Early warning method for instability catastrophe of softening ore rock

Abstract

The application discloses a kind of early warning methods of easy argillization rock instability mutation, including making rock sample, respectively on rock sample under the condition of uniaxial compression acoustic emission test, and obtain the displacement, load and acoustic emission parameter numerical value of each rock sample;Calculate and analyze the mutation characteristics of the evolution of elastic strain energy curve of easy argillization rock;Construct the early warning model of elastic strain energy strain sequence of easy argillization rock instability mutation, when the simultaneous difference set equation Δ>0 indicates that easy argillization rock is in stable state, Δ<0 when easy argillization rock is in unstable state, Δ=0 when easy argillization rock is in critical state.The method of the application can comprehensively, quickly and accurately predict the instability mutation failure of easy argillization rock, and provide scientific reference basis for early warning prevention and treatment of rock instability mutation of mine exploitation.

Description

Technical Field

[0001] This invention relates to early warning of surrounding rock damage in mining goaf areas, specifically to an early warning method for sudden instability of easily mud-forming ore rocks. Background Technology

[0002] With the increasing scarcity of shallow mineral resources, mining is gradually shifting towards deeper deposits. However, the complex geological conditions faced in deep mining, such as high geothermal activity, high ground pressure, humid environments, and high water content, cause some deep underground rocks to easily become muddy after absorbing water, resulting in deterioration of mechanical properties and sudden softening and destruction. This leads to deformation and damage of the surrounding rock in the goaf, endangering the lives and property of miners. Currently, early warning methods for easily muddy rock instability are mainly divided into three categories: macroscopic damage characteristics, deformation mechanics mechanisms, and numerical simulation analysis. Among these, early warning based on macroscopic damage characteristics mainly focuses on roof subsidence, floor bulging, and severe deformation on both sides of easily muddy rock roadways. This method is applicable to underground roadways at certain depths but not to non-roadway conditions. Early warning based on deformation mechanics mechanisms mainly defines warning points by identifying abrupt changes in the physical and mechanical parameters of rock samples from laboratory tests, such as elastic modulus, stress, strain, Poisson's ratio, and deformation modulus. Its disadvantage is that it exhibits significant individual variability. Numerical simulation analysis is widely used in early warning of rock materials. It mainly simulates and analyzes the stress field, displacement field and plastic zone distribution of rock samples under load to determine their early warning characteristics. However, it is difficult to simulate complex real geological conditions and has a certain degree of one-sidedness.

[0003] Identifying the precursory characteristics of ore and rock failure during mining is crucial for early warning and prevention of sudden instability. Furthermore, the damage evolution, strain changes, and instability of ore and rock are inevitably accompanied by energy changes, which permeate the entire failure process and represent a quantitative manifestation of internal damage. Therefore, analyzing the abrupt failure characteristics of ore and rock solely from an energy perspective is somewhat one-sided. The heterogeneity and discontinuity within ore and rock lead to multi-faceted and random variations in damage and failure, and catastrophe theory is well-suited to describe the abruptness and discontinuity of changes in a material. However, there are currently few reports on early warning methods that combine catastrophe theory with energy analysis for monitoring the abrupt instability and failure of easily mud-forming ore and rock. Summary of the Invention

[0004] To address the shortcomings of the existing technologies, this invention provides a method that, by establishing the coupling relationship between the internal energy and strain of easily mud-forming rocks and the cusp catastrophe model, can comprehensively, rapidly, and accurately predict the instability and sudden destruction of easily mud-forming rocks, providing a scientific reference for early warning and prevention of instability and sudden destruction of easily mud-forming rocks in mining.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] A method for early warning of sudden instability in easily mud-forming ore rocks includes the following steps:

[0007] Step 1: Prepare mineral and rock specimens, including easily mud-forming mineral and rock specimens and non-obvious mud-forming mineral and rock specimens;

[0008] Step 2: Conduct acoustic emission tests under uniaxial compression conditions on the mineral and rock specimens described in Step 1, and obtain the displacement, load, and acoustic emission parameter values ​​for each mineral and rock specimen;

[0009] Step 3: Calculate and analyze the abrupt change characteristics of the evolution of the elastic strain energy curve of easily mud-forming ore rocks;

[0010] Step 4: Construct an early warning model for the instability and sudden change of easily mud-forming ore rocks based on elastic strain energy strain sequence. The specific process is as follows:

[0011] The total work done by external forces on the rock can be obtained by calculating the area enclosed by the stress-strain curve and the strain axis using calculus. The total energy input into the rock's interior includes elastic strain energy and dissipated energy.

