A multi-parameter-based quantitative determination method for nonlinear fracture propagation length of coal rock

Abstract

The application discloses a kind of coal rock nonlinear fracture propagation length quantitative determination method based on multiple parameters, comprising: preparation of coal rock sample containing notch;Spray black and white speckle on the surface of sample, install acoustic emission sensor, clip type extensometer and displacement sensor;Carry out three-point bending peak after cycle loading and unloading fracture experiment, record load, crack opening, force point displacement, acoustic emission waveform and DIC image;Through COD-P and LPD-P curve calculation mechanics flexibility, back calculation to solve stress constraint crack length;From acoustic emission positioning, obtain the spatial distribution histogram of breakage dissipation energy, combined with DIC horizontal displacement gradient threshold cloud picture, determine equivalent crack tip and length;Further calculate coal rock fracture process zone length, and intuitively show nonlinear fracture propagation path.The application provides a kind of crack dynamic change quantitative determination method based on mechanics flexibility-displacement gradient-energy dissipation distribution multiple physical parameters, reduce the influence of human subjective consciousness, and the measurement result is accurate and reliable.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of rock fracture mechanics, and particularly relates to a method for quantitatively determining the nonlinear fracture propagation length of coal rock based on multiple parameters. BACKGROUND

[0002] In the construction and operation of underground rock mass engineering, engineering geological disasters such as rock burst, rock burst, tunnel collapse and induced earthquake often occur due to the instability of coal rock mass breakage. Research shows that these disasters are essentially the evolution results of coal rock mass crack initiation, propagation, nucleation and fracture disaster under the coupling effect of geological conditions and mining activities. How to quantitatively determine and accurately characterize the crack propagation process is a research hotspot in the field of rock mechanics. On the other hand, coal rock is a typical quasi-brittle material, and its significant feature is the existence of a non-negligible nonlinear fracture process zone, which makes its fracture propagation behavior deviate from the prediction of the linear elastic fracture mechanics model. How to describe the quasi-brittle fracture propagation process of coal rock and establish a nonlinear fracture criterion is a scientific problem to be solved, which involves the quantitative and accurate measurement of the nonlinear fracture propagation length of coal rock. Therefore, the quantitative determination of the nonlinear fracture propagation of coal rock has a positive role in promoting the further understanding of the evolution process and mechanism of rock mass disasters, the capture of dynamic change characteristics of crack parameters, the modification and verification of coal rock fracture criterion, etc.

[0003] At present, the research on coal rock fracture behavior at home and abroad generally adopts three-point bending loading method, and with the help of acoustic emission or digital image matching (DIC) and other monitoring means, the coal rock fracture mechanics response and crack evolution law are focused on, such as the patents CN113218766A and CN110686971A respectively disclose a method for identifying rock cracking stress and crack type based on acoustic emission parameters and DIC displacement field, the patent CN113885073A discloses a method for fine analysis of rock fracture process by acoustic emission energy, wave speed, frequency and focal mechanism, and the patent CN113466066A discloses a method for measuring concrete fatigue deformation and crack size based on DIC technology, etc. These technical methods still stay at the qualitative analysis level of the crack propagation process, and it is difficult to realize quantitative determination of the crack propagation length. At the same time, there are limitations of single acoustic emission or DIC technology: acoustic emission technology can obtain the spatial distribution form of micro-cracks through three-dimensional positioning, and then realize dynamic capture of the crack propagation process, but the acoustic emission positioning result has great dispersion and unavoidable error, so it is difficult to accurately determine the position of the crack tip; and the DIC technology can obtain the two-dimensional surface crack propagation characteristics by observing the displacement characteristics of the black and white speckles on the surface, but it cannot reflect the internal crack propagation state, and the measurement result is easily disturbed by subjective factors, lacks quantitative threshold determination index, and is also prone to large human error. In addition, the Barenblatt-Dugdale model shows that there are multiple nonlinear crack length characteristic parameters such as stress-free constraint crack, equivalent crack and fracture process zone in the quasi-brittle fracture process of coal rock material, and there is still a lack of effective method to combine theoretical model and experimental test to realize quantitative determination of these coal rock nonlinear crack length parameters.

[0004] In summary, there is an urgent need for a multi-parameter quantitative determination method for nonlinear fracture propagation length of coal rock. SUMMARY

[0005] The purpose of the present application is to provide a multi-parameter quantitative determination method for nonlinear fracture propagation length of coal rock, which realizes dynamic and accurate measurement of the crack length of coal rock.

