CN108802828B - Drilling grouting curtain quality detection method - Google Patents

Drilling grouting curtain quality detection method Download PDF

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CN108802828B
CN108802828B CN201810820293.6A CN201810820293A CN108802828B CN 108802828 B CN108802828 B CN 108802828B CN 201810820293 A CN201810820293 A CN 201810820293A CN 108802828 B CN108802828 B CN 108802828B
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curtain
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朱德兵
张磊
刘海飞
李小罗
贾朋涛
钟兆泓
陶望雄
张爱恒
汤自权
赖虔林
高堤
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Central South Univ
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Abstract

The invention discloses a method for detecting the quality of a borehole grouting curtain, which comprises the following steps: s1, arranging positive and negative power supply electrodes in the power supply drill holes at two ends of the curtain along the trend, connecting the power supply electrodes with the power supply terminals of the electrical prospecting instrument, S2, arranging measuring drill holes, arranging a pair of measuring electrodes in two adjacent power supply drill holes, wherein the measuring electrodes are connected with measuring terminals of an electrical prospecting instrument, S3, starting the electrical prospecting instrument, supplying power to the underground through a power supply electrode, measuring potential difference values or apparent resistivity values or polarizability values between two measuring electrodes, wherein a recording point is located at a geometric midpoint between the two measuring electrodes, S4, measuring the potential difference values or the apparent resistivity values or the polarizability values at the recording points of the measuring electrodes at different depth positions, S5, replacing the measuring electrodes into different measuring boreholes, repeating the steps S4 and S6, and drawing a curtain potential difference diagram or a curtain apparent resistivity contour diagram or a curtain polarizability contour diagram.

Description

Drilling grouting curtain quality detection method
Technical Field
The invention belongs to the technical field of seepage-proofing detection of curtain grouting engineering, and particularly relates to a drilling grouting curtain quality detection method.
Background
A continuous curtain needs to be built in underground surrounding rocks in large-scale water conservancy projects or mine auxiliary projects, and underground continuous water flow plugging barriers are formed in a drilling grouting mode. However, if the hidden trouble of leakage exists in the designed and constructed plugging curtain, the water plugging efficiency of the curtain can be influenced, and when the damage is serious, great loss is brought to the engineering main body. Therefore, the method has great significance for underground curtain engineering by effectively detecting the position of the hidden danger and timely processing the position.
In most cases, the resistivity is significantly lower than that of the surrounding geotechnical media due to the presence of water in the formation water or fractured water structure. After the curtain is adopted for grouting and plugging, if a grouting medium is a medium material with high resistivity and low polarizability, the completely plugged curtain forms a barrier with high resistivity and low polarizability, and the part with the grouting defect has relatively low resistivity and relatively high polarizability compared with surrounding rocks and the completely grouted part. By adopting the correlation of the distribution of the current field and the water flow field, the electrical prospecting is a hidden danger detection means with convenient construction and low cost.
The premise of completing the detection task by electrical prospecting is to acquire electric field observation data with high resolution by an effective equipment technology. The hidden danger of the underground curtain is detected by establishing and measuring an electric field in a half space, and the influence of the product effect is influenced, on one hand, the resolution capability of the electrical prospecting is limited, and on the other hand, the side abnormal interference is serious, so that the electrical prospecting is implemented to obtain a good effect, the established electric field is distributed as uniformly as possible to improve the abnormal resolution capability, and on the other hand, a measuring electrode needs to be close to a hidden danger target as much as possible.
The existing curtain detection means include: firstly, a foundation pit waterproof curtain (200910033689.7 a detection method for hidden danger of a waterproof curtain leakage channel, 201210571740.1 a potential mapping method for detecting the integrity of a high polymer impervious wall, 201210087153.5 an electric measurement method and device for detecting the high polymer impervious wall) is used for fitting a current field to perform waterproof curtain leakage detection and the like; and secondly, cross-hole power supply, electric field measurement and resistivity imaging are carried out through resistivity CT (201110241747.2 inter-well parallel resistivity CT testing method, 201210269261.4 underground engineering high-resolution three-dimensional resistivity CT imaging advanced prediction system and method). The former uses an electric flow field to simulate a water flow field for hidden danger detection, and establishes an electric field in a direction vertical to the trend of a curtain; the latter adopts an observation system, one hole supplies power and the other hole receives power according to the mode of cross-hole elastic wave or electromagnetic wave CT; the power supply electrode adopts a dipole, a monopole (B pole is at infinity), a dipole device or a multipole device, and the receiving electrode measures the potential or potential gradient. Because the observation point is close to the power supply point, the observation point is easily interfered by the abnormal conductivity of the medium around the power supply point, and the observation point is a three-dimensional underground space, the interpretation result is difficult to truly reflect the conductivity distribution information of the underground medium structure, so the method of 'resistivity CT' is a new idea, but has great difficulty in production practice.
