Evaluation method for brittle failure index of surrounding rock based on true triaxial complete stress-strain curve

Abstract

The present invention discloses a method for evaluating the brittle failure index of surrounding rock based on the true triaxial full stress-strain curve, belonging to the technical field of evaluating the mechanical properties of rocks. It includes: S1, fabricating rock samples with a cuboid shape; S2, installing the fabricated rock samples into a true triaxial testing machine, installing displacement sensors between the surface of the rock samples and the testing machine, and installing acoustic emission probes between the bottom of the rock samples and the testing machine; S3, plotting the full stress-strain curve according to the displacement changes in the directions of the three-dimensional stresses, and obtaining the brittle indexes, ; S4, acquiring acoustic emission signal data, calculating and obtaining the shear / tensile crack propagation and evolution characteristic curve, and calculating the brittle index through this characteristic curve; S5, obtaining the brittle index by using the method of multiplicative weight synthesis for the brittle indexes, and ; The method for evaluating the brittle failure index of surrounding rock based on the true triaxial full stress-strain curve provided by the present invention has a more reliable brittle index structure.

Description

Technical Field

[0001] The present invention relates to the technical field of evaluation of rock mechanical properties, and particularly to an evaluation method for brittle failure index of surrounding rock based on true triaxial complete stress-strain curve. Background Art

[0002] When excavating underground chambers in high in-situ stress hard rock areas, rock bursts, spalling and other damages may occur. Rock burst is a phenomenon in which the rock suddenly ruptures due to stress concentration in the rock mass, releasing a large amount of energy, resulting in the rock flying out or collapsing, usually accompanied by strong sounds and vibrations, with relatively large destructive power, posing a serious threat to construction workers and construction equipment. Spalling usually manifests as the gradual peeling or small piece collapse of the rock surface layer, with a relatively small scale, but if not dealt with in time, it may develop into a more serious geological disaster. Rock brittleness evaluation is an important part of studying the failure behavior of rocks under stress, and is one of the research and investigation tasks required before chamber excavation in medium and high in-situ stress areas. Brittleness evaluation is of great significance for predicting the failure mode of rocks to formulate reasonable support design and construction plans.

[0003] Previous studies mostly evaluated the brittleness of surrounding rock under uniaxial conditions ( ), or under pseudo-triaxial conditions ( ). Existing patents can be referred to, such as the patent application No. CN201710137576.6, titled "A method for obtaining rock brittleness index and a method for evaluating rock brittleness", which is a rock brittleness evaluation method established under pseudo-triaxial conditions through the changes of deformation and strength parameters before and after failure; or the patent application No. 201911399355.1, titled "Shale brittleness index evaluation method based on energy evolution", which is also a rock brittleness evaluation method established based on energy evolution under uniaxial conditions or pseudo-triaxial conditions. However, during the excavation of underground chambers, the stress actually received by the rock is true triaxial ( ). Evaluating the brittleness of surrounding rock under uniaxial conditions ( ), or under pseudo-triaxial conditions ( ) may reduce the reliability of the obtained results, bringing unnecessary risks to construction and design. Therefore, it is necessary to establish an evaluation method for rock brittle failure index under true triaxial stress by using the stress, strain and acoustic emission signal data obtained from true triaxial tests. Summary of the Invention

[0004] The purpose of the present invention is to provide an evaluation method for brittle failure index of surrounding rock based on true triaxial complete stress-strain curve to solve the problems in the above background art.

[0005] To achieve the above purpose, the present invention provides an evaluation method for brittle failure index of surrounding rock based on true triaxial complete stress-strain curve, including the following steps:

[0006] S1. Make a rock sample in the shape of a cuboid;

[0007] S2. Install the made rock sample into a true triaxial testing machine so that the three - dimensional stresses are vertically loaded on the six surfaces of the rock sample respectively. Install displacement sensors between the rock sample surface and the testing machine to monitor the displacement changes of the rock sample in the directions of the three - dimensional stresses; install acoustic emission probes between the bottom of the rock sample and the testing machine to monitor the acoustic emission signals of the rock sample when strain occurs;

