A bank rock slope stability evaluation method based on rock mass wave electric characteristics

Abstract

This invention discloses a method for evaluating the stability of reservoir bank rock slopes based on the wave electrical properties of rock mass, belonging to the field of reservoir bank slope stability analysis technology. The steps of this invention are as follows: S1: Predict the macroscopic mechanical parameters of the rock mass based on in-situ wave electrical testing; S2: Calculate the slope stability using the strength reduction method to obtain the slope safety factor; S3: Assuming that the measured rock mass damage at a certain moment is the initial damage, perform a time-cumulative damage evolution analysis to estimate the slope stability life; S4: Evaluate the slope stability by combining the slope safety factor and the slope stability life. This invention determines the rock mass parameters at the test moment, considers the parameter variation over time, further analyzes the internal damage evolution law of actual rock mass engineering, performs dynamic prediction of rock mass parameters, and uses this as a basis for numerical calculation of the safety factor and cumulative damage analysis to evaluate the slope stability.

Description

Technical Field

[0001] This invention belongs to the field of reservoir bank slope stability analysis technology, and in particular relates to a method for evaluating the stability of reservoir bank rock slopes based on the wave electrical properties of rock masses. Background Technology

[0002] When the reservoir bank rock mass is subjected to periodic saturation, water will move in the fractured rock mass. At this time, the water not only acts as a fluid medium to scour the pores or filling materials in the rock mass, causing an increase in rock porosity and reducing the strength of the rock mass, but also acts as a force directly on the rock, causing deformation and failure of the reservoir bank rock mass and affecting the stability of the slope.

[0003] Reservoir bank slopes are subjected to periodic fluctuations in water level over a long period of time, and the stability of the slope rock mass exhibits a dynamic changing trend. A reasonable assessment of the stability of reservoir bank slopes is crucial for ensuring reservoir safety. Traditional slope stability analysis methods include qualitative analysis, quantitative analysis, and uncertainty analysis. Qualitative and uncertainty analysis methods are estimation methods that consider comprehensive factors, and are susceptible to interference from uncertain factors, leading to relatively large errors in the analysis results.

[0004] Based on the engineering rock mechanics model established by quantitative calculation, the deformation and stability of rock mass under various force fields can be analyzed, providing a quantitative basis for rock engineering protection design and construction. The quantitative calculation methods include the limit equilibrium method and the numerical analysis method. The key indicator for quantitative calculation of stability analysis by both methods is the safety factor. Therefore, it is necessary to determine the slope stability by comprehensively considering multiple factors after understanding the relationship between damage variables and the safety factor. Under the action of periodic water level fluctuations, the impact of internal damage accumulation on rock mass stability cannot be ignored. As time goes by, the change of the slope safety factor is a dynamic process. Therefore, only by determining the variation law of the macroscopic mechanical parameters of the rock mass can a reasonable safety factor be calculated on this basis. To this end, we designed a method for evaluating the stability of reservoir bank rock slopes based on the wave electrical properties of rock mass. Summary of the Invention

[0005] The purpose of this invention is to provide a method for evaluating the stability of reservoir bank rock slopes based on the wave electrical properties of rock masses, so as to solve the problems mentioned in the background art.

[0006] To solve the above-mentioned technical problems, the present invention is achieved through the following technical solution:

[0007] This invention relates to a method for evaluating the stability of reservoir bank rock slopes based on the wave electrical properties of rock masses. The steps are as follows:

[0008] S1: Predicting macroscopic mechanical parameters of rock mass based on in-situ wave electrical testing;

[0009] S2: The MC strength criterion is selected for material treatment, and the soil and rock materials are regarded as ideal elastic-plastic materials. The strength reduction method is used to calculate the slope stability.

[0010] S3: Since the damage inside the rock mass of the bank slope is a gradual process, the degree of damage is a dynamic variable; now assume that the measured rock mass damage defined at a certain moment is the initial damage. From this moment on, after each dry-saturated cycle, the damage that accumulates inside the rock mass is the cumulative damage, which is the concept of cumulative damage related to the time factor, denoted as Dc.

[0011] S4: Evaluate the stability of the bank slope by taking into account the slope safety factor and the slope stability period.