[0006] To achieve the above purpose, the technical scheme adopted by the present application is as follows: a multi-parameter quantitative determination method for nonlinear fracture propagation length of coal rock, comprising the following steps:

[0007] a. Make a coal rock fracture test sample with a notch, the sample is a rectangular prism with length L, thickness W and height H, the sample span is S, and a through notch is cut at the center of the bottom of the sample, the notch height is H0;

[0008] b. Spraying random black and white speckles on the front surface of the sample prepared in step a to form the DIC image observation area of crack propagation; arranging an acoustic emission sensor array at a reasonable position on the sample surface for monitoring and locating the crack propagation position; installing a clamp-type extensometer at the bottom end of the sample notch for measuring crack opening displacement (COD) signals; installing a linear variable displacement transducer (LVDT) at the center of the top end of the back surface of the sample for measuring the force point displacement (LPD) amount;

[0009] c. Carrying out a coal rock three-point bending fracture quasi-static stable expansion experiment, wherein the stress path in the fracture experiment is set as a cyclic path of multiple unloading-reloading after peak load;

[0010] d. Simultaneously collecting and recording the load P, crack opening displacement COD, force point displacement LPD, acoustic emission waveform and DIC image data during the crack propagation process of the coal rock;

[0011] e. Drawing the COD-P and LPD-P mechanical curves from the data collected in step d, respectively calculating the mechanical compliances C COD and C LPD , and inversely calculating the stress-free constraint crack length a and a according to the linear elastic fracture mechanics theory (LEFM); According to the DIC displacement field data, calculating the horizontal displacement gradient, setting the gradient threshold and drawing the displacement gradient cloud map, and then determining the equivalent crack tip position and length a

[0012] f. Comprehensive use of mechanical compliance-displacement gradient-energy dissipation distribution of multiple physical quantities to quantitatively determine the stress-free constraint crack length l0, equivalent crack length l e , fracture process zone length l p and their dynamic change law of the coal rock nonlinear fracture expansion, and intuitively display the coal rock fracture propagation path.

[0013] Further, in step b, evenly apply white paint as the background color in the DIC observation area, and then spray black spots after the paint is fully solidified to form a random black and white speckle pattern;

[0014] The acoustic emission sensors are fixed on the front and back surfaces of the sample, the number of acoustic emission sensors is ≥4, and the sensor array formed covers the crack propagation area and is located outside the DIC observation area;

[0015] The installation mode of the clip-on extensometer is as follows: two four-prism metal clips with a right-angled trapezoidal cross section are respectively pasted on both sides of the bottom notch of the sample, the distance between the tips of the metal clips is consistent with the width of the notch, and the cantilever grooves on both sides of the clip-on extensometer are installed on the tips of the metal clips, so as to ensure that the measurement data of the clip-on extensometer is the notch opening displacement;

[0016] The installation mode of the linear variable displacement transducer (LVDT) is as follows: a right-angle steel sheet is fixed at the center position of the end of the rear surface of the sample, the LVDT sensor is clamped through a support frame, and the height and position of the LVDT sensor are adjusted to make it slightly contact with the lower surface of the right-angle steel sheet, so as to ensure that the data measured by the LVDT sensor is the force point displacement.

[0017] Further, in step c, the stress cycle path in the coal rock fracture quasi-static stable expansion experiment is specifically set as follows: the crack opening displacement (COD) signal is used as the feedback control signal of the press system, after loading to the peak load for a period of time, unloading is started, the unloading point is 97%-93% of the horizontal after the peak load of this cycle, the unloading is to the reloading point, and the reloading point load is 0.5 kN to ensure that the press is always in contact with the sample under stress, that is, “loading→peak load→peak unloading point→unloading→reloading point→loading” is a complete cycle of loading and unloading process, and the above cycle process is repeated multiple times until the experiment is completed;

[0018] The above-mentioned loading refers to the linear increase of the crack opening displacement (COD) rather than the increase of the applied load, and the unloading refers to the linear decrease of the crack opening displacement (COD) rather than the decrease of the applied load.

[0019] Further, in step e, the unconstrained crack length is quantitatively back calculated based on the COD-P mechanical compliance and LEFM theory, and the formula is as follows:

[0020]

[0021] Wherein, γ1, γ2, γ3 and γ4 are fitting functions related to the span S and the thickness W, that is, γ1=0.25S / W-0.0505(S / W) 3 / 2 +0.0033(S / W) 2 , γ2=1.155S / W+0.215(S / W) 3 / 2 -0.0278(S / W) 2 , γ3=-1.38+1.75S / W and γ4=0.506-1.057S / W+0.888(S / W) 2 ; C COD is the unloading mechanical compliance of the COD-P curve, that is, the COD-P data from the unloading point to the reloading point in each cycle is linearly fitted, and the reciprocal of the slope of the fitting straight line is C.COD .

