A method for detecting deep cavity orientation based on slurry diffusion theory

Abstract

The present invention discloses a method for detecting the orientation of deep cavities based on the theory of slurry diffusion, comprising: arranging detection holes based on geological data of the detection site; determining the slurry mix ratio, grouting the bottom of the detection hole, and recording grouting parameters including slurry injection rate, grouting time, grouting pressure, and slurry density; calculating a slurry injection rate time curve based on the theoretical formula of slurry diffusion and the recorded grouting parameter information, and calculating the distance between the detection hole and the cavity based on the two curves; calculating the distance from each detection hole to the cavity and the cavity radius based on several sets of grouting parameters; and determining the spatial position of the cavity based on the spatial positioning principle and combining the distance from each detection hole to the cavity and the cavity radius. The present invention can estimate the position and size of the cavity in a three-dimensional spatial model by comparing and analyzing the slurry injection rate time curve and the monitoring curve during the grouting process in combination with the specific geological conditions on site.

Description

Technical Field

[0001] The present invention relates to the field of underground detection, in particular to the field of cavity orientation detection, and specifically to a method for detecting the orientation of deep cavities based on slurry diffusion theory. Background Art

[0002] In engineering, underground cavities are a common geological defect that can lead to structural instability, foundation leakage, construction difficulties and other problems. Therefore, determining the location of cavities is of great significance to engineering safety.

[0003] Currently, commonly used cavity detection methods include ultrasonic detection, remote sensing cavitation, and electrical prospecting. Each of these methods has its advantages, but also significant drawbacks. For example, ultrasonic tomography requires high technical and environmental requirements, remote sensing technology is easily affected by surface cover, and electrical differential cavitation is affected by soil moisture. Furthermore, when the cavity is small, especially when located deep, the detection accuracy of these methods is significantly reduced, and may even be unrecognizable. Summary of the Invention

[0004] In order to overcome the above-mentioned deficiencies of the prior art, the present invention provides a method for detecting the orientation of deep cavities based on slurry diffusion theory. By utilizing drilling grouting technology, combining slurry diffusion theory and spatial positioning technology, a new method for detecting deep cavities is provided.

[0005] According to one aspect of the present invention, a method for detecting the location of deep cavities based on slurry diffusion theory is provided, comprising:

[0006] Arrange exploration holes based on the geological data of the exploration site;

[0007] Determine the slurry mix ratio, grout the bottom of the detection hole, and record the grouting parameters including slurry injection rate, grouting time, grouting pressure and slurry density;

[0008] Based on the theoretical formula of slurry diffusion and the recorded grouting parameter information, the slurry injection rate time history curve is calculated to determine whether the monitoring curve and the time history curve overlap. If so, the grouting parameters for this time are deleted, the detection hole position is re-determined, and the above steps are repeated. If not, the grouting parameters for this time are retained, and the positions of other detection holes are determined based on the position of the first detection hole. The above steps are repeated to obtain multiple sets of grouting parameters.

[0009] Based on several sets of grouting parameters, the distance from each detection hole to the cavity and the cavity radius are calculated respectively;

[0010] Based on the principle of spatial positioning, the spatial position of the cavity is determined by combining the distance from each detection hole to the cavity and the cavity radius.

[0011] As a further technical solution, based on the geological data of the detection site, detection holes are arranged, including: obtaining the geological data of the detection site, evaluating the possibility, development level and potential orientation of the local cavity, and digging a detection hole in the vicinity of the cavity.

[0012] As a further technical solution, the slurry mix ratio is determined, including: determining the slurry mix ratio based on the development degree of the detected ground fissures, selecting thick slurry when the nearby fissure opening is large, and selecting thin slurry when the nearby fissure opening is small.