[0012] Furthermore, after determining the rock mass integrity coefficient and structural plane type, the parameters of the rock block and rock mass are converted in conjunction with indoor tests;

[0013] The relationship between the deformation modulus of rock mass and rock block:

[0014]

[0015] Therefore, the strength conversion relationship between rock mass and rock block can be obtained:

[0016]

[0017] Based on the relationship between resistivity and porosity in the Archie formula, and considering the water saturation of the pores, the correction factor k1 can be calculated based on the measured resistivity, i.e.:

[0018]

[0019] Based on the GSI scoring standard, the conversion relationship between rock mass and rock block parameters is obtained, namely the generalized HB strength criterion:

[0020]

[0021]

[0022]

[0023]

[0024]

[0025] Where GSI is the geological strength index, E m E represents the elastic modulus of the rock mass. i D is the elastic modulus of the rock block; D is the construction disturbance factor, which is taken as 0-1 according to the on-site construction conditions; m b m iσ'1 and σ'3 are the Hoek-Brown constants for the rock mass and rock block, respectively; s and a are characteristic parameters of the rock mass; σ'1 and σ'3 are the maximum and minimum effective stresses at failure; σ ci It represents the uniaxial compressive strength of the rock block.

[0026] Furthermore, combining the strength reduction method for slope stability calculation, under cyclic saturation, the wave velocity or resistivity at a certain moment can be measured using acoustic or resistivity testing techniques, thereby calculating the instantaneous damage at that moment. The rock mass integrity coefficient is a physical index that reflects the quality and strength of the rock mass. When performing process damage analysis, an integrity coefficient K based on the acoustic velocity definition is introduced. V :

[0027]

[0028] In the formula: V Pm V represents the measured wave velocity of the rock mass. Pr Measured P-wave velocity of the rock block;

[0029] The better the rock integrity, the higher the K V The larger the value of K, the better. V The value can be selected by combining the measured P-wave velocity, joint number, RQD, and other index ranges of the rock sample. V The larger the value of , the slower the accumulation rate of process damage.

[0030] Furthermore, considering the characteristics of the rock mass, an equation describing dynamic damage is established, and a cumulative damage calculation model related to the time factor n is proposed, namely D. C The calculation formula is as follows:

[0031]

[0032] ΔD n =D n+1 -D n

[0033] In the formula: k1 is the correction coefficient considering test error; k2 is the correction coefficient considering time accumulation; D0 is the initial damage variable; K V is the rock mass integrity coefficient; n is the time parameter, with a period of one year; D n It is the process damage variable in the nth cycle; ΔD n This represents the incremental damage over the process from n to n+1 cycles, used to reflect the dynamic evolution of damage.

[0034] Under the action of the dry-saturated cycle, all indicators of the rock are in a dynamic state of change. Taking a certain moment when the rock mass is working normally as the starting point, i.e., n=0; since acoustic wave testing can be carried out under undisturbed conditions, the initial damage variable of the rock mass is calculated using the wave velocity expression formula as follows:

[0035]

[0036] In the formula: V P0 The measured value of the sound wave in m / s at a certain sampling time;

[0037] The initial damage value can also be determined by other methods. The relationship between the damage factor and porosity of rocks with initial damage is shown in the following formula:

[0038]

[0039] Therefore, we can conclude that:

[0040]

[0041] Determination of the correction factor k1: Based on the reduction of sound wave velocity by the internal pores of the rock and using the initial porosity at a certain moment as the basis for calculation, the correction factor k1 is defined as follows:

[0042]

[0043] Where φ is the rock porosity, the range of values ​​for the correction coefficient k1 is further obtained by fitting the data:

[0044] 0.5 < k1 ≤ 0.85.

[0045] Furthermore, the formula for calculating porosity can be obtained using the Archie formula:

[0046]

[0047] Among them, R W R represents the resistivity of a saturated solution, and S represents the resistivity of an unsaturated rock. W Indicates saturation.

[0048] Furthermore, for cyclically saturated sandstone, the main influencing factors of cumulative damage are porosity and saturation, which can be reflected by wave-electric properties. First, using porosity changes as a link, the damage variation law is analyzed, and the wave velocity of the solid matrix of the rock material is calculated using the Gassmann equation:

[0049]

[0050] Where: K S G is the bulk modulus of the rock matrix; S ρ is the shear modulus of the matrix. S This represents the matrix density.