[0022] Further, in step e, the unconstrained crack length a is quantitatively back calculated by using the LPD-P mechanical compliance and LEFM theory The formula is:

[0023]

[0024] where E is the equivalent elastic modulus; W and H are the specimen thickness and height; η1, η2 and η3 are the fitting functions related to the span S and thickness W, i.e. η1 = 0.98 + 3.77S / W, η2 = -(9.1 + 2.9S 2 / W 2 ) / (1 + 0.168S / W) and η3 = -3.2S / W + 9.8S 2 / W 2 ; C c is the additional compliance due to the crack growth, given by formula (3):

[0025]

[0026] where G is the shear modulus; κ is the shape factor; I is the moment of inertia, I = WH 3 / 12; C LPD is the LPD-P curve unloading mechanical compliance, i.e. the reciprocal of the slope of the straight line fitted to the LPD-P data from the unloading point to the reloading point in each cycle LPD .

[0027] Further, in step e, the spatial location of the crack source (x s , y s , z s ) is solved by the acoustic emission positioning simplex algorithm, and the crack dissipation energy value E c is characterized by the acoustic emission waveform root mean square value considering the geometric attenuation effect, i.e.

[0028]

[0029] where N is the number of acoustic emission sensors participating in positioning; R i is the distance between the crack source (x s , y s , z s ) and the i-th sensor (x i , y i , z i ); RMS i is the root mean square value of the effective signal in the waveform received by the i-th sensor;

[0030] Determining equivalent crack tip position and length based on broken dissipated energy space distribution histogram in step e The specific method is: combining acoustic emission positioning and energy calculation results, accumulating dissipated energy values E c along the fracture propagation direction with a resolution interval of 0.1 mm, drawing a dissipated energy distribution histogram along the fracture propagation direction, setting a dissipated energy threshold E m , determining the intersection points of the dissipated energy distribution histogram, and the position of the frontmost intersection point is the equivalent crack tip, and the length from the tip position to the bottom of the sample is the equivalent crack length l

[0031] Further, in the step e, the calculation formula of the horizontal displacement gradient is:

[0032]

[0033] Wherein, G h (x i ,y i ) is the spatial variation slope of the horizontal displacement at the position (x i ,y i ), which represents the degree of displacement discontinuity; d h (x i ,y i ) is the horizontal displacement at the position (x i ,y i ), which is given by the DIC system;

[0034] Determining equivalent crack tip position and length based on displacement gradient cloud map in step e The specific method is: drawing a horizontal displacement gradient cloud map from G h (x,y) data, setting a gradient threshold G m , setting the area with G h <G m as white, and setting the area with G h ≥G m as black, and the obtained black area is the equivalent crack, the tip of the black area is the equivalent crack tip position, and the length from the tip position to the bottom of the sample is the equivalent crack length l

[0035]

[0036] Further, in step f, the stress-free constraint crack length l0 is the average value of and , that is The equivalent crack length l e is and the average value of l the length of the fracture process zone (FPZ) l p the equivalent crack length l e the difference between the equivalent crack length l and the stress-free constraint crack length l0, i.e., l p = l e - l0;

[0037] According to the values of l0, l e and l p under each loading and unloading cycle, the dynamic variation law of the nonlinear fracture length of coal rock is quantitatively determined, and the energy dissipation distribution characteristics, the real-time position of the crack tip and the crack propagation path in the nonlinear fracture propagation process of coal rock are intuitively and dynamically displayed by combining the energy dissipation space distribution histogram and the displacement gradient cloud diagram, so that the visual display of the fracture propagation process of coal rock is realized.

[0038] Compared with the prior art, the present application has the following beneficial effects:

[0039] 1. The present application focuses on the quantitative determination of the crack propagation length in the quasi-brittle fracture process of coal rock, combines various measurement methods such as mechanical parameters, acoustic emission and DIC images, proposes a multi-physical parameter joint determination method of "mechanical flexibility + displacement gradient + energy dissipation distribution", and selects high-accuracy index parameters or quantitative thresholds for each measurement method and physical quantity, which can reduce the interference factors of human consciousness in the determination process and realize the dynamic and quantitative determination of various nonlinear fracture parameters such as stress-free constraint crack, equivalent crack length and fracture process zone length in the fracture propagation process of coal rock.

[0040] 2. In the present application, the related parameters of the nonlinear fracture length of coal rock are determined quantitatively by two or more methods, such as COD-P curve and LPD-P curve for stress-free constraint crack, acoustic emission energy dissipation distribution and DIC displacement gradient for equivalent crack length, and the combination of mechanical flexibility, displacement gradient and energy dissipation distribution for the quantitative determination of the length of the fracture process zone. Through the combination of "surface + internal" and "theory + experiment", the technical defects of single measurement method can be made up, and the result deviation caused by the measurement error of a certain physical quantity can be excluded, which has the advantages of high measurement accuracy and reliable result.

