire displacement sensing technology, a coaxial cable deformation sensing technology, an optical fiber deformation sensing technology, a parallel spiral transmission line deformation sensing technology and the like. The first three measuring methods have wide measuring range, the precision reaches 1mm, but the measuring methods are easily influenced by vegetation; the measurement precision of the stay wire displacement sensing technology can reach 0.1mm, but the anti-interference capability is poor. The distributed measurement of micro deformation always adopts an optical fiber deformation sensing technology, the precision can reach 100nm, but similar sensing methods and elements are lacked for the distributed measurement of large deformation of rock soil and strong tensile resistance.
Patent No. 201110361043.9 discloses a parallel helical transmission line structure for distributed measurement of geotechnical deformation, which is buried underground or on the earth surface, and when tensile deformation occurs, it is difficult to ensure that two conductors are parallel at any point, and there is no specific reference to how such a parallel helical transmission line structure is implemented. The patent only gives a positioning measurement method for rock-soil stretching, and the measurement of the stretching amount is not specifically given. Patent No. 201610560335.8 discloses building a rock-soil deformation position distribution measurement model based on parallel spiral transmission lines, and accurately measuring deformation positions by building a prediction model of a least square-support vector machine, the method firstly uses a time domain reflection measurement device to perform tensile measurement on the transmission lines, performs feature extraction on measured data to obtain feature vectors, and gives no description on the tensile mechanism of the transmission lines, the solution of the transmission line characteristic impedance and the relation between the characteristic impedance and the tensile quantity, while the distributed measurement of the rock-soil deformation is not given except for measuring the deformation positions, and more importantly, a measurement method for measuring the tensile quantity and the total tensile quantity of the deformation is also not given.
Disclosure of Invention
The invention provides a distributed measurement method for accurately measuring the rock-soil displacement amount of the stretching position and the stretching amount, aiming at overcoming the defects in the prior art.
In order to achieve the purpose, the invention adopts the following technical scheme:
a distributed measurement method for rock-soil displacement provides a solution model and a solution method for parallel spiral transmission line distribution parameters, so as to obtain a fitting function of characteristic impedance of the parallel spiral transmission line and rock-soil tensile quantity; the method specifically comprises the following steps:
(1) measuring the transmission time of a signal in an unstretched parallel spiral transmission line with a known length by using a time domain reflection technology to obtain the transmission speed of the signal in the parallel spiral transmission line, and measuring the characteristic impedance of the parallel spiral transmission line in an unstretched state;
(2) measuring the characteristic impedance of the parallel spiral transmission line in the working state according to a given characteristic impedance transformation threshold value, if the difference value between the measured characteristic impedance and the characteristic impedance in the non-stretched state is smaller than the transformation threshold value, judging that the parallel spiral transmission line is not stretched, and if the difference value between the measured characteristic impedance and the characteristic impedance in the non-stretched state is larger than or equal to the threshold value, judging that stretching occurs;
(3) measuring the time when the characteristic impedance changes and the time when the characteristic impedance recovers to a normal value, calculating the time difference, multiplying the time difference by the transmission speed of the signal to obtain the length of the stretching area, and calculating the time when the characteristic impedance changes, multiplying the time when the characteristic impedance changes by the transmission speed of the signal, and then halving the time to obtain the distance between the stretching point and the starting end of the parallel spiral transmission line;
(4) according to the measured maximum characteristic impedance in the stretching area, a fitting function is substituted to obtain the stretching amount;
(5) the number of turns of the parallel spiral transmission line in the stretching interval can be obtained by dividing the obtained length of the stretching area by the lead of the parallel spiral transmission line in the stretching state, and finally the total stretching amount can be obtained.