[0051] Furthermore, by fitting the logarithmic relationship, the variation of matrix wave velocity with porosity is found to satisfy the following equation:

[0052] V PS =AB·lnφ

[0053] In the formula: A and B are constants related to the characteristics of the rock sample;

[0054] In practical engineering, rock masses are often in an unsaturated state. Considering the good stability of acoustic wave testing, the damage variation law during the process can be analyzed based on this empirical formula, thus obtaining the dynamic relationship of acoustic wave velocity:

[0055]

[0056]

[0057] In the formula: V Pn The velocity of sound under n cycles is m / s; V P(dry) Wave velocity under dry conditions; V P(sat) The wave speed under saturation; φ n For dynamic porosity; S Wn The dynamic water saturation is represented by C1 and C2, which are constants considering wave velocities in the solution and air, respectively.

[0058]

[0059]

[0060] The wave velocity of rock in a dry state depends on the physical and mechanical properties of the matrix and the porosity. The wave velocity in a saturated state also needs to consider the type of pore solution. Based on the Wyllie time-averaged equation and combined with a microstructure equivalent model, the analysis is conducted as follows: It is assumed that the pores are entirely filled with air under dry conditions, and the saturation S... W =0, under saturation conditions, it is assumed that the pores are filled with water, S W =1:

[0061]

[0062]

[0063] In the formula: V A V represents the speed of sound in air. A =330m / s; V W V represents the speed of sound in water. W =1500m / s.

[0064] Furthermore, D is calculated by combining the wave velocity variation pattern under different cycle numbers. n Further analysis of the damage increment ΔD nThe variation of the time parameter n is investigated, where n≥1. Finally, considering the time effect, a correction coefficient k2 is used to correct the process damage increment. Taking into account the effects of porosity and saturation, D under different cycle periods is obtained. n Calculation formula:

[0065]

[0066]

[0067] ΔD n Calculation: First, calculate the damage increment:

[0068]

[0069] Furthermore, when 0 ≤ S Wn When ≤0.5, 0≤S Wn ≤0.5 and Substitute get:

[0070]

[0071] The porosity of the rock mass is relatively low under normal working conditions. To simplify the calculation, φ is assumed to be low. n Minimum value, neglecting higher-order minimum values ​​φ n 2 Simplified to:

[0072]

[0073] Combination Given C1 = -0.0024, its product with porosity can be considered a higher-order infinitesimal, which can be ignored. Further simplification yields:

[0074]

[0075] Similarly, (V) can be calculated. P(n+1) ) 2 :

[0076]

[0077] Will and Substitution After calculation and simplification, higher-order local minima φ are omitted. n ·φ n+1 Item, obtained:

[0078]

[0079] Since the porosity varies with n according to a logarithmic relationship, we assume that:

[0080] φ n =A·ln n+B

[0081] In the formula: A and B are fitting coefficients, and A>0, B>0; φ n Substituting = A·ln n+B

[0082]

[0083] have to:

[0084]

[0085] The time parameter n is a variable parameter, while all other parameters are available. The lossless wave velocity is related to the rock material type. If the rock damage is low, the lossless wave velocity and the matrix wave velocity can be approximated as equal, i.e., V0. Pf =V PS If the degree of damage is high V Pf >V PS Then V Pf -2 ·V PS 2 ≤1; When performing cumulative damage calculation, it is assumed that the constant term V in the denominator is removed. A +2B, take V Pf -2 ·V PS 2 =1, the increased damage increment simplifies to:

[0086]

[0087] ΔD n It is related to the time parameter and reflects the dynamic change pattern of damage increment.

[0088] Furthermore, when 0.5 ≤ S Wn When ≤1, 0.5≤S Wn ≤1 and Substitution calculate:

[0089]

[0090] Similarly, without considering higher-order minima φ n 2 Neglecting the product term where C2 = 0.0033, we get:

[0091]

[0092] Simplified (V) Pn ) 2Calculation formula and Similar, (V) P(n+1) ) 2 The calculation formula is also consistent with Similarly, it can be seen that the formula for calculating damage increment can be uniformly used. This indicates; however, when n=1, it is determined by... ΔD is calculated n =1, which is inconsistent with reality. This is due to the characteristic point relationship of the logarithmic fitting relationship. Based on this, we define: Under the condition of no loading, when the damage increment is less than the initial damage, based on The formula is only meaningful for studying cumulative damage, therefore n≥2 is taken when calculating damage increment;

[0093] After fitting, the variation of damage increment with time parameters satisfies the power function relationship well:

[0094] ΔD n =A·n -B

[0095] In the formula: A and B are fitting coefficients, and 0 <A<1、B> 1;

[0096] To determine the correction factor k2, we first analyze the relative rate of change of the damage increment. The relative rate of change is related to the time parameter, considering ΔD. n The fitting coefficients in the general formula are calculated, with B = 2:

[0097]

[0098] Based on the relative rate of change of damage increment, a correction factor considering the accumulation over time is defined:

[0099]

[0100] When n = 0, it represents the test time k2 = 0. The damage at this time can be directly determined by the initial damage, that is, the initial damage can be directly determined by combining the wave-electric test method. When calculating the cumulative damage after n ≥ 0, it can be determined that k2 < 1, and thus it can be determined that 0 ≤ k2 < 1.