[0041] 3. The present application not only can obtain the variation characteristics of the crack length in the fracture propagation process of coal rock, but also can intuitively and dynamically display the energy dissipation distribution characteristics, the real-time position of the crack tip and the crack propagation path in the nonlinear fracture propagation process of coal rock through the acoustic emission energy dissipation distribution diagram and the DIC displacement gradient cloud diagram, so that the visual display of the fracture propagation process of coal rock is realized. BRIEF DESCRIPTION OF DRAWINGS

[0042] Figure 1 It is the flow chart of the quantitative determination method of the nonlinear fracture propagation length of coal rock based on multiple parameters of the present application;

[0043] Figure 2 This is a schematic diagram of the coal and rock samples required in the embodiments of the present invention;

[0044] Figure 3 This is a schematic diagram of the three-point bending loading experiment and sensor arrangement for coal and rock fracture in an embodiment of the present invention;

[0045] In the figure: 1-Right-angle steel sheet, 2-LVDT sensor, 3-Support frame, 4-Sample, 5-Acoustic emission sensor, 6-DIC ​​observation area, 7-Pre-made notch, 8-Metal clip, 9-Clamp extensometer, 10-LED cold light lamp, 11-Preamplifier, 12-Acoustic emission acquisition instrument, 13-Pressure machine system, 14-Computer, 15-CCD camera;

[0046] Figure 4 This is the load path-time curve of multiple cycles of loading and unloading after the fracture peak of the sample in the embodiment of the present invention;

[0047] Figure 5 The crack opening displacement-load curve (COD-P curve) of the specimen in the embodiment of the present invention;

[0048] Figure 6 This invention uses the COD-P curve to determine the mechanical compliance C. COD A schematic diagram illustrating the calculation principle;

[0049] Figure 7 The force point displacement-load curve (LPD-P curve) of the specimen in the embodiment of the present invention;

[0050] Figure 8 This invention determines the mechanical compliance C based on the LPD-P curve. LPD A schematic diagram illustrating the calculation principle;

[0051] Figure 9 This is the dynamic evolution result of determining the equivalent crack tip position based on the spatial distribution histogram of fracture dissipation energy in an embodiment of the present invention;

[0052] Figure 10 This is a schematic diagram illustrating the principle of drawing a horizontal displacement gradient threshold cloud map based on DIC image data in this invention.

[0053] Figure 11 This is the dynamic evolution result of determining the equivalent crack tip position based on the displacement gradient cloud map in an embodiment of the present invention. Detailed Implementation

[0054] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0055] like Figure 1As shown, the present application provides a multi-parameter-based quantitative determination method for the nonlinear fracture propagation length of coal rock, which comprises the following steps:

[0056] a. A coal rock fracture test sample with a notch is prepared (see Figure 2 ), and the sample size used is L x W x H = 290.0 mm x 30.4 mm x 99.9 mm, and the sample span S = 270.0 mm. A through-notch is cut at the center of the bottom of the sample by a hydraulic cutting machine, and the notch height H0 is 13.5 mm.

[0057] b. In this embodiment, the coal rock fracture test system connection and sensor arrangement are shown in Figure 3 , and the specific process is as follows: first, a white paint is evenly applied as the background color on the front surface of the sample 4 prepared in step a. After the paint is fully solidified, black spots are sprayed to form a random distribution of black and white speckle patterns. The LED cold light lamp 10 is used for light supplement, and the surface displacement DIC image of the black and white speckle is captured by the CCD camera 15 and then transmitted to the computer 14 for storage and analysis.

[0058] Secondly, the acoustic emission sensor 5 array is arranged at a reasonable position on the surface of the sample 4 for monitoring and positioning the fracture propagation position. In this embodiment, eight S9225 type acoustic emission sensors 5 are used, which are fixed on the front and rear surfaces of the sample 4 by M-BOND200 adhesive to form a sensor array that covers the fracture propagation area and is located outside the DIC observation area 6. The waveform data collected by the acoustic emission sensor 5 is transmitted to the acoustic emission acquisition instrument 12 for recording and saving after being enhanced and amplified by the preamplifier 11.

[0059] After that, the clamp extensometer 9 is installed at the pre-notched 7 at the bottom end of the sample 4 for measuring the crack opening displacement (COD) signal. The specific installation method is as follows: two four-prism metal clamps 8 with right-angled trapezoidal cross-section are pasted on both sides of the pre-notched 7 at the bottom of the sample 4, the distance between the tips of the metal clamps 8 is consistent with the width of the pre-notched 7, and the cantilever grooves on both sides of the clamp extensometer 9 are installed on the tips of the metal clamps 8 to ensure that the measurement data of the clamp extensometer 9 is the notch opening displacement. The LVDT sensor 2 is installed at the center of the top end of the rear surface of the sample for measuring the force point displacement (LPD) physical quantity. The specific installation method is as follows: the right-angle steel sheet 1 is pasted and fixed at the center of the end of the rear surface of the sample 4, the LVDT sensor 2 is clamped by the support frame 3, and the height and position of the LVDT sensor 2 are adjusted to make it slightly contact with the lower surface of the right-angle steel sheet 1, so as to ensure that the measurement data of the LVDT sensor 2 is the force point displacement. The mechanical signals such as load P, COD and LPD collected by the sensors are transmitted to the MTS press system 13 for storage and display through the connecting lines.