[0012] U = U e +U d (1)

[0013] In the formula, U represents the total energy input into the rock by the press, measured in J; U e U represents the elastic strain energy inside the specimen, measured in J. d The cumulative dissipated energy is expressed in J; it is calculated using the following formulas:

[0014] Total Energy:

[0015]

[0016] In the formula: σ i ε is the stress borne by the specimen at time i, in MPa. i Let be the strain generated in the specimen at time i;

[0017] Elastic strain energy:

[0018]

[0019] Cumulative energy dissipation:

[0020] U d =UU e (4)

[0021] In the formula: σ i V represents the stress borne by the specimen at time i, in MPa; V is the volume of the specimen, in mm. 3 E e The elastic modulus of the specimen is expressed in MPa.

[0022] The three functional equations included in the cusp mutation model are as follows:

[0023] The standard potential function equation V(x) is:

[0024] V(x)=x 4 +ux 2 +zx (5)

[0025] In the formula: u and z are control variables, and x is a state variable;

[0026] The equation of the equilibrium surface V′(x) is:

[0027] V′(x)=4x 3 +2ux+z (6)

[0028] The equation V″(x) for the singularity set is:

[0029] V″(x)=12x 2 +2u (7)

[0030] The equilibrium surface equation and the singularity set equation must satisfy the condition that they are equal to 0. Combining equations (6) and (7), we can obtain the divergence set equation as follows:

[0031] Δ=8u 3 +27z 2 (8)

[0032] When Δ>0, it indicates that the easily mud-forming ore rock is in a stable state; when Δ<0, it indicates that the easily mud-forming ore rock is in an unstable state; and when Δ=0, it indicates that the easily mud-forming ore rock is in a critical state.

[0033] Furthermore, step four defines the abrupt change interval, warning point, and warning range, and verifies them using the precursor characteristics of acoustic emission parameters, assuming the elastic strain energy U e The mapping relationship with strain ε is f e (ε), expanded using Taylor's formula and rounded down to the fourth degree, yields:

[0034]

[0035] In the formula: ε0 is the strain value at a specific point, let... Furthermore, when strain ε0 = 0, k0 = 0, so equation (9) can be transformed into:

[0036] f e (ε)=k1ε+k2ε 2 +k3ε 3 +k4ε 4 (10)

[0037] In the formula: k j(j=1,2,3,4) can be approximately calculated using the least squares method. Let To convert equation (10) into the standard potential function form of the cusp catastrophe model, the first step is:

[0038]

[0039] The second step is to discard the constant terms that do not include x, and then set x to... 4 Since the coefficient is 1, we can obtain:

[0040]

[0041] Combining equations (5), (8), and (12), the expression for the divergence equation Δ can be obtained as follows:

[0042]

[0043] Based on the elastic strain energy sequence f of easily mud-forming rocks under uniaxial compression e Substituting (ε) into equation (10) for least squares calculation, we can obtain an approximate analytical expression for the relationship between elastic strain energy and strain:

[0044]

[0045] In the formula: f e d (ε) represents the elastic strain energy sequence of easily argillaceous rocks, f e n (ε) represents the elastic strain energy sequence of the undifferentiated argillaceous rock, which will be obtained by solving... Substituting the values, we obtain the analytical expressions for the divergence equation Δ as follows:

[0046]

[0047] The Δ values ​​corresponding to different strains are obtained according to equation (15). The minimum strain interval where the sign of the Δ value changes is defined as the mutation interval I. The strain point corresponding to the maximum value of Δ is called the warning point. The warning interval II is the strain interval corresponding to the 0.5% Δ interval to the left and right of the maximum value of Δ. The Δ value is further quantified to determine the mutation state of the easily mud-forming ore rock.