[0013] As a further technical solution, the theoretical formula for slurry diffusion is as follows:

[0014] (1);

[0015] Where, is the grouting time; is the number of monitoring points; is the slurry diffusion radius; is the monitoring value of slurry injection rate; For the The monitoring value of the slurry injection rate at the moment; V is the total volume of the slurry diffused in the space within a certain period of time; t is the moment of the grouting monitoring value; The grouting monitoring value a moment of time; The grouting monitoring value - 1 moment of time;

[0016] (2);

[0017] According to Darcy's law, we can get:

[0018] (3);

[0019] Where, is the permeability coefficient of the slurry in the formation; is the slurry hydraulic gradient; is the spherical diffusion area of ​​the slurry; is the pressure head, is the spherical diffusion radius of the slurry;

[0020] Integrating formula (3), we can get:

[0021] (4);

[0022] Where, is the pressure head of the slurry in the grouting hole; is the pressure head of groundwater; For the Calculated value of injection rate of moment-time curve; is the radius of the grouting hole;

[0023] Substituting formula (2) into formula (4), we can obtain:

[0024] (5).

[0025] As a further technical solution, judging whether the monitoring curve and the time history curve coincide with each other includes: comparing the slurry injection rate time history curve with the detection curve, and when the two are basically consistent over time and then show obvious differences (such as Figure 2 (a) shows that the slurry flows through the cavity. When the two are always basically consistent (as shown in Figure 2 (b) indicates that the slurry has not flowed through the cavity and the detection hole position needs to be re-determined.

[0026] As a further technical solution, when the slurry flows through the cavity, it includes the following steps: Figure 3 The following stages are shown:

[0027] Phase I ): The slurry has not yet flowed into the cavity, and the time course curve is consistent with the monitoring curve;

[0028] Phase II : The slurry flows into the cavity, and the time-history curve and the monitoring curve show obvious differences, and the former gradually becomes smaller than the latter. The difference between the two continues to expand with time. In formulas (1) and (2), let , calculate the distance from the detection hole to the cavity ;

[0029] Phase 3 : The cavity is filled with slurry. Since the slurry continues to flow along the cracks at this time, the theoretical formula of slurry diffusion is applicable again, so the calculation curve and the monitoring curve are distributed in parallel.

[0030] As a further technical solution, the cavity radius The calculation method is as follows:

[0031] (4);

[0032] (5);

[0033] Where, is the volume of the cavity, and the cavity is assumed to be spherical; is the calculated value of slurry injection rate; is the monitoring value of slurry injection rate; is the cavity radius; is the injection rate of the time history curve a moment of time; is the injection rate of the time history curve - 1 moment of time;

[0034] Calculate the cavity radius for each detection hole , and then take the average ;

[0035] when When ;

[0036] They are respectively the cavity radius corresponding to the first detection hole, the cavity radius corresponding to the second detection hole, the cavity radius corresponding to the third detection hole, and the cavity radius corresponding to the fourth detection hole.

[0037] As a further technical solution, the method for calculating the hole position is as follows:

[0038] Based on the principle of spatial positioning, the coordinates of the center point of the cavity obey the following equations:

[0039] (6);

[0040] Where, is the spatial coordinate of the bottom of the first detection hole; is the spatial coordinate of the bottom of the second detection hole; is the spatial coordinate of the bottom of the third detection hole; is the spatial coordinate of the bottom of the fourth detection hole; is the distance between the bottom of the first detection hole and the cavity surface; is the distance between the bottom of the second detection hole and the cavity surface; is the distance between the bottom of the third detection hole and the cavity surface; is the distance between the bottom of the fourth detection hole and the cavity surface; is the coordinate position of the center point of the hole; is the average value of the cavity radius of multiple detection holes;

[0041] The objective function of the hole center coordinates is as follows:

[0042] (7);

[0043] By finding the gradient of formula (9), we can get:

[0044] (8);

[0045] ;

[0046] The coordinates of the center point of the hole are solved by the gradient optimization method, and we can get:

[0047] (9);

[0048] Where, is the number of iterations; is the step length.

[0049] According to one aspect of the present invention, an electronic device is provided, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, the method for detecting the position of deep cavities based on slurry diffusion theory as described in any one of claims 1 to 7 is implemented.