Disclosure of Invention
The invention mainly aims to provide a method for detecting the quality of a borehole grouting curtain, and aims to solve the problems that hidden dangers cannot be well highlighted and the resolution capability is not enough in an electric field obtained by the existing curtain detection means.
In order to achieve the purpose, the invention provides a method for detecting the quality of a borehole grouting curtain, which comprises the following steps:
s1, drilling at least one pair of power supply drill holes at two ends of the curtain along the trend, laying at least one pair of corresponding positive and negative power supply electrodes in the power supply drill holes, connecting the power supply electrodes with power supply terminals of the electrical prospecting instrument,
s2, arranging a plurality of measuring drill holes on the curtain and on the connecting line between the positive and negative power supply electrodes, wherein the measuring drill holes are arranged at equal intervals, arranging a pair of measuring electrodes in two adjacent power supply drill holes, the measuring electrodes are connected with the measuring terminals of the electrical prospecting instrument,
s3, starting the electrical prospecting instrument, supplying power to the underground through the power supply electrode, measuring the potential difference value or apparent resistivity value or polarizability value between the two measuring electrodes, recording the geometric midpoint between the two measuring electrodes,
s4, moving the measuring electrode along the depth direction of the measuring drill hole at equal intervals, measuring the potential difference value or apparent resistivity value or polarizability value on the recording point of the measuring electrode at different depth positions,
s5, replacing the measuring electrode into a different measuring drill hole, repeating the step S4,
s6, drawing a curtain potential difference contour map or a curtain apparent resistivity contour map or a curtain polarizability contour map according to the steps S4 and S5, wherein an abnormal area in the map is a defect area of the grouting curtain.
Preferably, in step S1, the power supply electrodes are arranged at the peripheral position outside the curtain, and the curtain is arranged at the middle position of the positive and negative power supply electrodes.
Preferably, the distance between the positive and negative supply electrodes is at least 3 times the length of the curtain.
Preferably, in step S1, the power supply electrodes are disposed on a curtain, and the distance between the positive and negative power supply electrodes is smaller than the length of the curtain; and dividing the curtain into more than one section for subsection detection.
Preferably, the power supply terminal supplies power to the alternating current, or direct current, or periodic square wave signal power, or programming control variable frequency signal power.
Preferably, in step S1, the power supply electrodes are point power supplies or line power supplies, and when the point power supplies are more than one pair, the point power supplies are arranged at equal intervals in the vertical direction or in the direction perpendicular to the direction of the curtain.
Preferably, in the steps S3-S5, the apparent resistivity is calculated by:
the measuring potential difference between the two measuring electrodes is marked as delta U', the recording point is positioned at the geometric midpoint of the two electrodes, I is the current of a power supply loop during measurement, k is the device coefficient, and the expression is as follows:
Figure BDA0001741241330000031
wherein rho is the resistivity of the curtain grouting material, Ha and Hb are the depths of the positive and negative power supply electrodes respectively, L is the electrode distance between the positive and negative power supply electrodes, R1 is the distance between one of the two measuring electrodes and the positive power supply electrode, R2 is the distance between the other of the two measuring electrodes and the positive power supply electrode, h1 and h2 are the depths of the two measuring electrodes,
the apparent resistivity at this point is: rhos=k·ΔU’/I。
Preferably, the detection method further comprises:
s7, assuming that the curtain is provided with N drilling holes, and each drilling hole is provided with M depth points for observation, so as to obtain (N-1) M recording point data; wherein, the recording points at the same depth from the earth surface have M groups, and each group has (N-1) data; taking a group of data in the M groups of data to calculate an average value G, comparing data X of each measuring point in the group with the average value G, and calculating a relative change value, namely [ (X-G)/G ] as a new parameter of the measuring point; converting the potential difference value, the polarizability or the apparent resistivity data of each group of depth points into new parameters in such a way; and drawing a contour map after potential difference or polarization rate or apparent resistivity conversion by using the new parameters on the curtain, namely respectively mapping the potential difference relative variation, the polarization rate relative variation or the apparent resistivity relative variation.