[0060] c. Coal rock three-point bending fracture quasi-static stable expansion experiment is carried out, and a stress path is set in the experiment, that is, a cycle path of unloading-reloading after peak load, specifically: the crack opening displacement (COD) signal is used as the feedback control signal of the press system, the loading is unloaded after being loaded to the peak load for a period of time, the unloading point is 97%-93% of the peak load after the peak, the unloading is unloaded to the reloading point, and the reloading point load is 0.5kN to ensure that the press is always in contact with the sample under stress, that is, "loading→peak load→peak unloading point→unloading→reloading point→loading" is a complete cycle loading and unloading process, and the above cycle process is repeated multiple times until the experiment is completed, as shown in Figure 4 . The control loading refers to the linear increase of COD instead of the increase of applied load, and the unloading refers to the linear decrease of COD instead of the decrease of applied load.

[0061] d. The applied load P, crack opening displacement COD, force point displacement LPD, acoustic emission waveform and DIC image and other data in the coal rock fracture expansion process are synchronously collected and recorded.

[0062] e. The COD-P and LPD-P mechanical curves are drawn from the data collected in step d, the mechanical compliances C COD and C LPD are respectively calculated, the stress-free constraint crack length a and the equivalent crack tip length L are solved according to the linear elastic fracture mechanics theory (LEFM), the spatial location of the fracture source is located by using the acoustic emission waveform data, and the dissipated energy value is calculated, the spatial distribution histogram of the fracture dissipated energy is drawn, and the equivalent crack tip position and length L are determined according to the DIC displacement field data, the horizontal displacement gradient is calculated, the gradient threshold is set, and the displacement gradient cloud chart is drawn, and then the equivalent crack tip position and length L are determined. The specific calculation process is as follows:

[0063] Firstly, the formula for quantitatively calculating the unconstrained crack length a based on the COD-P curve (see Figure 5 ) mechanical compliance and LEFM theory is as follows:

[0064]

[0065] In the formula, γ1, γ2, γ3 and γ4 are fitting functions about span S and thickness W, that is, γ1=0.25S / W-0.0505(S / W) 3 / 2 +0.0033(S / W) 2 , γ2=1.155S / W+0.215(S / W) 3 / 2 -0.0278(S / W) 2, y3 = -1.38 + 1.75 S / W and y4 = 0.506 - 1.057 S / W + 0.888 (S / W) 2 In specific embodiments of the application, y1 = 0.475, y2 = 2.356, y3 = 3.349 and y4 = 4.134; C COD is the COD-P curve unloading mechanical compliance, i.e. the inverse of the slope of the straight line fitted to the COD-P data from the unloading point to the reloading point in each cycle COD As shown in Figure 6 .

[0066] Table 1 below is the crack length quantitatively back calculated from the COD-P curve mechanical compliance in each cycle Results.

[0067] Table 1 crack length quantitatively determined based on the COD-P curve mechanical compliance

[0068]

[0069] Secondly, the formula for quantitatively back calculating the unconstrained crack length based on the LPD-P curve (see Figure 7 ) mechanical compliance and LEFM theory is:

[0070]

[0071] where E is the equivalent elastic modulus; W and H are the specimen thickness and height; η1, η2 and η3 are fitting functions with respect to the span S and thickness W, i.e. η1 = 0.98 + 3.77 S / W, η2 = -(9.1 + 2.9 S 2 / W 2 ) / (1 + 0.168 S / W) and η3 = -3.2 S / W + 9.8 S 2 / W 2 In specific embodiments of the application, η1 = 11.16, η2 = -20.82 and η3 = 56.35; C c is the additional compliance due to the crack growth, given by equation (3):

[0072]

[0073] where G is the shear modulus; κ is the shape factor, taken as 1.2; I is the moment of inertia, I = WH 3 / 12; C LPD is the LPD-P curve unloading mechanical compliance, i.e. the inverse of the slope of the straight line fitted to the LPD-P data from the unloading point to the reloading point in each cycle LPD As shown in Figure 8as shown.

[0074] Table 2 below is the crack length quantitatively calculated by the mechanical flexibility of the LPD-P curve in each cycle Results.