[0050] According to one aspect of the present invention, a non-transitory computer-readable storage medium is provided, on which a computer program is stored. When the computer program is executed by a processor, the method for detecting the position of deep cavities based on slurry diffusion theory as described in any one of claims 1 to 7 is implemented.

[0051] Compared with existing technologies, the present invention has the following advantages: by combining the specific geological conditions of the site and comparing and analyzing the slurry injection rate time history curve and monitoring curve during the grouting process, the present invention can estimate the location and size of the cavity in a three-dimensional spatial model, thereby facilitating on-site decision-making for engineers. Since drilling grouting is an integral part of most engineering construction projects, this method can detect cavities without the need for additional detection equipment. Furthermore, the present invention can identify small cavities that are difficult to identify with traditional detection technologies, providing a new approach to deep cavity detection. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, a brief introduction will be given below to the drawings used in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0053] Figure 1 A flow chart of a method for detecting the orientation of deep cavities based on slurry diffusion theory provided in an embodiment of the present invention.

[0054] Figure 2 A time history curve of slurry injection rate for a method for detecting deep cavity orientation based on slurry diffusion theory provided in an embodiment of the present invention.

[0055] Figure 3 A diagram showing the stage division of a slurry injection rate time history curve for a method for detecting deep cavity orientation based on slurry diffusion theory provided in an embodiment of the present invention.

[0056] Figure 4A diagram showing the phase division of the injection rate time history curve of detection hole No. 1 in a method for detecting the orientation of deep cavities based on slurry diffusion theory provided in an embodiment of the present invention.

[0057] Figure 5 A diagram showing the stage division of the injection rate time history curve of detection hole No. 2 in a method for detecting the orientation of deep cavities based on slurry diffusion theory provided in an embodiment of the present invention.

[0058] Figure 6 A diagram showing the phase division of the injection rate time history curve of detection hole No. 3 in a method for detecting the orientation of deep cavities based on slurry diffusion theory provided in an embodiment of the present invention.

[0059] Figure 7 A diagram showing the stage division of the injection rate time history curve of detection hole No. 4 in a method for detecting the orientation of deep cavities based on slurry diffusion theory provided in an embodiment of the present invention.

[0060] Figure 8 A distribution diagram of detection holes and cavity positions in a method for detecting deep cavity positions based on slurry diffusion theory provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0061] The terms "including" and "having" and any variations thereof in the description and claims of the present invention and the above-mentioned drawings are intended to cover non-exclusive inclusions, for example, a process, method, system, product or apparatus that includes a series of steps or units is not necessarily limited to the steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to these processes, methods, products or apparatuses.

[0062] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention. In addition, the technical features in the various embodiments or single embodiments provided by the present invention are arbitrarily combined with each other to form a new technical solution. This combination is not restricted by the sequence of steps and / or structural composition mode, but must be based on the ability of ordinary technicians in this field to implement it. When the combination of technical solutions is contradictory or cannot be implemented, it should be deemed that this combination of technical solutions does not exist and is not within the scope of protection required by the present invention.

[0063] An embodiment of the present invention provides a method for detecting the location of deep cavities based on slurry diffusion theory, comprising:

[0064] Step 1: Arrange the exploration holes based on the geological data of the exploration site;

[0065] Step 2: Determine the slurry mix ratio, grout the bottom of the detection hole, and record the grouting parameters including slurry injection rate, grouting time, grouting pressure and slurry density;

[0066] Step 3: Based on the theoretical formula of slurry diffusion and the recorded grouting parameter information, calculate the slurry injection rate time history curve, determine whether the monitoring curve and the time history curve overlap, if so, delete the grouting parameters, re-determine the detection hole position, and repeat the above steps; if not, retain the grouting parameters, based on the position of the first detection hole, determine the position of other detection holes, repeat the above steps to obtain multiple sets of grouting parameters;

[0067] Step 4: Based on several sets of grouting parameters, the distance from each detection hole to the cavity and the cavity radius are calculated respectively;

[0068] Step 5: Based on the spatial positioning principle, the spatial position of the cavity is determined in combination with the distance from each detection hole to the cavity and the cavity radius.