[0008] S3. Obtain the strains of the rock sample in the directions of the three - dimensional stresses according to the displacement changes in the directions of the three - dimensional stresses 、 、 , and draw the complete stress - strain curve; based on the complete stress - strain curve, obtain the brittleness index 、 、 ;

[0009] S4. Obtain the acoustic emission signal data, calculate and obtain the shear / tensile crack propagation and evolution characteristic curve based on the acoustic emission signal data, and calculate the brittleness index considering crack evolution through this characteristic curve ;

[0010] S5. For the brittleness index 、 、 and adopt the method of multiplicative weight synthesis to obtain the brittleness index considering the true triaxial complete stress - strain curve and acoustic emission signals 。

[0011] Preferably, the three - dimensional stresses in step S2 include the maximum principal stress applied in the vertical direction , the intermediate principal stresses applied in two mutually orthogonal directions on the horizontal plane and the minimum principal stress 。

[0012] Preferably, step S3 specifically includes:

[0013] Obtain the strains of the rock sample in the three principal stress directions according to the displacement changes in the three principal stress directions 、 、 , and draw the complete stress - strain curve of the maximum principal stress and the strains in the three principal stress directions, calculate the crack volume strain at the same time, and draw the curve of crack volume strain - axial strain, find out the strain value corresponding to the minimum crack volume strain in the curve of crack volume strain - axial strain as the initiation strain, at the maximum principal stress and strain The maximum principal stress value corresponding to the crack initiation strain is found in the complete stress-strain curve as the crack initiation stress. The stress value when the maximum principal stress is the peak value is found in the three complete stress-strain curves as the peak stress. After finding the peak stress, the maximum principal stress and the strain The maximum principal stress value corresponding to the smooth section where the maximum principal stress value in the complete stress-strain curve drops is the residual stress. According to the peak stress The three complete stress-strain curves are divided into the pre-peak crack propagation section and the post-peak stress drop section, and the maximum principal stress and each strain The areas enclosed by them are the pre-peak and the post-peak Through the ratio of the post-peak to the pre-peak The brittleness indices in the three strain directions are obtained. , , , , which is .

[0014] Preferably, the crack volume strain is calculated , specifically:

[0015] First, calculate the volume strain of the rock sample at a certain moment under the loading of the three principal stresses :

[0016] ;

[0017] Calculate the elastic volume strain through Hooke's law :

[0018] ;

[0019] Among them, and respectively represent the elastic modulus and Poisson's ratio, and both are obtained through the elastic section of the complete stress-strain curve; the crack volume strain is:

[0020] .

[0021] Preferably, step S4 specifically includes:

[0022] S41. Calculate the rising angle of the acoustic emission signal by the ratio of the rising time to the maximum amplitude of the original signal monitoring data recorded by the acoustic emission probe :

[0023] ;

[0024] wherein, is the rise time; is the maximum amplitude;

[0025] S42. Calculate the average frequency of the acoustic emission signal by the ratio of the ring count to the duration of the original signal monitoring data recorded by the acoustic emission probe :

[0026] ;

[0027] wherein, is the ring count; is the duration;

[0028] S43. After calculating and obtaining the rise angle and the average frequency , obtain the ratio of each signal monitoring data :

[0029] ;

[0030] When , classify the acoustic emission signal as a tensile fracture signal; when , classify the acoustic emission signal as a shear fracture signal; and draw a graph of the tensile and shear fracture signals changing with time, and simultaneously determine the time when the rock sample reaches the initial fracture stress and the peak stress, and calculate the brittleness index:

[0031] ;

[0032] In the formula, is the tensile fracture signal count corresponding to the initial fracture stress; is the tensile fracture signal count corresponding to the peak stress; is the tensile fracture signal count corresponding to the residual stress; is the shear fracture signal count corresponding to the initial fracture stress; is the shear fracture signal count corresponding to the peak stress; is the shear fracture signal count corresponding to the residual stress; , are the weight coefficients of the tensile and shear fracture signals respectively, both set to 0.5.

[0033] Preferably, the brittleness index in step S5 is:

[0034] + + + ;

[0035] Among them, 、 、 respectively represent the weight coefficients of the brittleness index 、 、 、 ; and = = =0.8; =0.2; and , , .