[0101] Thus, a calculation model for cumulative damage variables that can be jointly characterized by wave-electric parameters was determined:

[0102]

[0103] in,

[0104] The present invention has the following beneficial effects:

[0105] This invention, through a series of structural improvements, enables dynamic prediction of rock mass parameters by analyzing the internal damage evolution law of actual rock mass engineering, and based on this, numerical calculation of safety factor and cumulative damage analysis are performed to evaluate the stability of the bank slope. Attached Figure Description

[0106] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0107] Figure 1 This is a flowchart of the slope stability evaluation method based on damage evolution of the present invention;

[0108] Figure 2 This is a graph showing the relationship between the safety factor and damage variables of this invention. Detailed Implementation

[0109] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0110] Please see Figures 1-2 As shown, this invention is a method for evaluating the stability of reservoir bank rock slopes based on the wave electrical properties of rock masses.

[0111] Under the influence of periodically varying water levels, the stability of the bank slope rock mass exhibits a dynamic changing trend.

[0112] To evaluate the stability of the bank slope, the stability life of the slope is estimated based on a cumulative damage model.

[0113] Given that the rock face of the reservoir slope is directly exposed to water after excavation, and some areas along the shore lack slope protection, the impact of annual water level fluctuations on slope stability cannot be ignored. When studying slope stability, the MC strength criterion is used for material treatment, and the soil and rock materials are treated as ideal elastic-plastic materials. The strength reduction method is employed for slope stability calculations.

[0114] Because damage within the rock mass of a riverbank slope is a gradual process, the degree of damage is a dynamic variable. Let's assume that the measured rock mass damage at a certain moment is the initial damage. From that moment onward, the damage that accumulates within the rock mass after each dry-saturation cycle is called cumulative damage, which is the concept of cumulative damage related to the time factor, denoted as (D...). c ).

[0115] For rock damage, considering initial damage and using the continuous change in porosity during damage accumulation as a standard, and referring to the number of cycles, the damage model is defined as a computational model jointly characterized by wave and electrical parameters. Based on the premise that the actual damage variable at rock mass failure does not exceed 1, a critical value for the cumulative damage variable is determined.

[0116] Specifically, combining empirical formulas, under cyclic saturation, acoustic or resistivity testing techniques can be used to measure wave velocity or resistivity at a specific moment, thereby calculating the instantaneous damage at that moment. When conducting process damage evolution analysis of rock masses, it is also necessary to comprehensively consider porosity, water content, and regional characteristics. The integrity coefficient of the rock mass is a physical indicator that reflects the quality and strength of the rock mass. To reflect the overall integrity of the rock mass under study, an integrity coefficient K based on acoustic velocity is introduced in process damage analysis. V :

[0117]

[0118] In the formula: V Pm V represents the measured wave velocity of the rock mass. Pr The measured longitudinal wave velocity of the rock block.

[0119] The better the rock integrity, the higher the K V The larger the value of K, the better. V The value can be selected by combining the measured P-wave velocity, joint number, RQD, and other index ranges of the rock sample. Theoretically, K V The larger the value of , the slower the accumulation rate of process damage should be. Therefore, the theoretical model proposed in this invention considers (1-K) V The relationship is a multiple reduction.

[0120] Considering the characteristics of the rock mass, an equation describing dynamic damage is established, and a cumulative damage calculation model related to the time factor n, namely D, is proposed. C The calculation formula is as follows:

[0121]

[0122] ΔD n =D n+1 -D n (2b)

[0123] In the formula: k1 is the correction coefficient considering test error; k2 is the correction coefficient considering time accumulation; D0 is the initial damage variable; K V is the rock mass integrity coefficient; n is the time parameter, with a period of one year; D n It is the process damage variable in the nth cycle; ΔD n This represents the incremental damage over the process from n to n+1 cycles, used to reflect the dynamic evolution of damage.