[0069] The method for arranging the detection holes in step 1 is specifically as follows: first, obtain geological data of a certain area, preliminarily estimate the possibility, development level, and potential location of the local cavity; and dig a detection hole in the vicinity of the possible cavity.

[0070] Determining the slurry mix ratio in step 2 includes: determining the slurry mix ratio based on the development degree of the detected ground fissures, selecting thick slurry when the nearby fissure opening is large, and selecting thin slurry when the nearby fissure opening is small.

[0071] The derivation process of the formula for the slurry injection rate time history curve in step 3 is as follows:

[0072] The total volume of slurry diffused in space within a certain period of time is:

[0073] (1);

[0074] Where, is the grouting time; is the number of monitoring points; is the slurry diffusion radius; is the monitoring value of slurry injection rate; For the The monitoring value of the slurry injection rate at the moment; V is the total volume of the slurry diffused in the space within a certain period of time; t is the moment of the grouting monitoring value; The grouting monitoring value a moment of time; The grouting monitoring value - 1 moment of time;

[0075] (2);

[0076] According to Darcy's law, we can get:

[0077] (3);

[0078] Where, is the permeability coefficient of the slurry in the formation; is the slurry hydraulic gradient; is the spherical diffusion area of ​​the slurry;

[0079] Integrating formula (3), we can get:

[0080] (4);

[0081] Where, is the pressure head of the slurry in the grouting hole; is the pressure head of groundwater; For the Calculated value of injection rate of moment-time curve; is the radius of the grouting hole;

[0082] Substituting formula (2) into formula (4), we can obtain:

[0083] (5);

[0084] Where, For the Calculated value of injection rate of moment-time curve; is the permeability coefficient of the slurry in the formation; is the pressure head of the slurry in the grouting hole; is the pressure head of groundwater; For the Monitoring value of slurry injection rate at every moment; is the radius of the grouting hole; is the injection rate of the time history curve a moment of time; is the injection rate of the time history curve -1 moment of time.

[0085] In step 3, it is determined whether the monitoring curve and the time history curve coincide with each other, including: comparing the slurry injection rate time history curve with the detection curve, when the two are basically consistent with each other over time, and then there is a significant difference (such as Figure 2 (a) shows that the slurry flows through the cavity. When the two are always basically consistent (as shown in Figure 2 (b) indicates that the slurry has not flowed through the cavity and the detection hole position needs to be re-determined.

[0086] When the slurry flows through the cavity, it specifically includes Figure 3 The following stages are shown:

[0087] Phase I ): The slurry has not yet flowed into the cavity, and the time-history curve is basically consistent with the monitoring curve;

[0088] Phase II : The slurry flows into the cavity. Since the slurry does not flow completely in the cracks at this time, the theoretical formula of slurry diffusion is no longer applicable. Therefore, there will be a significant difference between the time-history curve and the monitoring curve, and the former is gradually smaller than the latter. The difference between the two continues to expand over time. In formulas (1) and (2), let , calculate the distance from the detection hole to the cavity ;

[0089] Phase 3 : The cavity is filled with slurry. Since the slurry continues to flow along the cracks at this time, the theoretical formula of slurry diffusion is applicable again, so the time history curve and the monitoring curve are parallel to each other.

[0090] in, It is the dividing point between the two curves from the same injection rate to the different injection rate. It is the dividing point between the two curves from injection rate change to injection rate stability.

[0091] In step 4, the cavity radius The calculation method is as follows:

[0092] (6);

[0093] (7);

[0094] Where, is the volume of the cavity, and the cavity is assumed to be spherical; is the calculated value of slurry injection rate; is the monitoring value of slurry injection rate; is the cavity radius; is the injection rate of the time history curve a moment of time; is the injection rate of the time history curve - 1 moment of time;

[0095] Calculate the cavity radius for each detection hole , and then take the average ;

[0096] when When ;

[0097] They are respectively the cavity radius corresponding to the first detection hole, the cavity radius corresponding to the second detection hole, the cavity radius corresponding to the third detection hole, and the cavity radius corresponding to the fourth detection hole.