[0048] Furthermore, the easily mud-forming rock specimen mentioned in step one is a standard cylindrical rock with a height of 100 mm and a diameter of 50 mm.

[0049] Furthermore, the acoustic emission test in step two adopts a loading strain test with a loading rate of 0.005 mm / s. Loading is stopped when the specimen fails. The acoustic emission sampling threshold is 50 dB, the preamplifier gain is 45 dB, and the sampling rate is 3 MSPS.

[0050] Furthermore, the abrupt change characteristics of the elastic strain energy curve evolution of easily mud-forming rocks described in step three include: the period before the peak of the elastic strain energy curve of easily mud-forming rocks is divided into an initial energy dissipation stage and an elastic strain energy accumulation stage; the energy evolution after the peak of the elastic strain energy curve of easily mud-forming rocks is divided into "step-like" and "cliff-like" stages, which are determined by the number of abrupt change points in the energy curve.

[0051] The beneficial effects of this invention are:

[0052] This invention analyzes the abrupt change characteristics of easily mud-forming rocks by analyzing the total energy, elastic strain energy, and dissipated energy curves. It establishes a coupling relationship between internal energy and strain, and a cusp abrupt change model, combining abrupt changes with energy to monitor the instability and sudden failure of easily mud-forming rocks. This comprehensively simulates complex real geological conditions and rapidly and accurately predicts the instability and sudden failure of easily mud-forming rocks. Based on the magnitude of the divergence set Δ, it defines the abrupt change interval, warning point, and warning range for easily mud-forming rocks under uniaxial compression. The point where the sign of the divergence set Δ value changes is the abrupt change interval of the easily mud-forming rocks; the maximum value of the divergence set Δ value is the warning point; and the interval within 0.5%Δ around the maximum value is the warning range. The Δ value further quantifies the abrupt change state of the easily mud-forming rocks. The rationality and accuracy of the warning model are verified by the precursor characteristics of acoustic emission parameters. The method of this invention can rapidly and accurately predict the instability and sudden failure of easily mud-forming rocks, providing a scientific reference for the early warning and prevention of instability and sudden changes in mining operations. Attached Figure Description

[0053] Figure 1 This is a stress-strain diagram of an easily mud-forming rock specimen according to an embodiment of the present invention;

[0054] Figure 2a This is a stress-energy-strain diagram of easily mud-forming rock specimen a in an embodiment of the present invention;

[0055] Figure 2b This is a stress-energy-strain diagram of easily mud-forming rock specimen b in an embodiment of the present invention;

[0056] Figure 2c This is a stress-energy-strain diagram of easily mud-forming rock specimen c in an embodiment of the present invention;

[0057] Figure 3 This is a schematic diagram of the relationships between the equations in the cusp catastrophe model for easily mud-forming ore rocks according to an embodiment of the present invention;

[0058] Figure 4a This is a schematic diagram illustrating the early warning of instability and sudden change in easily mud-forming ore specimen a according to an embodiment of the present invention;

[0059] Figure 4b This is a schematic diagram illustrating the early warning of instability and sudden change in easily mud-forming ore specimen b according to an embodiment of the present invention;

[0060] Figure 4c This is a schematic diagram illustrating the early warning of instability and sudden change in easily mud-forming ore specimen c according to an embodiment of the present invention;

[0061] Figure 4d This is a schematic diagram illustrating the early warning of instability and sudden change in a non-obliterated ore rock specimen according to an embodiment of the present invention;

[0062] Figure 5a This is a test chart of the acoustic emission ringing count rate of easily mud-forming rock specimen a in an embodiment of the present invention;

[0063] Figure 5b This is a test chart of acoustic emission ringing count rate for non-obliterated argillaceous rock specimens in an embodiment of the present invention;

[0064] Figure 6a This is an acoustic emission energy rate test diagram of easily mud-forming rock specimen a in an embodiment of the present invention;

[0065] Figure 6b This is an acoustic emission energy rate test diagram of a non-obliterated mudstone specimen from an embodiment of the present invention. Detailed Implementation

[0066] A method for early warning of sudden instability in easily mud-forming ore rocks includes the following steps:

[0067] Step 1: Prepare mineral and rock specimens, including easily mud-forming mineral and rock specimens a, b, and c, and non-obvious mud-forming mineral and rock specimens.