The parallel spiral transmission line designed by the invention is used for distributed measurement of rock-soil stretching amount as a sensing element, based on the proposed distributed parameter model of the parallel spiral transmission line during stretching, the distributed capacitance and the distributed inductance of the parallel spiral transmission line are obtained, the theoretical formula and the fitting function of the characteristic impedance of the parallel spiral transmission line and the rock-soil stretching amount are finally obtained, and the time domain reflection technology and the compiled upper computer software are combined, so that the stretching position and the stretching amount can be accurately measured, the distributed measurement of the rock-soil stretching is realized, the method can realize the measurement of the larger stretching amount of the rock-soil, and the accurate and easily-realized measurement and monitoring method is provided for greatly reducing the harm of address catastrophe to human beings.
Preferably, the parallel spiral transmission line comprises a central silica gel strip, parallel copper wires and a silica gel protective sleeve, the parallel copper wires are spirally wound on the outer side surface of the central silica gel strip, the silica gel protective sleeve is coated on the outer side of the parallel copper wires, the parallel copper wires comprise a silica gel sheath and two copper wires, the silica gel sheath is coated on the copper wires, the two copper wires are adhered through silica gel, the distance d between the two copper wires is a fixed value, the lead of the spirally-wound parallel spiral transmission line is d + s, the initial value of the stretching amount s is equal to d, and when the parallel spiral transmission line is stretched, the stretching amount s gradually increases along with the stretching; the diameter of the central silica gel strip is D and cannot change along with tensile deformation, and the included angle between the parallel spiral transmission line wound by the parallel copper conducting wires and the vertical direction of the central line of the central silica gel strip is theta.
Preferably, two copper wires in the middle of the parallel copper wires are wound by adopting one of four wire gauges of 40/60/100/150, and each tinned copper wire is 0.08mm in diameter.
Preferably, the solution model of the distribution parameters of the parallel spiral transmission line is as follows: the parallel spiral transmission line is divided into a normal unstretched area, a gradual change area, a stretched area, a gradual change area and a normal unstretched area from left to right in sequence, when an incident signal is added into the parallel spiral transmission line, a certain point in the center of the stretched area is taken to calculate the electric field intensity of the parallel spiral transmission line at the point, the voltage between two copper conductors can be obtained through the electric field intensity, so that the distributed capacitance and the distributed inductance are obtained according to the ratio of the charge density between the two copper conductors to the voltage between the two copper conductors according to the capacitance between the two copper conductors with unit length, a characteristic impedance expression of the parallel spiral transmission line is deduced according to an expression of the characteristic impedance of a lossless transmission line or a low-loss transmission line, and then a fitting function of the rock and soil stretching amount.
Preferably, the specific calculation method is as follows:
the central parallel spiral transmission line of the stretching area is defined as A0And B0Wherein A is0At B0Left side of (A)0And B0Located above the central silica gel strip, A0' and B0' below the central silicone strip, assuming n pairs of stretched parallel helical transmission lines on the left and n pairs of stretched parallel helical transmission lines on the right,
when an incident signal is added to the copper wires, assuming that the two copper wires are uniformly charged wires, the charge linear densities thereof are-eta and eta, respectively, the electric field direction thereof is perpendicular to the radial vector direction of the copper wires, and the center B of the stretching area is taken now0And AR1A distance B between0A P point is arranged at the position x, and a live wire B with limited length is arranged according to the Biot-Saval theorem0B’0The electric field strength at point P is expressed along the x-axis as
Where ε is the relative permittivity of the medium, LpLive conductor B of finite length D/2cos theta0B’0The axis is y axis, the axis which is vertical to the y axis and faces to the P point direction is x axis, and the electric field intensity generated by all the live wires at the P point according to the superposition theorem is
E＝EAL+EBR+EBL+EAR (2)
The first letter of subscript on the right side of the equation indicates that two copper wires in the parallel spiral transmission line are respectively A and B, the second letter of subscript indicates that the position of the parallel spiral transmission line is located on the left side L and the right side R of the point P, and the electric field strengths of 4 items in the equation are respectively:
k in the formula is the number of all parallel spiral transmission lines on the left side and the right side of a point P, and can be 3-5 on the premise of simplifying calculation and ensuring certain precision;