[0098] The calculation method for the hole position in step 6 is as follows:

[0099] Based on the principle of spatial positioning, the coordinates of the center point of the cavity obey the following equations:

[0100] (8);

[0101] Where, is the spatial coordinate of the bottom of the first detection hole; is the spatial coordinate of the bottom of the second detection hole; is the spatial coordinate of the bottom of the third detection hole; is the spatial coordinate of the bottom of the fourth detection hole; is the distance between the bottom of the first detection hole and the cavity surface; is the distance between the bottom of the second detection hole and the cavity surface; is the distance between the bottom of the third detection hole and the cavity surface; is the distance between the bottom of the fourth detection hole and the cavity surface; is the coordinate position of the center point of the hole; is the average value of the cavity radius of multiple detection holes;

[0102] The objective function of the hole center coordinates is as follows:

[0103] (9);

[0104] By finding the gradient of formula (9), we can get:

[0105] (10);

[0106] ;

[0107] The coordinates of the center point of the hole are solved by the gradient optimization method, and we can get:

[0108] (11);

[0109] Where, is the number of iterations; is the step length.

[0110] Through the above detection method, the distance between the first detection hole and the hole and the hole radius are calculated. Based on the first detection hole, the positions of the other three detection holes are determined, and then steps S1-S3 are repeated, and the distance between the detection hole and the hole and the hole radius are calculated respectively. Finally, based on the spatial positioning principle, the spatial position of the hole is determined.

[0111] Experimental example:

[0112] Based on the geological and hydrological data of a certain area, the orientation of the hole is roughly determined. In the vicinity of the hole, the east is the x-axis, the north is the y-axis, and the vertical direction is the z-axis. The coordinates of the center of the ground of the No. 1 detection hole are set as the origin. The depth of the No. 1 detection hole is 20m, so the coordinates of its bottom hole are ,like Figure 8 As shown. Grouting is performed in the No. 1 detection hole, and the slurry injection rate, grouting time, grouting pressure, and slurry density are recorded. The slurry injection rate time history curve is calculated by formula (1) and formula (2) as follows: Figure 4 As shown in the figure, after 35 minutes, there is a significant difference between the calculated injection rate and the monitored value, and the gap continues to expand. It is thus determined that the No. 1 detection hole is connected to the cavity. The distance between the bottom of the No. 1 detection hole and the cavity surface is calculated by formula (4) and formula (5) as follows: .

[0113] In the vicinity of detection hole No. 1, similarly determine the spatial coordinates of the bottom of detection holes No. 2, No. 3, and No. 4: 、 、 ,like Figure 5 Repeat the above process and calculate the slurry injection rate time history curve using formula (1) and formula (2) as shown below: Figure 5 、 Figure 6 and Figure 7 The calculated distances between the bottoms of detection holes 2, 3, and 4 and the cavity surface are: 、 and .

[0114] The cavity radius is calculated by equations (6) and (7): , and the corresponding average value is: The hole orientation is calculated by equations (9), (10) and (11): ,like Figure 8 shown.

[0115] The present invention further provides an electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, the method for detecting the location of deep cavities based on slurry diffusion theory is implemented as shown below:

[0116] Arrange exploration holes based on the geological data of the exploration site;

[0117] Determine the slurry mix ratio, grout the bottom of the detection hole, and record the grouting parameters including slurry injection rate, grouting time, grouting pressure and slurry density;

[0118] Based on the theoretical formula of slurry diffusion and the recorded grouting parameter information, the slurry injection rate time history curve is calculated to determine whether the monitoring curve and the time history curve overlap. If so, the grouting parameters for this time are deleted, the detection hole position is re-determined, and the above steps are repeated. If not, the grouting parameters for this time are retained, and the positions of other detection holes are determined based on the position of the first detection hole. The above steps are repeated to obtain multiple sets of grouting parameters.

[0119] Based on several sets of grouting parameters, the distance from each detection hole to the cavity and the cavity radius are calculated respectively;

[0120] Based on the principle of spatial positioning, the spatial position of the cavity is determined by combining the distance from each detection hole to the cavity and the cavity radius.