[0124] Determining the initial damage is fundamental to calculating cumulative damage. Depending on the starting point of the test, the initial damage is not a fixed value, but it must be ensured that the rock mass is in its normal operating phase under the initial damage conditions. Under the action of the dry-saturated cycle, all rock parameters are in a dynamic state of change. Taking a certain moment when the rock mass is operating normally as the starting point, i.e., n=0, we can use this as the starting point. Since acoustic testing can be conducted under undisturbed conditions, the formula for calculating the initial damage variable of the rock mass using wave velocity is as follows:

[0125]

[0126] In the formula: V P0 The measured value of the sound wave (m / s) at a certain sampling time.

[0127] The initial damage value can also be determined by other methods. According to the Mohr-Coulomb failure criterion, the theoretical relationship between the damage factor and porosity of rocks with initial damage is as follows:

[0128]

[0129] Therefore, we can conclude that:

[0130]

[0131] Determination of the correction factor k1: For engineering rock masses, the complex occurrence conditions interfere with acoustic wave testing, resulting in a lower measured wave velocity than the actual wave velocity. This leads to an overestimation of the initial damage when determining acoustic wave parameters. Considering the reduction of acoustic wave velocity due to internal rock pores, and using the initial porosity at a certain moment as the basis for calculation, the correction factor k1 is defined as follows:

[0132]

[0133] Where φ represents the rock porosity. To determine the range of the correction coefficient, we first assume different porosities and calculate the correction coefficient using the above formula. The larger the initial porosity, the larger the correction coefficient, and the smaller the reduction in initial damage, i.e., the larger the initial damage correction value, satisfying the damage principle. For engineering rock masses, the initial porosity φ0 ≠ 0, so k1 > 0.5. To ensure the normal operation of the rock mass, the initial porosity cannot be too large, i.e., φ0 ≠ 1. We also need to consider that the correction coefficient proposed in this invention is to reduce the initial damage calculation value based on wave velocity. Therefore, we can initially determine 0.5 < k1 ≤ 1. The porosity under normal rock mass operation cannot be too large. We take the upper limit of the study as φ0 = 0.25, and further obtain the range of values ​​for the correction coefficient k1 through fitting data.

[0134] 0.5<k1≤0.85 (7)

[0135] To determine the initial porosity, we can analyze it in conjunction with measured resistivity. Under unsaturated conditions, the relationship between resistivity, porosity, and saturation is as follows: under the same porosity conditions, resistivity decreases with increasing saturation; under the same saturation conditions, the smaller the porosity, the larger the resistivity. If the porosity of dense sandstone is relatively small, the relationship between resistivity and porosity satisfies the Archie relation well. Therefore, taking a saturation index of 2 and a cementation index of 1.5 for dense sandstone, the formula for calculating porosity can be obtained from the Archie formula:

[0136]

[0137] Among them, R W Represents the resistivity of a saturated solution. R The resistivity of unsaturated rock, S W Indicates saturation.

[0138] If the resistivity of the solution, the measured resistivity and saturation of the rock mass at a certain sampling time are known, the porosity of the rock mass can be calculated.

[0139] D n Analysis: Strictly speaking, the damage changes of engineering rock masses during operation are unpredictable. The process damage calculation formulas involved below include the following basic assumptions: it is assumed that the occurrence environment of the rock mass is basically stable within the calculation period; the influence of water level rise and fall is reflected through changes in porosity and saturation, and other external loads are not considered; it is assumed that the process damage increment satisfies continuity and can be quantitatively analyzed using the relationship of the time parameter n.

[0140] For cyclically saturated sandstone, the main factors influencing cumulative damage are porosity and saturation, which can be reflected by wave-electric properties. First, using porosity variation as a link, the damage variation law is analyzed, and the wave velocity of the solid matrix of the rock material is calculated using the Gassmann equation:

[0141]

[0142] Where: K S G is the bulk modulus of the rock matrix; S ρ is the shear modulus of the matrix. S This represents the matrix density.

[0143] The calculated matrix velocity is essentially equal to the measured wave velocity under dry conditions. However, the matrix wave velocity differs significantly from the theoretical dry wave velocity, but the difference between the theoretical dry and saturated wave velocities is roughly the same as the difference between the measured wave velocities. Under high saturation conditions, the calculation results based on the Sayed formula are basically the same as those based on porosity. Under low saturation conditions, the calculated results are larger, indicating that when calculating damage based on sound wave velocity, the higher the degree of saturation, the greater the measured sound wave velocity, which is consistent with the theoretical analysis results.