b can be obtained according to the Gaussian theorem0And AR1A voltage of
Take K to 3 and then the integral constant is
The capacitance between two copper wires is the ratio of the charge density to the voltage between the two copper wires, and the distributed capacitance is obtained
The distributed inductance can be obtained according to the formula of inductance capacitance in the medium with constitutive parameter (mu, epsilon), mu is relative magnetic conductivity, and the expression of the distributed inductance is
The characteristic impedance expression of the parallel spiral transmission line, which is derived from the expression of the characteristic impedance of the lossless transmission line or the low-loss transmission line, is as follows:
from this formula, it can be derived that the characteristic impedance of the parallel spiral transmission line is only related to the structural characteristic parameters (r, D, theta);
respectively substituting the characteristic parameters of the four wire gauge spiral lines into a formula (8), and obtaining a curve of characteristic impedance changing along with s when the parallel spiral transmission line is stretched;
when s is a fixed value, the characteristic impedance gradually decreases from the maximum value in the middle of the stretching area to the minimum fixed value of the normal unstretched area through the gradual change area, and according to the characteristics of the stretching structure, the characteristic impedance changes along with the position, namely the characteristic impedance of the middle position of the stretching is the maximum value and gradually decreases towards the two sides until the minimum fixed value of the unstretched area is reached;
based on the time domain reflection technology, the stretching amount s is determined according to the measured characteristic impedance, and then the inverse function of the formula (8) needs to be obtained, but the formula (8) is very complex, and for the convenience of practical application and operation, the curve obtained by the formula (8) adopts a function fitting method, and the fitting formula is that
Where a, b and c are fitting coefficients, the amount of stretch can be determined using the measured characteristic impedance according to equation (9).
The invention has the beneficial effects that: the method can realize the measurement of the large stretching amount of the rock soil, and provides an accurate and easily-realized measuring and monitoring method for greatly reducing the damage of address catastrophe to human beings.
Drawings
FIG. 1 is a schematic diagram of the structure of two parallel spiral transmission lines according to the present invention;
FIG. 2 is a cross-sectional view of the parallel copper conductor of FIG. 1;
FIG. 3 is a model for solving the distribution parameters of the parallel helical transmission lines according to the present invention;
FIG. 4 is a schematic diagram of electric field solution;
FIG. 5 is a graph of characteristic impedance versus the amount of stretch s for a parallel helical transmission line of four wire gauges;
fig. 6 is a flow chart of a method of the present invention.
In the figure: 1. the novel copper-clad cable comprises a central silica gel strip, 2 parallel copper wires, 3 silica gel protective sleeves, 4 copper wires and 5 silica gel outer skins.
Detailed Description
The invention is further described with reference to the following figures and detailed description.
In the embodiment shown in fig. 6, a distributed measurement method of rock-soil displacement is provided, which is a solving model and a solving method of parallel spiral transmission line distribution parameters, so as to obtain a fitting function of characteristic impedance of the parallel spiral transmission line and rock-soil tensile quantity;
the solution model of the parallel spiral transmission line distribution parameters is as follows: the parallel spiral transmission line is sequentially divided into a normal unstretched area, a gradual change area, a stretched area, a gradual change area and a normal unstretched area from left to right, when an incident signal is added into the parallel spiral transmission line, a certain point in the center of the stretched area is taken to calculate the electric field intensity of the parallel spiral transmission line at the point, the voltage between two copper conductors can be obtained through the electric field intensity, so that the distributed capacitance and the distributed inductance are obtained according to the ratio of the charge density between the two copper conductors to the voltage between the two copper conductors according to the capacitance between the two copper conductors with unit length, a characteristic impedance expression of the parallel spiral transmission line is deduced according to an expression of the characteristic impedance of a lossless transmission line or a low-loss transmission line, and then a fitting function of the rock and soil stretching amount is;
the method specifically comprises the following steps:
(1) measuring the transmission time of a signal in an unstretched parallel spiral transmission line with a known length by using a time domain reflection technology to obtain the transmission speed of the signal in the parallel spiral transmission line, and measuring the characteristic impedance of the parallel spiral transmission line in an unstretched state;