Compared with the prior art, the technical scheme of the invention has the beneficial effects that:
the method adopts a reasonable electric field arrangement mode, on one hand, the electric field can cover the full section of the detected curtain, the electrode distance of the power supply electrode is enlarged as much as possible, and the curtain is positioned in the middle of the electrode connecting line, so that the electric field is uniformly distributed in the range of the curtain to highlight possible abnormal hidden dangers; a plurality of pairs of power supply electrodes are adopted for supplying power, so that an electric field of a line of the curtain is further homogenized, and good conditions are provided for high-precision and high-resolution detection; on the other hand, the measuring electrodes are arranged by means of grouting drilling, and the resolution capability of electrical prospecting is also guaranteed because the electrodes are close to potential targets. In a comprehensive way, the method establishes an underground continuous current field along the direction of the curtain, closely observes the electric field through drilling, and transversely compares the sections of the full curtain (section contour lines) through the electric field or calculated resistivity, thereby providing a relatively complete technical guarantee for the integrity detection of the grouting curtain.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the structures shown in the drawings without creative efforts.
Fig. 1 is a schematic diagram illustrating a detection principle of a method for detecting quality of a borehole grouting curtain according to an embodiment of the present invention;
FIG. 2 is a flow chart of the detection of the quality detection method of the borehole grouting curtain proposed in FIG. 1;
FIG. 3 is a cross-sectional view of a field work arrangement using multiple pairs of vertical point power supplies in accordance with a second embodiment of the present invention;
FIG. 4 is a top view of an example of a field work arrangement using multiple pairs of horizontal point power supplies according to a third embodiment of the present invention;
FIG. 5 is a cross-sectional view of four field work arrangements using a line power supply according to an embodiment of the present invention;
FIG. 6 is a schematic view of a contour of a section of a drape based on parameters of potential difference, polarizability, apparent resistivity or resistivity.
Detailed Description
The technical solutions in the embodiments of the present invention are clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, not all, embodiments of the present invention.
Example one
Referring to fig. 1 and fig. 2, fig. 1 is a schematic diagram illustrating a detection principle of a method for detecting quality of a grouting curtain in a borehole according to the present invention, wherein reference numerals in fig. 1 are: 1-electrical prospecting power supply equipment, 2-electrical prospecting measuring equipment, 3-grouting, drilling and numbering, 4-measuring electrodes, 5-measuring electrode leads, 6-underground half-space current lines, 7-power supply electrodes, 8-power supply electrode leads, 9-power supply current size and direction, and 10-hidden defects in a curtain.
FIG. 2 is a flow chart of field quality detection by using the drilling grouting curtain quality detection method provided by FIG. 1.
The invention provides a method for detecting the quality of a borehole grouting curtain, which comprises the following steps:
1. selecting materials such as cement for curtain grouting, wherein the materials such as cement are cured to have high resistivity or low polarizability, and waiting for a maintenance period or a grouting material solidification period to start curtain quality detection according to the maintenance period determined by the grouting material and the grouting process.
2. Paired positive and negative power supply electrodes are arranged on extension lines at two ends of the row of curtains along the trend of the row of curtains and are respectively connected to power supply terminals of an electrical prospecting instrument through wires;
a plurality of measuring drill holes are drilled on a connecting line between the positive power supply electrode and the negative power supply electrode, measuring electrodes for measuring a ground electric field are respectively put in two adjacent drill holes, and the measuring electrodes are connected to measuring terminals of an electrical prospecting instrument.
3. Starting an electrical prospecting instrument, supplying power to the underground through a power supply electrode, measuring the potential difference or the polarizability between two electrodes through a measuring electrode, and positioning a recording point of the potential difference value and the polarizability value at the geometric midpoint between the two measuring electrodes;
and calculating the apparent resistivity by using an apparent resistivity calculation method and corresponding power supply current and geometric position parameters of the power supply electrode and the measuring electrode, wherein the apparent resistivity parameter falls on the recording point.