[0068] The ore sample used in this embodiment was taken from a thick tantalum-niobium ore deposit in southern Jiangxi Province that is prone to mud formation. Fresh rock samples were taken from a depth of 200m underground. After being cored in January 2014, the ore samples were placed in the natural environment on the surface and allowed to absorb water and weather for 7 years. Standard cylindrical ore specimens with a height of 100mm and a diameter of 50mm were made. Ore specimens with no obvious joints and cracks on the surface were selected from the standard samples for testing.

[0069] Step 2: Conduct acoustic emission tests under uniaxial compression conditions on the mineral and rock specimens described in Step 1, and obtain the displacement, load, and acoustic emission parameter values ​​for each mineral and rock specimen;

[0070] like Figure 1 As shown, the stress peak of the easily mud-forming rock exhibits a significant abrupt change under uniaxial compression. The stress value decreases dramatically even with relatively small strain, leading to the failure of the easily mud-forming rock specimen and loss of its load-bearing capacity.

[0071] Step 3: Calculate and analyze the abrupt change characteristics of the evolution of the elastic strain energy curve of easily mud-forming ore rocks;

[0072] U = U e +U d (1)

[0073] In the formula, U represents the total energy input into the rock by the press, measured in J; U e U represents the elastic strain energy inside the specimen, measured in J. d The cumulative dissipated energy is expressed in J; it is calculated using the following formulas:

[0074] Total Energy:

[0075]

[0076] In the formula: σ i ε is the stress borne by the specimen at time i, in MPa. i Let be the strain generated in the specimen at time i;

[0077] Elastic strain energy:

[0078]

[0079] Cumulative energy dissipation:

[0080] U d =UU e (4)

[0081] In the formula: σ i V represents the stress borne by the specimen at time i, in MPa; V is the volume of the specimen, in mm. 3 E e The elastic modulus of the specimen is expressed in MPa.

[0082] like Figure 2a , Figure 2b , Figure 2c As shown, the elastic strain energy curve before its peak is divided into three stages: the initial energy dissipation stage (Ⅰ), the elastic strain energy accumulation stage (Ⅱ), and the elastic strain energy dissipation stage (Ⅲ). The energy evolution after the peak of the elastic strain energy curve can be divided into two forms: "step-like" and "cliff-like". The elastic strain energy curve of the easily mud-forming rock specimen exhibiting a "step-like" pattern has three energy abrupt change points after the peak, occurring when the average strain increases by 2 × 10⁻⁶. -4 The elastic strain energy decreased by 18.62 J, 57.91 J, and 39.09 J respectively, accounting for 18.34%, 57.05%, and 38.51% of the peak elastic strain energy, indicating that the energy conversion mechanism of the easily mud-forming rock specimen after peak stress is unstable and has abrupt change characteristics; the elastic strain energy of the easily mud-forming rock specimen with a "cliff-like" shape after peak stress decreased by more than 50% in a small strain range, showing obvious abrupt change characteristics.

[0083] Step 4: Construct an early warning model for the instability of easily mud-forming ore rocks based on elastic strain energy strain sequences, define the abrupt change interval, warning point, and warning interval, and verify it using the precursor characteristics of acoustic emission parameters. The specific process is as follows:

[0084] Rock, as a brittle material, is prone to transitioning from a stable to an unstable state under strong external disturbances, leading to unstable abrupt destruction. Catastrophe theory classifies catastrophe models into seven main types based on the type of catastrophe, among which cusp catastrophe, butterfly catastrophe, and swallowtail catastrophe models are the most widely used and have high reliability. Therefore, this embodiment selects the cusp catastrophe model to analyze the unstable catastrophe mechanism of easily argillaceous rocks.