[0036] Therefore, the present invention adopts the above-mentioned method for evaluating the brittleness failure index of surrounding rock based on the true triaxial full stress-strain curve, and has the following beneficial effects:

[0037] (1) It considers the brittleness index obtained from the true triaxial full stress-strain curve of the rock;

[0038] (2) By combining the acoustic emission signal parameters, a brittleness index considering the evolution of fracture signals is obtained;

[0039] (3) The brittleness index obtained in the above way is more reliable than evaluating the brittleness of surrounding rock under uniaxial conditions or pseudo-triaxial conditions, making the construction and design more in line with the real environment and safer.

[0040] The technical solution of the present invention will be further described in detail below with reference to the drawings and embodiments. Description of the Drawings

[0041] Figure 1 is the flow chart of the method for evaluating the brittleness failure index of surrounding rock based on the true triaxial full stress-strain curve of the present invention;

[0042] Figure 2 is the schematic diagram of the true triaxial full stress-strain curve and the crack volume-axial strain curve of the embodiment of the method for evaluating the brittleness failure index of surrounding rock based on the true triaxial full stress-strain curve of the present invention;

[0043] Figure 3 is the schematic diagram of the variation curve of the maximum principal stress with the test time and the variation curve of the shear fracture signal with the time in the embodiment of the present invention;

[0044] Figure 4 is the schematic diagram of the variation curve of the maximum principal stress with the test time and the variation curve of the tensile fracture signal with the time in the embodiment of the present invention;

[0045] Figure 5The position and direction distribution diagram of the three orthogonal principal stress directions outside the rock sample in the embodiment of the present invention;

[0046] Figure 6 The brittle index diagram of altered rock under different intermediate principal stresses in the embodiment of the present invention. Specific embodiments

[0047] The following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the claimed invention, but merely represents selected embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts fall within the scope of protection of the present invention.

[0048] As Figure 1 shown, a method for evaluating the brittle failure index of surrounding rock based on the true triaxial full stress-strain curve. In this embodiment, altered rock granite is used as the implementation object, and the stress-strain and acoustic emission data obtained through true triaxial tests by applying, respectively, an intermediate principal stress of 20 MPa, a minimum principal stress of 10 MPa, and a maximum principal stress in three orthogonal directions to the rock sample are used to evaluate the brittleness of the rock properties, including the following steps:

[0049] Step 1: Fabricate a granite cuboid rock sample with a length and width of 50 mm and a height of 100 mm according to the test standard;

[0050] Step 2: Install the fabricated rock sample into a true triaxial testing machine, and at the same time install displacement sensors in three orthogonal principal stress directions, and install an acoustic emission probe at the bottom of the rock sample to monitor acoustic emission signals. The true triaxial testing machine applies, respectively, a set intermediate principal stress of 20 MPa and a minimum principal stress of 10 MPa to the rock sample in two orthogonal directions (also called circumferential directions) on the horizontal plane, and the true triaxial testing machine also applies the maximum principal stress to the rock sample in the vertical direction (also called axial direction) perpendicular to the horizontal plane until the rock sample is compressed to failure, while simultaneously monitoring the changes in displacement and stress in three orthogonal principal stress directions in real time, and monitoring the changes in acoustic emission signals. The position and direction distribution of the three orthogonal principal stress directions outside the rock sample is as Figure 5 shown.

[0051] Step 3: After the test, based on the obtained displacements and stresses, plot the full stress-strain curve of the true triaxial test, and based on the obtained full stress-strain curve, obtain the brittle indices , , .

[0052] The calculation method is as follows:

[0053] First, the maximum principal stress Plotted with the strain curves in the three principal stress directions, as Figure 2 The right black line in a of [figure number] is the maximum principal stress and the strain in the direction of the maximum principal stress axial strain variation curve, as Figure 2 The thick black solid line with circular pattern in [figure number] is the maximum principal stress and the strain in the direction of the minimum principal stress circumferential strain variation curve, as Figure 2 The thick black solid line with triangular pattern in [figure number] is the maximum principal stress and the strain in the direction of the intermediate principal stress circumferential strain variation curve. When not compressed, the rock fractures are open, and the axial strain and the circumferential strains in two horizontal orthogonal directions 、 are 0. After the rock sample is subjected to triaxial stress, it begins to be compressed. Axially, as the maximum principal stress increases, the axial compression causes the axial strain to increase; in the two horizontal orthogonal directions, as the maximum principal stress increases, new cracks are generated, causing circumferential expansion, as shown on the left side in Figure 2 the strain 、 decreases.