4. The depth position of the measuring electrode in the drilling hole is changed, and the potential difference or the polarizability or the apparent resistivity at different recording points is measured or calculated.
5. And (4) replacing the measuring drill holes, and repeating the measuring and calculating processes in the step (3) and the step (4) to ensure that the recording points are uniformly distributed on the grouting curtain.
6. And (5) drawing a potential difference contour map, a polarizability contour map or an apparent resistivity contour map of the grouting curtain according to the recording result of the step (5), and identifying the defect size and the geometric position of the grouting curtain by combining engineering geological and hydrogeological data from the abnormal region of the potential difference, polarizability or apparent resistivity on the contour map.
7. In step 3, the calculation principle and method of the apparent resistivity:
theoretically, for a horizontal uniform half space with the resistivity of rho, the embedding depths of a positive power supply electrode and a negative power supply electrode are Ha and Hb respectively, the electrode distance L and the power supply current are I; the horizontal distance from one measuring electrode to the positive power supply electrode is R1, the depth is h1, the horizontal distance from the other measuring electrode to the positive power supply electrode is R2, and the depth is h 2; the theoretical potential values on the two measuring electrodes are respectively represented by U1 and U2, and the theoretical potential difference between the two measuring electrodes is represented as:
in the actual grouting curtain detection, the measurement potential difference between two measurement electrodes is marked as delta U', a recording point is positioned at the geometric midpoint of the two electrodes, I is the current of a power supply loop during measurement, k is a device coefficient, and the expression is as follows:
Figure BDA0001741241330000052
the apparent resistivity at this point is expressed as: rhos=k·ΔU’/I。
8. Besides drawing a curtain electric field and apparent resistivity profile contour map to determine the curtain hidden danger abnormity, actually measuring curtain electric field distribution data or calculating apparent resistivity data, and realizing inversion of the curtain resistivity according to an electrical prospecting principle, determining a resistivity abnormal area by inverting the resistivity profile contour map, and identifying the defect size and the geometric position of the grouting curtain by combining engineering geology and hydrogeology data.
In addition, the detection method can also be used for detecting the quality of the grouting curtain of the non-vertical drilling hole.
Example two
Referring to fig. 3, a second embodiment of the present invention provides a method for detecting quality of a borehole grouting curtain, wherein a plurality of pairs of point power supplies are vertically arranged in a working site, and fig. 3 is a vertical cross-sectional view of a site operation during curtain detection, and the method includes:
1. drilling a pair of power supply drill holes at the positions, which are 200m long, of two ends of the linear arrangement curtain along the trend of the linear arrangement curtain, wherein 3 pairs of positive and negative power supply electrodes (power supply points are vertically arranged) are arranged in the drill holes at equal intervals in the vertical direction, and the power supply electrodes are respectively connected to power supply terminals of an electrical prospecting instrument through leads;
2. drilling 11 borehole measurement drill holes of zk 1-zk 11 on a connecting line between the positive power supply electrode and the negative power supply electrode, respectively putting a measurement electrode for measuring the earth electric field in two adjacent drill holes of the 11 measurement drill holes, and connecting the measurement electrodes to a measurement terminal of an electrical prospecting instrument;
3. starting an electrical prospecting instrument, supplying power to the underground through a power supply electrode, enabling a measuring electrode to move synchronously at equal depth along the depth direction of a measured drill hole, and measuring the potential difference between the two electrodes, wherein a recording point of the potential difference is positioned at the geometric midpoint of the two electrodes;
4. replacing the measuring electrode and putting the measuring electrode into different measuring drill holes, repeating the step 3, and repeating the calculation process to uniformly distribute the recording points in the grouting curtain;
5. drawing a potential difference contour map of the grouting curtain according to potential difference values of different recording point positions, and identifying the defect size and the geometric position of the grouting curtain from a potential difference abnormal area on the contour map by combining engineering geology and hydrogeology data with reference to FIG. 6.