[0075] Table 2 is the crack length quantitatively determined based on the mechanical flexibility of the LPD-P curve

[0076]

[0077] Then, the specific method for determining the equivalent crack tip position and length based on the spatial distribution histogram of the fracture dissipation energy is: through the collected acoustic emission waveform data, the spatial position (x s ,y s ,z s ) of the fracture source is iteratively solved by using the acoustic emission positioning simplex algorithm, and the fracture dissipation energy value E c is characterized by the root mean square value of the acoustic emission waveform considering the geometric attenuation effect, that is, formula (4); combined with the acoustic emission positioning and energy calculation results, the dissipation energy value E c is accumulated along the fracture propagation direction with a resolution interval of 0.1 mm, and a dissipation energy distribution histogram along the fracture propagation direction is drawn, a dissipation energy threshold E m = 1 V 2 × mm 2 is set to determine the intersection point thereof, and the most front intersection position is the equivalent crack tip, and the length from the tip position to the bottom of the sample is the equivalent crack length The tip position of the equivalent crack propagation in each cycle in the embodiment is shown in Figure 9 .

[0078]

[0079] Wherein: N is the number of acoustic emission sensors participating in positioning; R i is the distance between the fracture source (x s ,y s ,z s ) and the i-th sensor (x i ,y i ,z i ); RMS i is the root mean square value of the effective signal in the waveform received by the i-th sensor;

[0080] Finally, the specific method for determining the equivalent crack tip position and length based on the displacement gradient cloud map is: the horizontal displacement gradient G h (x,y) at any position is calculated by formula (5) combined with the speckle horizontal displacement d h(x, y), according to the calculated G h (x, y) data plot horizontal displacement gradient cloud, set gradient threshold G m = 1.25 x 10 -3 , G h < G m The region is set to white, and the region of G h ≥ G m is set to black, and the resulting black area is the equivalent crack, and the tip of the black area is the equivalent crack tip position (see Figure 10 ), and the length from the tip position to the bottom of the sample is the equivalent crack length The tip position of the equivalent crack propagation in each cycle in the example is shown in Figure 11 .

[0081]

[0082] Where, G h (x i ,y i ) is the spatial variation slope of the horizontal displacement at the position (x i ,y i ) along the horizontal direction, which represents the degree of displacement discontinuity; d h (x i ,y i ) is the horizontal displacement at the position (x i ,y i ), given by the DIC system.

[0083] f. Comprehensive use of mechanical compliance-displacement gradient-energy dissipation distribution multi-physical quantity to determine the nonlinear fracture propagation parameters of coal and rock. The stress-free crack length l0 is the average value of and , that is The equivalent crack length l e is the average value of and , that is The nonlinear fracture process zone (FPZ) length l p is the difference between the equivalent crack length l e and the stress-free crack length l0, that is l p = l e -l0.

[0084] Table 3 is the result of determining the nonlinear fracture crack length of coal and rock by mechanical compliance-displacement gradient-energy dissipation distribution multi-physical quantity in each cycle.

[0085] Table 3 is the result of determining the nonlinear fracture crack length of coal and rock by mechanical compliance-displacement gradient-energy dissipation distribution multi-physical quantity in each cycle.

[0086]

[0087] As can be seen from Table 3, in the 10 cycles of loading and unloading in the embodiment, the stress-free constraint crack lengths quantitatively calculated based on the COD-P and LPD-P mechanical flexibility are close to each other, and the difference is within 0.2 mm, indicating that the mechanical experiment step in the method of the application is reliable and normative, and the credibility of quantitatively calculating the stress-free constraint crack length of coal rock fracture expansion is high; the equivalent crack lengths quantitatively determined by the energy consumption distribution and displacement gradient are also close to each other, and the difference is less than 0.4 mm, indicating that the selected acoustic emission energy consumption distribution and DIC displacement gradient index parameters in the method of the application are reasonable, and the result of quantitatively measuring the equivalent crack length of coal rock fracture expansion is reliable; the average value of the difference between the equivalent crack length and the stress-free constraint crack length in each cycle is 5.1 mm, and the size of the nonlinear fracture process zone l p in the range of [4.7 mm, 5.4 mm] fluctuates stably, so it can be considered that the size of the fracture process zone is an inherent property of the coal rock material. Under the size of the embodiment, the size of the fracture process zone is relatively large and cannot be ignored, and the combination of theory and experiment (i.e., the mismatch between the LEFM flexibility theory calculation and the acoustic emission / DIC measurement of the crack length) also fully verifies that the linear elastic fracture mechanics model cannot be applied to the description of the crack propagation process of the quasi-brittle material of coal rock, so it is necessary to establish a nonlinear fracture criterion considering the influence of the fracture process zone.

[0088] Combined with the broken dissipated energy space distribution histogram ( Figure 9 ) and the displacement gradient cloud chart ( Figure 11 ), the coal rock fracture expansion path can be directly and intuitively displayed, and it can be seen that in the embodiment, the crack propagation path is not straight, but presents a nonlinear extension of zigzag upward.