[0054] Then, by calculating the crack volume strain, a curve of crack volume strain - axial strain is plotted. At a certain moment during true triaxial stress loading, the volume strain of the rock sample is:

[0055] ;

[0056] wherein, are the strains in the three principal stress directions respectively.

[0057] The elastic modulus and Poisson's ratio can be obtained from the elastic section of the uniaxial compression stress - strain curve

[0058] ;

[0059] ;

[0060] where 、 、 、 are the compression stress in the elastic stage of the rock during uniaxial compression and its corresponding strain respectively, 、 are the lateral strain and axial strain of uniaxial compression respectively.

[0061] For the volumetric strain of rock samples, it can be divided into elastic volumetric strain and plastic volumetric strain due to the opening or expansion of primary cracks. For the elastic volumetric strain, it can be obtained through Hooke's law:

[0062] ;

[0063] In the formula, is the elastic volumetric strain, is the volumetric strain of the rock sample; is the maximum principal stress, which is the value at a certain moment during loading; is the intermediate principal stress, which is a fixed value of 20 MPa; is the minimum principal stress, which is a fixed value of 10 MPa.

[0064] Thus, the volumetric strain of the test crack can be obtained as , and the volumetric strain of the crack obtained by calculation, as Figure 2 shown by the black solid line in, draw the crack volumetric strain - axial strain curve. When the rock is not compressed, the cracks are open. After being subjected to triaxial stresses, it starts to be compressed, and the closure of the cracks leads to an increase in axial strain while the crack volumetric strain decreases. Therefore, Figure 2 the right curve in reaches the highest point (the point with the minimum crack volumetric strain). Continuing to compress will generate new crack failures and openings, resulting in axial compression while the circumferential direction expands outward. The circumferential expansion amount is greater than the axial compression amount. Therefore, the crack volumetric strain - axial strain curve gradually decreases from the highest point, and the crack volumetric strain increases. The axial strain corresponding to the boundary where the curve changes from compression to expansion (i.e., the highest point of the crack volumetric strain - axial strain curve) in the crack volumetric strain - axial strain curve is the crack initiation axial strain.

[0065] Taking the axial strain variation curve as an example, find the axial stress corresponding to the crack initiation axial strain in the axial strain variation curve as the crack initiation stress is 174.156 MPa. Then, find the axial stress corresponding to the highest point in the axial strain variation curve as the peak stress of the rock sample: 380.732 MPa. Then, find the axial stress corresponding to the smooth section where the axial strain variation curve drops after the peak stress in the axial strain variation curve, which is the residual stress of the curve: 155.08 MPa.

[0066] And in the circumferential strain variation curve, the crack initiation stress Similar to the axial strain variation curve, the peak stress is the axial stress corresponding to the highest point of the circumferential strain variation curve, and the residual stress is the axial stress corresponding to the smooth section where the circumferential strain variation curve drops after the peak stress; in the circumferential strain variation curve, the peak stress is the axial stress corresponding to the highest point of the circumferential strain variation curve, and the residual stress is the axial stress corresponding to the smooth section where the circumferential strain variation curve drops after the peak stress.

[0067] Then, based on the peak stress, the axial strain variation curve, the circumferential strain variation curve, and the circumferential strain variation curve can be divided into the pre-peak crack propagation section and the post-peak stress steep drop section, which can be calculated by the following formula Stress in the post-peak stress steep drop section and strain The enclosed area, Stress in the pre-peak crack propagation section and strain The enclosed area, :

[0068] ;

[0069] ;

[0070] Then, the brittleness index determined by the maximum principal stress, the intermediate principal stress, and the minimum principal stress is:

[0071] ;

[0072] Step 4: Based on the acquired acoustic emission signal data, calculate the shear / tensile crack propagation evolution characteristic curve, and calculate the brittleness index considering crack evolution through this curve :

[0073] The calculation method of the acoustic emission signal data processing in Step 4 is as follows:

[0074] Calculate the rise angle of the acoustic emission signal by the ratio of the rise time to the maximum amplitude :

[0075] ;

[0076] Among them, is the rise time; is the maximum amplitude, both of which can be directly monitored from the original signal recorded by the acoustic emission probe.