[0085] The cusp catastrophe model comprises three functional equations: the standard potential function equation, the equilibrium surface equation, and the singularity set equation. The standard potential function equation V(x) is:

[0086] V(x)=x 4 +ux 2 +zx (5)

[0087] In the formula: u and z are control variables, and x is a state variable.

[0088] The equation of the equilibrium surface V′(x) is:

[0089] V′(x)=4x 3 +2ux+z (6)

[0090] The equation V″(x) for the singularity set is:

[0091] V″(x)=12x 2 +2u (7)

[0092] The equations for the equilibrium surface and the singularity set must both be equal to 0. Combining these two equations, we obtain the equation for the divergence set:

[0093] Δ=8u 3 +27z 2 (8)

[0094] The relationships between the equations are as follows Figure 3 As shown, the equilibrium surface consists of three parts: the top leaf, the middle leaf, and the bottom leaf. The middle leaf represents the unstable state of the system, which can be determined by calculating the value of Δ. When Δ > 0, the system is in a stable state; when Δ < 0, the system is in an unstable state; and when Δ = 0, the system is in a critical state.

[0095] The elastic strain energy of easily argillaceous rocks during the experiment was selected as the research object, and a cusp catastrophe model was established. The elastic strain energy U is assumed to be... e The mapping relationship with strain ε is f e Expanding (ε) using Taylor's formula and retaining up to the fourth degree, we get the following equation:

[0096]

[0097] In the formula: ε0 is the strain value at a specific point, let... Furthermore, when strain ε0 = 0, k0 = 0, so equation (9) can be transformed into:

[0098] f e (ε)=k1ε+k2ε 2 +k3ε 3 +k4ε 4 (10)

[0099] In the formula: k j (j=1,2,3,4) can be approximately calculated using the least squares method. Let To convert equation (10) into the standard potential function form of the cusp catastrophe model, the first step is:

[0100]

[0101] The second step is to discard the constant terms that do not include x, and then set x to... 4 Since the coefficient is 1, we can obtain:

[0102]

[0103] Combining equations (5), (8), and (12), we can obtain the expression for the divergence equation Δ as follows:

[0104]

[0105] Based on the elastic strain energy sequence f of easily mud-forming rocks under uniaxial compression e Substituting (ε) into equation (10) for least squares calculation, we can obtain an approximate analytical expression for the relationship between elastic strain energy and strain:

[0106]

[0107] In the formula: f e d (ε) represents the elastic strain energy sequence of easily argillaceous rocks, f e n (ε) represents the elastic strain energy sequence of the undifferentiated argillaceous rock, which will be obtained by solving... Substituting the values, we obtain the analytical expressions for the divergence equation Δ as follows:

[0108]

[0109] The Δ values ​​corresponding to different strains are obtained according to equation (15). The minimum strain interval where the sign of the Δ value changes is defined as abrupt change interval I; the strain point corresponding to the maximum value of Δ is called the warning point, and the warning interval II is the strain interval corresponding to the 0.5% Δ interval to the left and right of the maximum value of Δ; the Δ value can help to further quantify and judge the abrupt change state of easily mud-forming rocks. Figure 4a , Figure 4b , Figure 4c , Figure 4d It can be seen that the energy instability mutation patterns among different easily argillaceous rock samples are similar, with the mutation sequence being from mutation interval (Ⅰ) to warning interval (Ⅱ). The first mutation of easily argillaceous rock occurs near the region transitioning from the compaction stage to the elastic deformation stage. During this stage, the original pores inside the sample close under external load, begin to accumulate elastic strain energy and reduce the release of dissipated energy. The change in the internal energy conversion mode causes the rock to exhibit a "pseudo-instability" phenomenon, creating the illusion that the rock is about to undergo a sudden instability mutation. The releaseable elastic strain energy accumulated inside the rock controls the decrease in rock strength after the stress peak. Therefore, the change pattern of elastic strain energy determines the change pattern of rock instability mutation, thus causing the generation of mutation interval (Ⅰ). The warning interval (Ⅱ) is located before the stress peak, near the region where the easily argillaceous rock sample transitions from the elastic deformation stage to the plastic yielding stage. The warning interval is the range of strain change corresponding to the transition from the rising peak to the falling stage of the elastic strain energy Δ value. In this interval, the elastic strain energy accumulation capacity of easily argillaceous rock gradually decreases from the peak value, indicating that the rock sample strength is about to decrease. The previous stage of rock formation resulted in a significant accumulation of elastic strain energy, placing the sample in an unstable state. Under relatively small external disturbances, it was highly susceptible to sudden and unstable failure, leading to a rapid release of elastic strain energy. Furthermore, the warning zones for different easily mud-forming rocks exhibited high consistency, indicating that the warning model has good universality.