[0144] By fitting the logarithmic relationship, the variation of matrix wave velocity with porosity is obtained, satisfying the following equation:

[0145] V PS =AB·lnφ (10)

[0146] In the formula: A and B are constants related to the characteristics of the rock sample.

[0147] In practical engineering, rock masses are often in an unsaturated state. Considering the good stability of acoustic wave testing, the damage variation law during the process can be analyzed based on this empirical formula, thus obtaining the dynamic relationship of acoustic wave velocity:

[0148]

[0149]

[0150] In the formula: V Pn V is the velocity of sound (m / s) over n cycles; P(dry) Wave velocity under dry conditions; V P(sat) The wave speed under saturation; φ n For dynamic porosity; S Wn The dynamic water saturation is represented by C1 and C2, which are constants considering wave velocities in the solution and air, respectively.

[0151]

[0152]

[0153] The wave velocity of rock in a dry state depends on the physical and mechanical properties of the matrix and the porosity. The wave velocity in a saturated state also needs to consider the type of pore solution. Based on the Wyllie time-averaged equation and combined with a microstructure equivalent model, the analysis is conducted as follows: It is assumed that the pores are entirely filled with air under dry conditions, and the saturation S... W =0, under saturation conditions, it is assumed that the pores are filled with water, S W =1:

[0154]

[0155]

[0156] In the formula: V A V represents the speed of sound in air. A =330m / s; V W V represents the speed of sound in water. W =1500m / s.

[0157] Based on the above theory, and combined with the wave velocity variation pattern under different cycle numbers, D is calculated. n Further analysis of the damage increment ΔD n The variation of the time parameter n is investigated, where n≥1. Finally, considering the time effect, a correction coefficient k2 is used to correct the process damage increment. Taking into account the effects of porosity and saturation, D under different cycle periods is obtained. n Theoretical formulas for calculation:

[0158]

[0159]

[0160] In the formula, D n V represents the process damage variable in the nth cycle, where n is a time parameter with a cycle of one year; Pn V is the velocity of sound (m / s) over n cycles; Pf V represents the longitudinal wave velocity (m / s) of the undamaged rock. PS V represents the wave velocity of the solid matrix of the rock, which is composed of clay minerals and quartz minerals; A V is the speed at which sound waves travel in air. A =330 (m / s); V W V is the speed at which sound waves propagate in water. W =1500 (m / s); φ n S represents the porosity of the nth period; Wn C1 and C2 are constants that take into account the wave velocity in the solution and the wave velocity in the air, respectively, representing the saturation of the nth period.

[0161] ΔD nTheoretical calculation: First, calculate the damage increment:

[0162]

[0163] (1) When 0 ≤ S Wn When ≤0.5, substituting (11a) and (13a) into (15) yields:

[0164]

[0165] The porosity of the rock mass is relatively low under normal working conditions. To simplify the calculation, φ is assumed to be low. n Minimum value, neglecting higher-order minimum values ​​φ n 2 The above formula simplifies to:

[0166]

[0167] Combining (12a) to determine C1 = -0.0024, the product of C1 and porosity can be considered a higher-order infinitesimal, which is ignored. The above equation is further simplified to:

[0168]

[0169] Similarly, (V) can be calculated. P(n+1) ) 2 :

[0170]

[0171] Substituting equations (16c) and (17) into equation (15) for calculation, and after rearranging, neglecting the higher-order minimum value φ. n ·φ n+1 Item, obtained:

[0172]

[0173] Since the porosity varies with n according to a logarithmic relationship, we assume that:

[0174] φ n =A·ln n+B (19)

[0175] In the formula: A and B are fitting coefficients, and A>0 and B>0.

[0176] Substituting equation (19) into equation (18), we get:

[0177]

[0178] In the above formula, the time parameter n is a variable parameter, while the other parameters are all obtainable parameters. The lossless wave velocity is related to the type of rock material. If the rock damage is low, the lossless wave velocity and the matrix wave velocity can be approximated as equal, i.e., V. Pf=V PS If the degree of damage is high V Pf >V PS Then V Pf -2 ·V PS 2 ≤1. When performing cumulative damage calculations, it is assumed that the constant term V in the denominator is removed. A +2B, take V Pf -2 ·V PS 2 =1, the increased damage increment simplifies to:

[0179]

[0180] ΔD n It is related to the time parameter, reflects the dynamic change law of damage increment, and the calculation formula is relatively simple.