[0077] Then, calculate the average frequency of the acoustic emission signal by the ratio of the ring count ( ) and the duration ( ) :

[0078] ;

[0079] Among them, the ring count ( ) and the duration ( ) can directly monitor the data of the original signal recorded by the acoustic emission probe. The ring count is the number of oscillations in the acoustic emission signal waveform that exceed a preset threshold. That is, the number of times the amplitude exceeds the preset threshold (also known as the acoustic emission threshold).

[0080] After calculating and obtaining the rise angle and the average frequency , the ratio :

[0081] ;

[0082] In the prior art, the value of the acoustic emission signal of granite can be used to distinguish between fracture and tensile signals. When , the acoustic emission signal is classified as a tensile fracture signal; when , the acoustic emission signal is classified as a shear fracture signal; The

[0083] ;

[0084] ;

[0085] Through the above discrimination, the monitored acoustic emission signals can be divided into shear fracture signals and tensile fracture signals. Further, the cumulative amounts of shear and tensile fracture signals over time are obtained, and the changes in the cumulative amounts of shear and tensile fracture signals over time are plotted, as shown in Figure 3 and Figure 4 respectively. At the same time, the variation of the maximum principal stress over time is plotted in Figure 3 and Figure 4 , and then the tensile fracture signal count and shear fracture signal count corresponding to the moments when the maximum principal stress reaches the crack initiation stress, peak stress, and residual stress are determined.

[0086] Specifically, is the tensile fracture signal count corresponding to the crack initiation stress; is the tensile fracture signal count corresponding to the peak stress; is the tensile fracture signal count corresponding to the residual stress; is the shear fracture signal count corresponding to the crack initiation stress; is the shear fracture signal count corresponding to the peak stress; is the shear fracture signal count corresponding to the residual stress. From Figure 3 andFigure 4 It can be seen that:

[0087] Therefore, the brittleness index calculated according to the acoustic emission parameters is as follows:

[0088] ;

[0089] In the above formula, the evolution characteristics of the shear and tensile fracture signals are different and need to be explained separately. However, both are equally important and have equal weights. Therefore, , are both 0.5.

[0090] Step 5: For the brittleness indices , , and , use the method of multiplicative weight synthesis to obtain the brittleness index considering the true triaxial full stress-strain curve and acoustic emission signal.

[0091] In summary, the evaluation of the brittleness index considering the true triaxial full stress-strain curve and acoustic emission signal is as follows:

[0092] ;

[0093] Among them, , are respectively considered as 80% of the ratio of each principal stress to the principal stress invariant, and considers the proportion weight of 20%.

[0094] , , ;

[0095] Figure 6 is the evaluation result diagram of the brittleness index of the altered rock. Under four different intermediate principal stresses, while keeping the same minimum principal stress, the true triaxial full stress-strain curve and acoustic emission signal data are obtained. According to the above brittleness evaluation method, the brittleness index B is obtained. It can be seen from the figure that as the intermediate principal stress increases, the brittleness of granite increases, which is consistent with the research results of the brittleness of rocks in the true triaxial environment in most current existing technologies.

[0096] Therefore, the brittleness index obtained by using the above method for evaluating the brittle failure index of surrounding rock based on the true triaxial full stress-strain curve in the present invention is more reliable in structure.

[0097] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions of the present invention or make equivalent replacements, and these modifications or equivalent replacements cannot make the modified technical solutions deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for evaluating surrounding rock brittle failure index based on true triaxial full stress-strain curve, characterized in that: The following steps are involved: S1. Prepare a rock sample in the shape of a cuboid; S2. Install the prepared rock sample into a true triaxial testing machine so that the three-axis stress is vertically loaded on the six surfaces of the rock sample respectively. Install a displacement sensor between the surface of the rock sample and the testing machine to monitor the displacement change of the rock sample in the three-axis stress direction; install an acoustic emission probe between the bottom of the rock sample and the testing machine to monitor the acoustic emission signal of the rock sample when strain occurs; S3. According to the displacement changes in the three stress directions, the strain of the rock sample in the three stress directions is obtained. , , , and draw the total stress-strain curve; based on the total stress-strain curve, obtain the brittleness index , , ; S4. Acquire acoustic emission signal data and calculate the shear / tensile crack extension evolution characteristic curve, and calculate the brittleness index through the characteristic curve ; S5, Brittleness Index , , and The fragility index is obtained by using the multiplication weight synthesis method. .