[0110] Compared with non-argillaceous rocks, easily argillaceous rocks exhibit larger strain in the abrupt change and warning ranges. This is because easily argillaceous rocks are subjected to long-term effects from water, high temperatures, high ground stress, and weathering erosion, resulting in a large number of secondary deposits within them. These secondary deposits weaken the rock's brittleness and enhance its ductility under load, allowing it to generate more strain as it approaches failure. However, these secondary deposits, along with micropores and voids, also significantly reduce the rock's strength, causing a sudden drop in strength and abrupt rock instability even under relatively low stress.

[0111] Depend on Figure 5a , Figure 5b and Figure 6a , Figure 6bIt can be seen that the mutation interval, warning point, and warning range obtained from the cusp mutation model of easily argillaceous rocks have a high degree of agreement with the precursor characteristics of acoustic emission ringing count rate and acoustic emission cumulative energy rate. Therefore, this cusp mutation model can effectively predict the unstable and sudden failure of easily argillaceous rocks under uniaxial compression. However, the mutation interval, warning point, and warning range of non-argillaceous rock specimens are inconsistent with the precursor characteristics of acoustic emission ringing count and acoustic emission cumulative energy rate, indicating a certain lag. The mutation interval, warning range, and warning point of easily argillaceous rock specimens are shown in Table 1, where A-7, A-10, and A-11 are easily argillaceous rock samples, and CB-2 is a non-obviously argillaceous rock sample.

[0112] Table 1. Test results of acoustic emission parameters

[0113]

[0114] This invention constructs a cusp mutation model for the instability of easily argillaceous rocks by combining strain and elastic strain energy, quantifying the abrupt failure of easily argillaceous rocks. This model enables comprehensive, rapid, and accurate prediction of abrupt failure of easily argillaceous rocks, providing a scientific reference for early warning and prevention of surrounding rock instability in mining. The above-disclosed embodiments are merely preferred embodiments of the invention and should not be construed as limiting the scope of the invention. Therefore, equivalent variations made within the scope of this invention are still within its coverage.

Claims

1. A method for early warning of sudden instability in easily mud-forming ore rocks, characterized in that, Includes the following steps: Step 1: Prepare mineral and rock specimens, including easily mud-forming mineral and rock specimens and non-obvious mud-forming mineral and rock specimens; Step 2: Conduct acoustic emission tests under uniaxial compression conditions on the mineral and rock specimens described in Step 1, and obtain the displacement, load, and acoustic emission parameter values ​​for each mineral and rock specimen; Step 3: Calculate and analyze the abrupt change characteristics of the evolution of the elastic strain energy curve of easily mud-forming ore rocks; Step 4: Construct an early warning model for the instability and sudden change of easily mud-forming ore rocks based on elastic strain energy strain sequence. The specific process is as follows: The total work done by external forces on the rock can be obtained by calculating the area enclosed by the stress-strain curve and the strain axis using calculus. The total energy input into the rock's interior includes elastic strain energy and dissipated energy. U=U e +U d (1) In the formula, U represents the total energy input into the rock by the press, measured in J; U e U represents the elastic strain energy inside the specimen, measured in J. d The cumulative dissipated energy is expressed in J; it is calculated using the following formulas: Total Energy: In the formula: σ i ε is the stress borne by the specimen at time i, in MPa. i The strain generated in the specimen at time i; elastic strain energy: Cumulative energy dissipation: IN d =UU e (4) In the formula: σ i V represents the stress borne by the specimen at time i, in MPa; V is the volume of the specimen, in mm. 3 E e The elastic modulus of the specimen is expressed in MPa. The three functional equations included in the cusp mutation model are as follows: The standard potential function equation V(x) is: V(x)=x 4 +ux 2 +zx (5) In the formula: u and z are control variables, and x is a state variable; The equation of the equilibrium surface V′(x) is: V′(x)=4x 3 +2ux+z (6) The equation V″(x) for the singularity set is: V″(x)=12x 2 +2u (7) The equilibrium surface equation and the singularity set equation must satisfy the condition that they are equal to 0. Combining equations (6) and (7), we can obtain the divergence set equation as follows: Δ=8u 3 +27z 2 (8) When Δ>0, it indicates that the easily mud-forming ore rock is in a stable state; when Δ<0, it indicates that the easily mud-forming ore rock is in an unstable state; and when Δ=0, it indicates that the easily mud-forming ore rock is in a critical state.