[0181] (2) When 0.5 ≤ S Wn When ≤1, substitute (11b) and (13b) into equation (15) to calculate:

[0182]

[0183] Similarly, without considering higher-order minima φ n 2 Neglecting the product term where C2 = 0.0033, we get:

[0184]

[0185] In the formula, V Pn V is the velocity of sound (m / s) over n cycles; PS V represents the wave velocity of the solid matrix of the rock, which is composed of clay minerals and quartz minerals; W V is the speed at which sound waves propagate in water. W =1500 (m / s); φ n S represents the porosity of the nth period; Wn C1 and C2 are constants that take into account the wave velocity in the solution and the wave velocity in the air, respectively, representing the saturation of the nth period.

[0186] Simplified (V) Pn ) 2 The calculation formula is similar to (16c), (V P(n+1) ) 2 The calculation formula is similar to that of (17), thus it can be seen that the calculation formula for damage increment can be uniformly expressed by (20b). However, when n=1, ΔD is calculated by (20b). n=1, which is inconsistent with reality. This is due to the characteristic point relationship of the logarithmic fitting relationship. Based on this, we define: In the case of no loading, when the damage increment is less than the initial damage, it is meaningful to study the cumulative damage based on equation (20b). Therefore, when calculating the damage increment, n≥2 is taken.

[0187] After fitting, the variation of damage increment with time parameters satisfies the power function relationship well:

[0188] ΔD n =A·n -B (twenty three)

[0189] In the formula: A and B are fitting coefficients, and 0 <A<1、B> 1.

[0190] Determination of the correction factor k2: The analysis of the damage increment calculation shows that the simplified damage increment is larger and does not reflect the influence of water saturation on the damage increment. To reduce the theoretical calculation error, a reduction factor k2 can be introduced to adjust ΔD. n The calculation results are corrected based on the general formula. Damage increment decreases as the time parameter increases, but actual process damage accumulates continuously. The magnitude of process damage at a given moment needs to consider the cumulative damage increment from the initial state to that moment. Analysis of the damage increment shows that the accumulation rate is fast in the early stages and slows down later. To determine the correction coefficient, the relative rate of change of the damage increment is first analyzed. The relative rate of change is related to the time parameter, considering ΔD. n The fitting coefficients in the general formula are calculated, with B = 2:

[0191]

[0192] In the formula, ΔD n The process damage increment from n to n+1 cycles is used to reflect the dynamic evolution of damage; as mentioned before, A and B are fitting coefficients; n is a time parameter with a period of one year.

[0193] Based on the relative rate of change of damage increment, a correction factor considering the accumulation over time is defined:

[0194]

[0195] When n = 0, it represents the test time k2 = 0. The damage at this time can be directly determined by the initial damage, that is, the initial damage can be directly determined by combining the wave-electric test method. When calculating the cumulative damage after n ≥ 0, it can be determined that k2 < 1, and thus it can be determined that 0 ≤ k2 < 1.

[0196] Thus, a calculation model for cumulative damage variables that can be jointly characterized by wave-electric parameters was determined:

[0197]

[0198] As mentioned earlier, in the formula, k1 and k2 are the correction coefficients mentioned earlier, respectively considering test error and time accumulation; D0 is the initial damage variable; K V The rock mass integrity coefficient. Among them, V Pm V represents the measured wave velocity of the rock mass. Pr φ0 represents the measured P-wave velocity of the rock block; φ0 represents the initial porosity. R W R0 is the resistivity of the saturated solution, R0 is the resistivity of the initial unsaturated rock, and S0 is the resistivity of the saturated solution. W0 V represents the initial saturation. Pf V represents the longitudinal wave velocity (m / s) of the undamaged rock. P0 is the measured value of the sound wave at a certain sampling time (m / s); n is a time parameter with a period of one year.

[0199] When performing cumulative damage calculations using the above model, in addition to the measured wave-electric parameters, the following steps are required to obtain the relevant parameters:

[0200] (1) Test the solution resistivity of the water body where the rock mass is located, test the instantaneous resistivity of the rock mass, estimate the water saturation of the rock mass, and then calculate the initial porosity to determine the correction coefficient k1;

[0201] (2) Test the instantaneous longitudinal wave velocity of the rock mass, determine the wave velocity value under the undamaged state based on the regional lithological characteristics, and calculate the initial damage variables;

[0202] (3) Determine the correction coefficient based on the research period, and sum the damage increments in combination with the damage increment calculation formula;

[0203] (4) Determine the integrity coefficient K based on the measured wave velocities of rock blocks and rock masses. V ;

[0204] (5) Calculate the cumulative damage size under a certain time period according to formula (26) and analyze the damage evolution law.