EXAMPLE III
Referring to fig. 4, a third embodiment of the present invention provides a method for detecting quality of a grouting curtain for drilling, a work site is arranged in a horizontal direction by using multiple pairs of point power supplies, and fig. 4 is a top view of a site operation during curtain detection, where the method includes:
1. 3 pairs of positive and negative power supply electrodes are arranged perpendicular to the trend of the curtain (connecting lines of 3 positive power supply electrodes or connecting lines of 3 negative power supply electrodes are perpendicular to the trend of the curtain, and the 3 pairs of positive and negative power supply electrodes are positioned in the same horizontal plane) at the positions of 500m long and 500m extended from two ends of the trend of the curtain linearly arranged at the interval of 10m of grouting holes, and are respectively connected to power supply terminals of an electrical prospecting instrument through leads;
2. thus, a measuring electrode for measuring the earth electric field is respectively put in two adjacent boreholes of 51 boreholes such as zk 1-zk 51, and the measuring electrodes are connected to a measuring terminal of an electrical prospecting instrument;
3. starting an electrical prospecting instrument, supplying power to the underground through a power supply electrode, measuring an induced polarizability parameter between two electrodes through equal depth and synchronous movement of a measuring electrode, wherein a recording point of polarizability is positioned at the geometric midpoint of the two electrodes;
4. replacing the drill hole to repeat measurement, so that the recording points are uniformly distributed on the grouting curtain;
5. and drawing a contour map of the polarizability of the grouting curtain, and identifying the size and the geometric position of the defect of the grouting curtain from the polarizability abnormal area on the contour map by combining engineering geology and hydrogeology data, similar to the diagram 6.
Example four
Referring to fig. 5, a fourth embodiment of the present invention provides a method for detecting quality of a grouting curtain in a borehole, wherein a line power supply is disposed in a working site, and fig. 5 is a cross-sectional view of the working site with the line power supply, the method includes:
1. dividing a linearly arranged curtain with the length of 2000m and the distance between grouting holes of 10m into 4 sections, wherein each section is 500m long, drilling a pair of power supply drill holes (a certain grouting drill hole can be utilized) at the positions of two ends of the curtain, which are respectively extended by 500m, vertically arranging 1 pair of linear positive and negative power supply electrodes in the drill holes, and respectively connecting the linear positive and negative power supply electrodes to power supply terminals of an electrical prospecting instrument through leads;
2. thus, a measuring electrode for measuring the earth electric field is respectively put in two adjacent boreholes of 51 boreholes such as zk 1-zk 51, and the measuring electrodes are connected to a measuring terminal of an electrical prospecting instrument;
3. starting an electrical prospecting instrument, supplying power to the underground through a power supply electrode, measuring the potential difference and the induced polarization rate between the two electrodes through measuring the equal depth and synchronous movement of the electrodes, and positioning a recording point of two parameter values at the geometric midpoint of the two electrodes;
4. replacing the drill hole to repeat measurement, so that the recording points are uniformly distributed on the section of grouting curtain;
5. replacing the curtain section, repeating the process, and acquiring parameter data of the full curtain section;
6. and calculating the apparent resistivity of each recording point through an apparent resistivity calculation formula, respectively drawing an apparent resistivity and polarizability contour map of the grouting curtain, and identifying the size and the geometric position of the defect of the grouting curtain by combining engineering geological and hydrogeological data from the identified comprehensive abnormal region on the apparent resistivity and polarizability contour map with reference to fig. 6.
EXAMPLE five
Based on the potential difference contour map, the polarization rate contour map or the apparent resistivity contour map of the grouting curtain drawn by the method for detecting the quality of the grouting curtain in the first embodiment to the fourth embodiment, the fifth embodiment further discloses a method for further calculating the relative variation of potential difference to be mapped, or the relative variation of polarization rate to be mapped, or the relative variation of apparent resistivity to be mapped:
1. assuming that the curtain is provided with N drilling holes, wherein each drilling hole is provided with M depth points for observation, and obtaining (N-1) M recording point data in total; wherein, the recording points at the same depth from the earth surface have M groups, and each group has (N-1) data;
2. taking a group of data in the M groups of data to calculate an average value G, comparing data X of each measuring point in the group with the average value G, and calculating a relative change value, namely [ (X-G)/G ] as a new parameter of the measuring point;
3. converting the data of each group of depth points into new parameters in this way;
4. and drawing a contour map after potential difference or polarizability or apparent resistivity conversion by using new parameters on the curtain, and identifying the defect size and the geometric position of the grouting curtain by combining engineering geology and hydrogeology data according to a positive or negative abnormal area on the contour map.