(2) measuring the characteristic impedance of the parallel spiral transmission line in the working state according to a given characteristic impedance transformation threshold value, if the difference value between the measured characteristic impedance and the characteristic impedance in the non-stretched state is smaller than the transformation threshold value, judging that the parallel spiral transmission line is not stretched, and if the difference value between the measured characteristic impedance and the characteristic impedance in the non-stretched state is larger than or equal to the threshold value, judging that stretching occurs;
(3) measuring the time when the characteristic impedance changes and the time when the characteristic impedance recovers to a normal value, calculating the time difference, multiplying the time difference by the transmission speed of the signal to obtain the length of the stretching area, and calculating the time when the characteristic impedance changes, multiplying the time when the characteristic impedance changes by the transmission speed of the signal, and then halving the time to obtain the distance between the stretching point and the starting end of the parallel spiral transmission line;
(4) according to the measured maximum characteristic impedance in the stretching area, a fitting function is substituted to obtain the stretching amount;
(5) the number of turns of the parallel spiral transmission line in the stretching interval can be obtained by dividing the obtained length of the stretching area by the lead of the parallel spiral transmission line in the stretching state, and finally the total stretching amount can be obtained.
Wherein: as shown in fig. 1, the parallel spiral transmission line includes a central silica gel strip 1, a parallel copper wire 2 and a silica gel protective sleeve 3, the parallel copper wire 2 is spirally wound on the outer side surface of the central silica gel strip 1, the silica gel protective sleeve 3 is coated on the outer side of the parallel copper wire 2, and the central silica gel strip 1 has certain elasticity to ensure that the parallel spiral transmission line has better tensile property; wherein: as shown in fig. 2, the parallel copper wires 2 include a silica gel sheath 5 and two copper wires 4, the silica gel sheath 5 covers the copper wires 4, the two copper wires 4 are bonded through silica gel, the middle bonded silica gel has the function of ensuring that the distance d between the two copper wires 4 is a fixed value, the lead of the spirally wound parallel spiral transmission line is d + s, wherein the initial value of the stretching amount s is equal to d, and when the parallel spiral transmission line is stretched, the stretching amount s gradually increases along with the stretching; the diameter of the central silica gel strip 1 is D and cannot change along with tensile deformation, and the included angle between the parallel spiral transmission line wound by the parallel copper wires 2 and the central line of the central silica gel strip 1 in the vertical direction is theta. Two copper wires 4 in the middle of the parallel copper wires 2 are wound by adopting one of four wire gauges of 40/60/100/150, and each tinned copper wire with the diameter of 0.08 mm.
In order to obtain the proposed relationship between the characteristic impedance of the parallel spiral transmission line and the tensile deformation position and the tensile deformation amount, the established distribution parameter solution model of the parallel spiral transmission line during stretching is shown in fig. 3. During stretching, the parallel spiral transmission line is divided into a stretching area, a gradual change area and a normal unstretched area, the s value of the stretching area is the largest, and the s value is gradually reduced to an initial value d through the gradual change area. The central parallel spiral transmission line of the stretching area is defined as A0And B0Let it be assumed that there are n pairs of stretched parallel helical transmission lines on the left and n pairs of stretched parallel helical transmission lines on the right.
When an incident signal is added to the copper wires, assuming that the two copper wires are uniformly charged wires, the charge linear densities thereof are-eta and eta, respectively, the electric field direction thereof is perpendicular to the radial vector direction of the copper wires, and the center B of the stretching area is taken now0And AR1A distance B between0A P point is arranged at the position x, and a live wire B with limited length is arranged according to the Biot-Saval theorem0B’0The electric field strength at point P is expressed along the x-axis as
Where ε is the relative permittivity of the medium, LpThe electric field strength solving diagram is shown in fig. 4, D/2cos θ. All according to the superposition theoremThe electric field intensity generated by the charged conductor at the point P is
E＝EAL+EBR+EBL+EAR (2)
The first letter of the subscript on the right side of the equation indicates that two copper wires in the parallel spiral transmission line are respectively A and B, and the second letter of the subscript indicates that the position of the parallel spiral transmission line is located on the left side L and the right side R of the point P. The 4 terms electric field strength in the equation are:
k in the formula is the number of all parallel spiral transmission lines on the left side and the right side of the point P. K can be 3-5 under the premise of simplifying calculation and ensuring certain precision.