[0089] The above is only a specific embodiment of the application, but the protection scope of the application is not limited thereto, and any modification, equivalent replacement and improvement made by any person skilled in the art within the technical range disclosed by the application and within the spirit and principles of the application shall be covered within the protection scope of the application.

Claims

1. A quantitative method for determining the propagation length of nonlinear fractures in coal and rock based on multiple parameters, characterized in that, Includes the following steps: a. Prepare test specimens for coal and rock fracture experiments with notches; the specimens are long... L ×Thick W ×High H A cuboid, the span of the sample is S A through notch is cut at the center of the bottom of the sample, the height of which is... H 0; b. Spray random black and white speckle patterns on the front surface of the specimen prepared in step a to form a DIC image observation area for fracture propagation; arrange an acoustic emission sensor array at a reasonable position on the specimen surface to monitor and locate the fracture propagation location; install a clamp-type extensometer at the notch at the bottom of the specimen to measure the crack opening displacement signal; install a linear transformer displacement sensor at the center of the top of the rear surface of the specimen to measure the displacement of the force point. c. Conduct a quasi-static stability propagation test of three-point bending fracture of coal and rock, wherein the stress path in the test is set as a cyclic path of multiple unloading-reloading after peak load; d. Synchronously acquire and record the applied load P, crack opening displacement COD, force point displacement LPD, acoustic emission waveform and DIC image data during the coal and rock fracture propagation process; e. Plot the COD-P and LPD-P mechanical curves from the data collected in step d, and calculate the mechanical compliance respectively. C COD and C LPD The length of the unstressed crack was calculated based on the linear elastic fracture mechanics theory. and ; The fracture source was spatially located using acoustic emission waveform data, and its dissipated energy was calculated. A histogram of the spatial distribution of fracture dissipated energy was plotted, thereby determining the location and length of the equivalent crack tip. The horizontal displacement gradient is calculated based on the DIC displacement field data. A gradient threshold is set, and a displacement gradient contour map is plotted to determine the location and length of the equivalent crack tip. ; f. Quantitatively determine the unconstrained crack length of nonlinear fracture propagation in coal and rock by comprehensively employing multiple physical quantities, including mechanical flexibility, displacement gradient, and energy distribution. l 0. Equivalent crack length l e Length of the fracture process zone l p It shows the dynamic changes of coal and rock fractures and intuitively demonstrates their propagation paths.

2. The method for quantitatively determining the propagation length of nonlinear fractures in coal and rock based on multiple parameters according to claim 1, characterized in that: In step b, a thin layer of white paint is evenly applied as a background color within the DIC observation area. After it has fully solidified, black spots are sprayed on to form a randomly distributed black and white speckle pattern. The acoustic emission sensors are fixed on the front and rear surfaces of the sample, the number of acoustic emission sensors is ≥4, and the sensor array formed should cover the fracture propagation area and be located outside the DIC observation area; The clamp-type extensometer is installed as follows: two quadrangular prism metal clips with right-angled trapezoidal cross sections are respectively pasted on both sides of the bottom notch of the sample, with the distance between the tips of the metal clips being consistent with the width of the notch. The cantilever grooves on both sides of the clamp-type extensometer are installed on the tips of the metal clips to ensure that the measurement data of the clamp-type extensometer is the notch opening displacement. The linear pressure displacement sensor is installed as follows: a right-angle steel sheet is fixed at the center of the rear surface of the sample, and the linear pressure displacement sensor is clamped by a support frame. The height and position of the linear pressure displacement sensor are adjusted so that it is in slight contact with the lower surface of the right-angle steel sheet, ensuring that the data measured by the linear pressure displacement sensor is the displacement of the force point.

3. The method for quantitatively determining the propagation length of nonlinear fractures in coal and rock based on multiple parameters according to claim 1, characterized in that: In step c, the stress cycle path in the quasi-static stability propagation experiment of coal and rock fracture is specifically set as follows: the crack opening displacement signal is used as the feedback control signal of the press system. After loading to the peak load for a period of time, unloading begins. The unloading point is 97%-93% of the peak load level of this cycle. Unloading continues until the reloading point is reached. The reloading point load is 0.5kN to ensure that the press is always in contact with the sample and subjected to force. That is, "loading → peak load → unloading point after peak load → unloading → reloading point → loading" is a complete cycle of loading and unloading. The above cycle process is repeated multiple times until the test ends.