The above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention, and all modifications and equivalents of the present invention, which are made by the contents of the present specification and the accompanying drawings, or directly/indirectly applied to other related technical fields, are included in the scope of the present invention.

Claims (4)

1. A borehole grouting curtain quality detection method is characterized by comprising the following steps:
s1, drilling a plurality of pairs of power supply drill holes at two ends of the curtain along the trend, laying a plurality of corresponding pairs of positive and negative power supply electrodes in the power supply drill holes, wherein the power supply electrodes are arranged at the peripheral position outside the curtain, the curtain is positioned at the middle position of the positive and negative power supply electrodes, the distance between the positive and negative power supply electrodes is at least 3 times of the length of the curtain, the power supply electrodes are point power supplies or line power supplies, the point power supplies are arranged at equal intervals along the vertical direction or are arranged at equal intervals along the direction vertical to the trend of the curtain, and the power supply electrodes are connected with power supply terminals of an electrical prospecting instrument,
s2, arranging a plurality of measuring drill holes on the curtain and on the connecting line between the positive power supply electrode and the negative power supply electrode, wherein the measuring drill holes are grouting drill holes, the measuring drill holes are arranged at equal intervals, a pair of measuring electrodes are arranged in two adjacent measuring drill holes and are connected with measuring terminals of an electrical prospecting instrument,
s3, starting the electrical prospecting instrument, supplying power to the underground through the power supply electrode, measuring the potential difference value or apparent resistivity value or polarizability value between the two measuring electrodes, recording the geometric midpoint between the two measuring electrodes,
s4, moving the measuring electrode along the depth direction of the measuring drill hole at equal intervals, measuring the potential difference value or apparent resistivity value or polarizability value on the recording point of the measuring electrode at different depth positions,
s5, replacing the measuring electrode into a different measuring drill hole, repeating the step S4,
s6, drawing a curtain potential difference contour map or a curtain apparent resistivity contour map or a curtain polarizability contour map according to the steps S4 and S5, wherein an abnormal area in the map is a defect area of the grouting curtain.
2. The method for detecting quality of a borehole grouting curtain as claimed in claim 1, wherein the power supply terminal supplies power to be alternating current or direct current.
3. The method for detecting the quality of the grouting curtain for the drilling hole as claimed in claim 1, wherein in the steps S3-S5, the calculation method of the apparent resistivity is as follows:
the measuring potential difference between the two measuring electrodes is marked as delta U', the recording point is positioned at the geometric midpoint of the two measuring electrodes, I is the current of a power supply loop during measurement, k is the device coefficient, and the expression is as follows:
Figure FDA0002259245890000011
wherein Ha and Hb are the depths of the positive and negative power supply electrodes respectively, L is the electrode distance between the positive and negative power supply electrodes, R1 is the distance between one of the two measuring electrodes and the positive power supply electrode, R2 is the distance between the other of the two measuring electrodes and the positive power supply electrode, h1 and h2 are the depths of the two measuring electrodes,
the apparent resistivity at this point is: rhos=k·ΔU’/I。
4. The method of detecting quality of a borehole grouting curtain as claimed in claim 3, wherein the method of detecting further comprises:
s7, assuming that the curtain is provided with N measuring drill holes, and each measuring drill hole is provided with M depth points for observation, so as to obtain (N-1) M recording point data; the recording points at the same depth from the earth's surface have M groups, and each group has N-1 data; taking a group of data in the M groups of data to calculate an average value G, comparing data X of each measuring point in the group with the average value G, and calculating a relative change value, namely [ (X-G)/G ] as a new parameter of the measuring point; converting the potential difference value, the polarizability or the apparent resistivity data of each group of depth points into new parameters in such a way; and drawing a contour map after potential difference or polarization rate or apparent resistivity conversion by using the new parameters on the curtain, namely respectively corresponding to a graph of potential difference relative variation, a graph of polarization rate relative variation or a graph of apparent resistivity relative variation.
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