B can be obtained according to the Gaussian theorem0And AR1A voltage of
Take K to 3 and then the integral constant is
The capacitance between two copper wires is the ratio of the charge density to the voltage between the two copper wires, and the distributed capacitance is obtained
The distributed inductance can be obtained according to the formula of inductance capacitance in the medium with constitutive parameter (mu, epsilon), mu is relative magnetic conductivity, and the expression of the distributed inductance is
The characteristic impedance expression of the parallel spiral transmission line, which is derived from the expression of the characteristic impedance of the lossless transmission line or the low-loss transmission line, is as follows:
from this equation it can be derived that the characteristic impedance of a parallel helical transmission line is related only to its structural characteristic parameters (r, D, θ).
A conductor wound by 40 tinned copper wires with the diameter of 0.08mm, the radius of each tinned copper wire is 0.04mm, and the total sectional area of each single wire is 40 multiplied by pi multiplied by 0.042mm2The equivalent diameter is about 0.5mm, and the characteristic parameters of the parallel spiral transmission line are r is 0.25mm, D is 1.6mm, D is 4.6mm, and θ is 30. The equivalent diameter and characteristic parameters of the conductor wound by 60/100/150 tinned copper wires in the conductor can be determined. The characteristic parameters of the four wire gauge spiral lines are respectively substituted into the formula (8), and the curve of the characteristic impedance of the parallel spiral transmission line changing along with s can be obtained, as shown in fig. 5.
As can be seen from fig. 5, when s is a fixed value, the characteristic impedance gradually decreases from the maximum value in the middle of the stretched region to the minimum fixed value in the normal unstretched region through the gradual change region, and according to the stretching structure characteristics, the characteristic impedance with position change characteristics are that the characteristic impedance at the middle position of the stretching is a maximum value and gradually decreases to the minimum fixed value in the unstretched region.
Based on the time domain reflection technique, the stretching amount s is determined according to the measured characteristic impedance, and thus the inverse function of the formula (8) needs to be obtained, but the formula (8) is very complex, and for the convenience of practical application and operation, the method of function fitting is adopted in the diagram 5 obtained by the formula (8), and the fitting formula is
Where a, b and c are fitting coefficients, the amount of stretch can be determined using the measured characteristic impedance according to equation (9).
Based on the time domain reflection technology, the programmed upper computer software realizes a method flowchart of positioning measurement of the stretching position and measuring the stretching amount, as shown in fig. 6. The method specifically comprises the following steps:
(1) measuring the transmission time T of the undrawn parallel spiral transmission line, and calculating the transmission speed v of the signal in the parallel spiral transmission line as L/(2T) according to the known line length L of the parallel spiral transmission line;
(2) measuring the characteristic impedance Z of the parallel spiral transmission line which is not stretched, and setting a characteristic impedance transformation threshold value delta Z during stretching;
(3) measuring the characteristic impedance Z 'of the parallel spiral transmission line in real time under the working state, judging whether Z' -Z > -delta Z is met or not in real time, if not, continuing to measure in real time, and if so, going to the next step;
(4) measuring the propagation time T of the characteristic impedance from the beginning of the parallel spiral transmission line to the change1And then returns to normal time T2Calculating the distance between the stretching point and the initial end as vT1Calculating the length of the stretching interval as Ltotal＝v(T2-T1)；
(5) The maximum value of the characteristic impedance of the stretching interval is measured and is substituted into the formula (9) of the fitting function to obtain the stretchingQuantity s, calculating the number of turns N ═ L in the stretching sectiontotal(s + d), the total amount of stretch is calculated as N (s-d).