[0121] The present invention further provides a non-transitory computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, the method for detecting the location of deep cavities based on slurry diffusion theory is implemented as follows:

[0122] Arrange exploration holes based on the geological data of the exploration site;

[0123] Determine the slurry mix ratio, grout the bottom of the detection hole, and record the grouting parameters including slurry injection rate, grouting time, grouting pressure and slurry density;

[0124] Based on the theoretical formula of slurry diffusion and the recorded grouting parameter information, the slurry injection rate time history curve is calculated to determine whether the monitoring curve and the time history curve overlap. If so, the grouting parameters for this time are deleted, the detection hole position is re-determined, and the above steps are repeated. If not, the grouting parameters for this time are retained, and the positions of other detection holes are determined based on the position of the first detection hole. The above steps are repeated to obtain multiple sets of grouting parameters.

[0125] Based on several sets of grouting parameters, the distance from each detection hole to the cavity and the cavity radius are calculated respectively;

[0126] Based on the principle of spatial positioning, the spatial position of the cavity is determined by combining the distance from each detection hole to the cavity and the cavity radius.

[0127] In summary, the present invention combines the specific geological conditions of the site and compares and analyzes the slurry injection rate time history curve and monitoring curve during the grouting process. This allows the location and size of the cavity to be estimated in a three-dimensional spatial model, thereby facilitating on-site decision-making for engineers. Since borehole grouting is an integral part of most engineering construction projects, this method can detect cavities without the need for additional detection equipment. Furthermore, the present invention can identify small cavities that are difficult to identify with traditional detection techniques, providing a new approach to deep cavity detection.

[0128] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the technical solutions of the embodiments of the present invention.

Claims

1. A method for detecting the location of deep cavities based on slurry diffusion theory, characterized in that: include: Arrange exploration holes based on the geological data of the exploration site; Determine the slurry mix ratio, grout the bottom of the detection hole, and record the grouting parameters including slurry injection rate, grouting time, grouting pressure and slurry density; Based on the theoretical formula of slurry diffusion and the recorded grouting parameter information, the slurry injection rate time history curve is calculated to determine whether the monitoring curve and the time history curve overlap. If so, the grouting parameters for this time are deleted, the detection hole position is re-determined, and the above steps are repeated. If not, the grouting parameters for this time are retained, and the positions of other detection holes are determined based on the position of the first detection hole. The above steps are repeated to obtain multiple sets of grouting parameters. Based on several sets of grouting parameters, the distance from each detection hole to the cavity and the cavity radius are calculated respectively; Based on the principle of spatial positioning, the spatial position of the cavity is determined by combining the distance from each detection hole to the cavity and the cavity radius.

2. The method for detecting the position of deep cavities based on slurry diffusion theory according to claim 1, characterized in that: Arrange the exploration hole based on the geological data of the exploration site, including: obtaining the geological data of the exploration site, evaluating the possibility, development level and potential orientation of the local cavity, and digging a exploration hole in the vicinity of the cavity.

3. The method for detecting the position of deep cavities based on slurry diffusion theory according to claim 1, characterized in that: Determining the mix ratio of the slurry includes: determining the mix ratio of the slurry based on the development degree of the detected ground fissures, selecting thick slurry when the opening of the nearby fissures is large, and selecting thin slurry when the opening of the nearby fissures is small.