4. The method for quantitatively determining the propagation length of nonlinear fractures in coal and rock based on multiple parameters according to claim 1, characterized in that: In step e, the unconstrained crack length is quantitatively calculated using COD-P mechanical compliance and LEFM theory. The formula is: （1） Where γ1, γ2, γ3, and γ4 are fitting functions for the span S and thickness W, i.e., γ1 = 0.25S / W - 0.0505(S / W). 3 / 2 +0.0033 (S / W) 2 γ2 = 1.155S / W + 0.215(S / W) 3 / 2 -0.0278 (S / W) 2 , γ3=-1.38+1.75S / W and γ4=0.506-1.057S / W+0.888(S / W) 2 ; C COD This refers to the unloading mechanical compliance of the COD-P curve, which is calculated by fitting a straight line to the COD-P data from the unloading point to the reloading point in each cycle. The reciprocal of the slope of the fitted line is... C COD .

5. The method for quantitatively determining the propagation length of nonlinear fractures in coal and rock based on multiple parameters according to claim 1, characterized in that: In step e, the unconstrained crack length is quantitatively calculated using LPD-P mechanical compliance and LEFM theory. The formula is: （2） Where: E is the equivalent elastic modulus; W and H are the sample thickness and height; η1, η2, and η3 are fitting functions of the span S and thickness W, i.e., η1 = 0.98 + 3.77S / W, η2 = -(9.1 + 2.9S / W), η3 = -(9.1 + 2.9S / W), η4 = -(9.1 + 2.9S / W), η5 = -(9.1 + 2.9S / W), η6 = -(9.1 + 2.9S / W), η7 = -(9.1 + 2.9S / W), η8 = -(9.1 + 2.9S / W), η9 = -(9.1 + 2.9S / W), η2 = -(9.1 + 2.9S / W), η3 = -(9.1 + 2.9S / W), η4 = -(9 2 / W 2 ) / (1+0.168S / W) and η3=-3.2S / W+9.8S 2 / W 2 ; C c The additional compliance is generated by fracture propagation, given by formula (3): （3） Where: G is the shear modulus; κ is the shape factor; I is the moment of inertia, I=WH 3 / 12; C LPD The unloading mechanical compliance of the LPD-P curve is determined by fitting a straight line to the LPD-P data from the unloading point to the reloading point in each cycle. The reciprocal of the slope of the fitted line is... C LPD .

6. The method for quantitatively determining the propagation length of nonlinear fractures in coal and rock based on multiple parameters according to claim 1, characterized in that: In step e, the spatial location of the rupture source (x) s ,y s ,z s The acoustic emission localization was solved iteratively using the simplex algorithm, and the fracture dissipation energy value was obtained. E c Characterized by the root mean square value of the acoustic emission waveform considering geometric attenuation effect, i.e. （4） in: N The number of acoustic emission sensors involved in the positioning process; R i For the fracture source (x) s ,y s ,z s ) and the i-th sensor (x) i ,y i ,z i Distance between ( ); RMS i The i-th sensor receives the root mean square value of the valid signal in the waveform; In step e, the location and length of the equivalent crack tip are determined based on the spatial distribution histogram of fracture dissipation energy. The specific method is as follows: combining acoustic emission localization and energy calculation results, the dissipated energy value is calculated along the fracture propagation direction with a resolution interval of 0.1 mm. E c Accumulate the energy and plot a histogram of dissipated energy distribution along the fracture propagation direction, then set a dissipated energy threshold. E m The intersection point between the crack tip and the dissipated energy distribution histogram is determined. The most prominent intersection point is the equivalent crack tip, and the length from the crack tip to the bottom of the sample is the equivalent crack length. .

7. The method for quantitatively determining the propagation length of nonlinear fractures in coal and rock based on multiple parameters according to claim 1, characterized in that: In step e, the formula for calculating the horizontal displacement gradient is: （5） in, G h ( x i , y i ) is in ( x i , y i The slope of the horizontal displacement at a given location along the horizontal direction represents the degree of displacement discontinuity. d h ( x i , y i )for( x i , y i The horizontal displacement at the location is given by the DIC system; In step e, the position and length of the equivalent crack tip are determined based on the displacement gradient contour map. The specific method is as follows: by G h ( x , y ) Plot the horizontal displacement gradient cloud map based on the set gradient threshold. G m ,Will G h < G m Set the area to white, and G h ≥ G m The area is set to black, and the resulting black area represents the equivalent crack. The tip of the black area is the equivalent crack tip position, and the length from the tip position to the bottom of the sample is the equivalent crack length. .

8. The method for quantitatively determining the propagation length of nonlinear fractures in coal and rock based on multiple parameters according to claim 1, characterized in that: In step f, the length of the unstressed crack l 0 is and The average value, equivalent crack length l e for and The average value, length of the fracture process zone l p Equivalent crack length l e and unstress-constrained crack length l The difference of 0; Based on the loading and unloading in each cycle l 0、 l e and l p The value is used to quantitatively determine the dynamic variation law of the nonlinear fracture length of coal and rock, and to intuitively visualize the fracture propagation path of coal and rock by combining the spatial distribution histogram of fracture dissipation energy and displacement gradient cloud map.

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