The method designed by the invention uses the parallel spiral transmission line as a sensing element for distributed measurement of the rock-soil stretching amount, obtains the distributed capacitance and the distributed inductance of the parallel spiral transmission line based on the proposed distributed parameter model of the parallel spiral transmission line during stretching, finally obtains the fitting function of the characteristic impedance of the parallel spiral transmission line and the rock-soil stretching amount, and combines the time domain reflection technology and the compiled upper computer software to accurately measure the stretching position and the stretching amount and realize the distributed measurement of the rock-soil stretching.
Claims (3)
1. A distributed measurement method of rock-soil displacement is characterized in that a solving model and a solving method of parallel spiral transmission line distribution parameters are provided, so that a fitting function of characteristic impedance of the parallel spiral transmission line and rock-soil stretching amount is obtained; the method specifically comprises the following steps:
(1) measuring the transmission time of a signal in an unstretched parallel spiral transmission line with a known length by using a time domain reflection technology to obtain the transmission speed of the signal in the parallel spiral transmission line, and measuring the characteristic impedance of the parallel spiral transmission line in an unstretched state;
(2) measuring the characteristic impedance of the parallel spiral transmission line in the working state according to a given characteristic impedance transformation threshold value, if the difference value between the measured characteristic impedance and the characteristic impedance in the non-stretched state is smaller than the transformation threshold value, judging that the parallel spiral transmission line is not stretched, and if the difference value between the measured characteristic impedance and the characteristic impedance in the non-stretched state is larger than or equal to the threshold value, judging that stretching occurs;
(3) measuring the time when the characteristic impedance changes and the time when the characteristic impedance recovers to a normal value, calculating the time difference, multiplying the time difference by the transmission speed of the signal to obtain the length of the stretching area, and calculating the time when the characteristic impedance changes, multiplying the time when the characteristic impedance changes by the transmission speed of the signal, and then halving the time to obtain the distance between the stretching point and the starting end of the parallel spiral transmission line;
(4) according to the measured maximum characteristic impedance in the stretching area, a fitting function is substituted to obtain the stretching amount;
(5) the number of turns of the parallel spiral transmission line in the stretching interval can be obtained by dividing the obtained length of the stretching area by the lead of the parallel spiral transmission line in the stretching state, and finally the total stretching amount can be obtained;
wherein: the parallel spiral transmission line comprises a central silica gel strip (1), parallel copper wires (2) and a silica gel protective sleeve (3), wherein the parallel copper wires (2) are spirally wound on the outer side surface of the central silica gel strip (1), the silica gel protective sleeve (3) covers the outer side of the parallel copper wires (2), the parallel copper wires (2) comprise a silica gel sheath (5) and two copper wires (4), the silica gel sheath (5) covers the copper wires (4), the two copper wires (4) are adhered through silica gel, the distance d between the two copper wires (4) is a fixed value, the lead of the spirally wound parallel spiral transmission line is d + s, the initial value of the stretching amount s is equal to d, and when the parallel spiral transmission line is stretched, the stretching amount s gradually increases along with stretching; the diameter of the central silica gel strip (1) is D and cannot change along with tensile deformation, and the included angle between the parallel spiral transmission line wound by the parallel copper wires (2) and the central line of the central silica gel strip (1) in the vertical direction is theta;
the solution model of the parallel spiral transmission line distribution parameters is as follows: the parallel spiral transmission line is divided into a normal unstretched area, a gradual change area, a stretched area, a gradual change area and a normal unstretched area from left to right in sequence, when an incident signal is added into the parallel spiral transmission line, a certain point in the center of the stretched area is taken to calculate the electric field intensity of the parallel spiral transmission line at the point, the voltage between two copper conductors can be obtained through the electric field intensity, so that the distributed capacitance and the distributed inductance are obtained according to the ratio of the charge density between the two copper conductors to the voltage between the two copper conductors according to the capacitance between the two copper conductors with unit length, a characteristic impedance expression of the parallel spiral transmission line is deduced according to an expression of the characteristic impedance of a lossless transmission line or a low-loss transmission line, and then a fitting function of the rock and soil stretching amount.