4. The method for detecting the position of deep cavities based on slurry diffusion theory according to claim 1, characterized in that: The theoretical formula for the slurry diffusion is as follows: （1）； Where, is the grouting time; is the number of monitoring points; is the slurry diffusion radius; is the monitoring value of slurry injection rate; For the The monitoring value of the slurry injection rate at the moment; V is the total volume of the slurry diffused in the space within a certain period of time; t is the moment of the grouting monitoring value; The grouting monitoring value a moment of time; The grouting monitoring value - 1 moment of time; （2）； According to Darcy's law, we can get: （3）； Where, is the permeability coefficient of the slurry in the formation; J is the hydraulic gradient of the slurry; is the spherical diffusion area of ​​the slurry; is the pressure head, is the spherical diffusion radius of the slurry; Integrating formula (3), we can get: （4）； Where, is the pressure head of the slurry in the grouting hole; is the pressure head of groundwater; For the Calculated value of injection rate of moment-time curve; is the radius of the grouting hole; Substituting formula (2) into formula (4), we can obtain: （5）。 5. The method for detecting the position of deep cavities based on slurry diffusion theory according to claim 4, characterized in that: Determine whether the monitoring curve and the time-history curve coincide, including: comparing the slurry injection rate time-history curve with the detection curve. When the two are basically consistent with time and then show obvious differences, it indicates that the slurry flows through the hole. When the two are always basically consistent, it indicates that the slurry does not flow through the hole and the detection hole position needs to be re-determined.

6. The method for detecting the position of deep cavities based on slurry diffusion theory according to claim 5, characterized in that: When the slurry flows through the cavity, it includes the following stages: Phase 1 : The slurry has not yet flowed into the cavity, and the time course curve is consistent with the monitoring curve; Phase II : The slurry flows into the cavity, and the time-history curve and the monitoring curve show obvious differences, and the former gradually becomes smaller than the latter. The difference between the two continues to expand with time. In formulas (1) and (2), let , calculate the distance from the detection hole to the cavity ; Phase 3 : The cavity is filled with slurry. Since the slurry continues to flow along the cracks, the theoretical formula of slurry diffusion is applicable again, so the calculation curve and the monitoring curve are parallel; in, is the grouting time; It is the dividing point between the two curves from the same injection rate to the different injection rate. It is the dividing point between the two curves from injection rate change to injection rate stability.

7. The method for detecting the position of deep cavities based on slurry diffusion theory according to claim 1, characterized in that: Cavity radius The calculation method is as follows: （6）； （7）； Where, is the volume of the cavity, and the cavity is assumed to be spherical; is the calculated value of slurry injection rate; is the monitoring value of slurry injection rate; is the cavity radius; is the injection rate of the time history curve a moment of time; is the injection rate of the time history curve - 1 moment of time; For the The calculated value of the injection rate of the time history curve, is the dividing point between the two curves from the same injection rate to the different injection rate, m is the mth moment, It is the dividing point between the two curves from injection rate change to injection rate stability, and l is the lth moment; For the Monitoring value of slurry injection rate at every moment; Calculate the cavity radius for each detection hole , and then take the average ; when When, take ; They are respectively the cavity radius corresponding to the first detection hole, the cavity radius corresponding to the second detection hole, the cavity radius corresponding to the third detection hole, and the cavity radius corresponding to the fourth detection hole.

8. The method for detecting the position of deep cavities based on slurry diffusion theory according to claim 1, characterized in that: The calculation method of the hole position is as follows: Based on the principle of spatial positioning, the coordinates of the center point of the cavity obey the following equations: （8）； Where, is the spatial coordinate of the bottom of the first detection hole; is the spatial coordinate of the bottom of the second detection hole; is the spatial coordinate of the bottom of the third detection hole; is the spatial coordinate of the bottom of the fourth detection hole; is the distance between the bottom of the first detection hole and the cavity surface; is the distance between the bottom of the second detection hole and the cavity surface; is the distance between the bottom of the third detection hole and the cavity surface; is the distance between the bottom of the fourth detection hole and the cavity surface; is the coordinate position of the center point of the hole; is the average value of the cavity radius of multiple detection holes; The objective function of the hole center coordinates is as follows: （9）； By finding the gradient of formula (9), we can get: （10）； ； The coordinates of the center point of the hole are solved by the gradient optimization method, and we can get: （11）； Where, is the number of iterations; is the step length.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the method for detecting the position of deep cavities based on slurry diffusion theory as described in any one of claims 1 to 7 is implemented.

10. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the method for detecting the position of deep cavities based on slurry diffusion theory as claimed in any one of claims 1 to 7 is implemented.

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