2. The early warning method for sudden instability of easily mud-forming ore rocks according to claim 1, characterized in that, Step four defines the abrupt change interval, warning point, and warning range, and verifies them using the precursor characteristics of acoustic emission parameters. The specific process is as follows: assuming the elastic strain energy U e The mapping relationship with strain ε is f e (ε), expanded using Taylor's formula and rounded down to the fourth degree, yields: In the formula: ε0 is the strain value at a specific point, let... Furthermore, when strain ε0 = 0, k0 = 0, equation (9) can be transformed into: f e (ε)=k1ε+k2ε 2 +k3e 3 +k4e 4 (10) In the formula: k j (j=1,2,3,4) can be approximately calculated using the least squares method. Let To convert equation (10) into the standard potential function form of the cusp catastrophe model, the first step is: The second step is to discard the constant term without x and set x to... 4 Since the coefficient is 1, we can obtain: Combining equations (5), (8), and (12), the expression for the divergence equation Δ can be obtained as follows: Based on the elastic strain energy sequence f of easily mud-forming rocks under uniaxial compression e Substituting (ε) into equation (10) for least squares calculation, we can obtain an approximate analytical expression for the relationship between elastic strain energy and strain: In the formula: f e d (ε) represents the elastic strain energy sequence of easily argillaceous rocks, f e n (ε) represents the elastic strain energy sequence of the undifferentiated argillaceous rock, which will be obtained by solving... Substituting these values, we obtain the analytical expressions for the divergence equation Δ as follows: The Δ values ​​corresponding to different strains are obtained according to equation (15). The minimum strain interval where the sign of the Δ value changes is defined as the mutation interval I. The strain point corresponding to the maximum value of Δ is called the warning point. The warning interval II is the strain interval corresponding to the 0.5% Δ interval to the left and right of the maximum value of Δ. The Δ value is further quantified to determine the mutation state of the easily mud-forming ore rock.

3. A method for early warning of sudden instability in easily mud-forming ore rocks according to claim 1 or 2, characterized in that, The easily mud-forming rock specimen mentioned in step one is a standard cylindrical rock with a height of 100 mm and a diameter of 50 mm.

4. A method for early warning of sudden instability in easily mud-forming ore rocks according to claim 1 or 2, characterized in that, The acoustic emission test described in step two adopts a loading strain test with a loading rate of 0.005 mm / s. Loading is stopped when the specimen fails. The acoustic emission sampling threshold is 50 dB, the preamplifier gain is 45 dB, and the sampling rate is 3 MSPS.

5. A method for early warning of sudden instability in easily mud-forming ore rocks according to claim 1 or 2, characterized in that, The abrupt change characteristics of the elastic strain energy curve evolution of easily mud-forming rocks described in step three include: the stage before the peak of the elastic strain energy curve of easily mud-forming rocks is divided into an initial energy dissipation stage and an elastic strain energy accumulation stage; the energy evolution after the peak of the elastic strain energy curve of easily mud-forming rocks is divided into a step-like and a cliff-like stage, which is determined by the number of abrupt change points in the energy curve.

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