2. The distributed measurement method for the rock soil displacement according to claim 1, wherein two copper wires (4) in the middle of the parallel copper wires (2) are wound by using one of four wire gauges of 40/60/100/150, and each tinned copper wire is 0.08mm in diameter.
3. The distributed measurement method of the rock-soil displacement according to claim 1, wherein the specific calculation method is as follows:
the central parallel spiral transmission line of the stretching area is defined as A0And B0Wherein A is0At B0Left side of (A)0And B0Located above the central silica gel strip, A0' and B0The central silica gel strip is located below the central silica gel strip, n pairs of stretched parallel spiral transmission lines are supposed to be arranged on the left side, n pairs of stretched parallel spiral transmission lines are supposed to be arranged on the right side, when an incident signal is added into the copper conductors, the two copper conductors are supposed to be uniformly charged conductors, the charge linear densities of the two copper conductors are respectively-eta and eta, the electric field direction of the two copper conductors is vertical to the radial vector direction of the two copper conductors, and the center B of the stretching area is taken at present0And AR1A distance B between0A P point is arranged at the position x, and a live wire B with limited length is arranged according to the Biot-Saval theorem0B′0The electric field strength at point P is expressed along the x-axis as
Where ε is the relative permittivity of the medium, LpLive conductor B of finite length D/2cos theta0B′0The axis is y axis, the axis which is vertical to the y axis and faces to the P point direction is x axis, and the electric field intensity generated by all the live wires at the P point according to the superposition theorem is
E＝EAL+EBR+EBL+EAR (2)
The first letter of subscript on the right side of the equation indicates that two copper wires in the parallel spiral transmission line are respectively A and B, the second letter of subscript indicates that the position of the parallel spiral transmission line is located on the left side L and the right side R of the point P, and the electric field strengths of 4 items in the equation are respectively:
k in the formula is the number of all parallel spiral transmission lines on the left side and the right side of a point P, and can be 3-5 on the premise of simplifying calculation and ensuring certain precision;
b can be obtained according to the Gaussian theorem0And AR1A voltage of
Take K to 3 and then the integral constant is
The capacitance between two copper wires is the ratio of the charge density to the voltage between the two copper wires, and the distributed capacitance is obtained
The distributed inductance can be obtained according to the formula of inductance capacitance in the medium with constitutive parameter (mu, epsilon), mu is relative magnetic conductivity, and the expression of the distributed inductance is
The characteristic impedance expression of the parallel spiral transmission line, which is derived from the expression of the characteristic impedance of the lossless transmission line or the low-loss transmission line, is as follows:
from this formula, it can be derived that the characteristic impedance of the parallel spiral transmission line is only related to the structural characteristic parameters (r, D, theta);
respectively substituting the characteristic parameters of the four wire gauge spiral lines into a formula (8), and obtaining a curve of characteristic impedance changing along with s when the parallel spiral transmission line is stretched;
when s is a fixed value, the characteristic impedance gradually decreases from the maximum value in the middle of the stretching area to the minimum fixed value of the normal unstretched area through the gradual change area, and according to the characteristics of the stretching structure, the characteristic impedance changes along with the position, namely the characteristic impedance of the middle position of the stretching is the maximum value and gradually decreases towards the two sides until the minimum fixed value of the unstretched area is reached;
based on the time domain reflection technology, the stretching amount s is determined according to the measured characteristic impedance, and then the inverse function of the formula (8) needs to be obtained, but the formula (8) is very complex, and for the convenience of practical application and operation, the curve obtained by the formula (8) adopts a function fitting method, and the fitting formula is that
Where a, b and c are fitting coefficients, the amount of stretch can be determined using the measured characteristic impedance according to equation (9).
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910619103.9A CN110243278B (en) | 2019-07-10 | 2019-07-10 | Distributed measurement method for rock-soil displacement |
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| Application Number | Priority Date | Filing Date | Title |
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