2. The surrounding rock brittle failure index evaluation method based on true triaxial full stress-strain curve according to claim 1 is characterized by: The three-dimensional stress in step S2 includes the maximum principal stress applied in the vertical direction , the intermediate principal stresses applied in two mutually orthogonal directions on the horizontal plane and minimum principal stress .

3. The surrounding rock brittle failure index evaluation method based on true triaxial full stress-strain curve according to claim 2 is characterized in that: Step S3 specifically includes: According to the displacement changes in the three principal stress directions, the strain of the rock sample in the three principal stress directions is obtained. , , , and plot the maximum principal stress The full stress-strain curve of the strain in the three principal stress directions and the calculation of the crack volume strain , and draw the crack volume strain-axial strain curve, find the strain value corresponding to the minimum crack volume strain in the crack volume strain-axial strain curve as the crack initiation strain, and at the maximum principal stress With strain The maximum principal stress corresponding to the crack initiation strain in the total stress-strain curve is the crack initiation stress. , find the stress value when the maximum principal stress is the peak value in the three full stress-strain curves as the peak stress , find the maximum principal stress after the peak stress With strain The maximum principal stress value in the full stress-strain curve of the residual stress corresponds to the maximum principal stress value of the smooth section where the maximum principal stress value drops to , according to the peak stress The three total stress-strain curves are divided into the pre-peak crack extension section and the post-peak stress steep drop section, and the maximum principal stress in the pre-peak crack extension section and the post-peak stress steep drop section on the three total stress-strain curves is calculated. With each strain The area enclosed by the peak After the peak , after passing the peak With Fengqian The ratio of the three strain directions is obtained. , , , ,for .

4. The surrounding rock brittle failure index evaluation method based on true triaxial full stress-strain curve according to claim 3 is characterized in that: Calculation of crack volume strain , specifically: First, calculate the volume strain of the rock sample at a certain moment when the three principal stresses are applied : ； Calculation of elastic volume strain using Hooke's law : ； in, and Represent the elastic modulus and Poisson's ratio, respectively, and are obtained through the elastic segment of the total stress-strain curve; crack volume strain for: 。 5. The surrounding rock brittle failure index evaluation method based on true triaxial full stress-strain curve according to claim 1 is characterized in that: Step S4 specifically includes: S41. Calculate the rise angle of the acoustic emission signal by the ratio of the rise time and the maximum amplitude of the original signal monitoring data recorded by the acoustic emission probe : ； in, is the rise time; is the maximum value; S42, calculating the average frequency of the acoustic emission signal by the ratio of the ring count and duration of the original signal monitoring data recorded by the acoustic emission probe : ； in, Count the rings; for duration; S43, calculate and obtain the rising angle and the average frequency After that, the ratio of each signal monitoring data is obtained : ； when When , the acoustic emission signal is classified as a tensile fracture signal; when When the AE signal is classified as a shear fracture signal, the tensile and shear fracture signals are plotted over time, and the time when the rock sample reaches the cracking stress and peak stress is determined, and the brittleness index is calculated: ； In the formula, The tensile fracture signal count corresponding to the crack initiation stress is reached; It is the tensile fracture signal count corresponding to the peak stress; The tensile fracture signal counts corresponding to the residual stress; The shear fracture signal count corresponding to the crack initiation stress is reached; is the shear fracture signal count corresponding to the peak stress; The corresponding shear fracture signal counts when the residual stress is reached; , are the weight coefficients of the tensile and shear fracture signals, respectively, and are both set to 0.

5.

6. The surrounding rock brittle failure index evaluation method based on true triaxial full stress-strain curve according to claim 3 is characterized in that: Brittleness index in step S5 for: + + + ； in, , , Represents the brittleness index , , , The weight coefficient of = = =0.8; =0.2; , , .

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