[0205] Acoustic wave and resistivity testing are effective methods for studying the dynamic changes of macroscopic and microscopic parameters and for cumulative damage analysis. The evolution of rock damage reflects the changing patterns of physical and mechanical properties.

[0206] The impact of internal damage accumulation on rock mass stability is significant. However, the key indicator for quantitative stability analysis using traditional methods is the safety factor. As time progresses, the change in the safety factor is a dynamic process. By determining the variation law of the macroscopic mechanical parameters of the rock mass, a reasonable safety factor can be calculated.

[0207] After determining the rock mass integrity coefficient and structural plane type, the parameters of the rock block and rock mass are converted based on the indoor test.

[0208] The relationship between the deformation modulus of rock mass and rock block:

[0209]

[0210] In the formula, V Pm V represents the measured wave velocity of the rock mass. Pr is the measured P-wave velocity of the rock block; k1 is a correction factor considering test error; For the effective damage variable of the damaged material; E represents the effective elastic modulus of the damaged material; E represents the elastic modulus in the undamaged state.

[0211] Therefore, the strength conversion relationship between rock mass and rock block can be obtained:

[0212]

[0213] In the formula, V Pm V represents the measured wave velocity of the rock mass. Pr is the measured P-wave velocity of the rock block; k1 is a correction factor considering test error; For the effective damage variable of the damaged material; σ represents the effective stress of the damaged material; σ represents the stress of the undamaged material.

[0214] Based on the relationship between resistivity and porosity in the Archie formula, and considering the water saturation of the pores, the correction factor k1 can be calculated based on the measured resistivity, i.e.:

[0215]

[0216] In the formula, R W R is the resistivity of the saturated solution; R is the resistivity of the unsaturated rock; S W The saturation level of unsaturated rocks.

[0217] Based on the GSI scoring standard, the conversion relationship between rock mass and rock block parameters is obtained, namely the generalized HB strength criterion:

[0218]

[0219]

[0220]

[0221]

[0222]

[0223] Where GSI is the geological strength index, E m E represents the elastic modulus of the rock mass (MPa). i denoted as _m_, representing the elastic modulus of the rock block (MPa); _D_, representing the construction disturbance factor, is taken as a value from 0 to 1 based on the on-site construction conditions; _m_ b m i σ1 and σ3 are the Hoek-Brown constants for the rock mass and rock block, respectively; s and a are characteristic parameters of the rock mass; σ1' and σ3' are the maximum and minimum effective stresses (MPa) at failure; σ1 ci The uniaxial compressive strength of the rock block (MPa).

[0224] In summary, by determining the rock mass parameters at the test time and considering the variation of these parameters over time, we can analyze the internal damage evolution of actual rock mass engineering projects, perform dynamic prediction of rock mass parameters, and based on this, conduct numerical calculation of the safety factor and cumulative damage analysis to evaluate the stability of the bank slope.

[0225] The advantages and effects of this invention are significant: by combining the results of field and indoor tests on wave electrical parameters, and by studying the relationship between damage variables and safety factors, stability analysis of rock slopes is conducted based on the wave electrical properties of rock materials.

[0226] It is known that the initial state of the bank slope rock mass is relatively intact, so we take the integrity coefficient K. V =0.5, corresponding to the wave velocity V of the undamaged rock mass Pf =3.5km / s, and D0 = 0.186 can be calculated from the relationship between the measured wave velocity and the undamaged wave velocity; the calculated safety factor of the slope model is shown in Table 1; the theoretically calculated stable lifespan for different damage thresholds is shown in Table 2, and the curve comparing the safety factor and damage variables is shown in... Figure 2 As shown.

[0227] Table 1 Calculated safety factor values ​​for the slope model

[0228]

[0229] Table 2. Stable life estimation based on theoretical model

[0230]

[0231] Several characteristic points with the same time node can be found from the relationship curve. The changes are significant when n ≤ 20, and gradually approach the limit value after 20 < n ≤ 100. Using n = 100 as the control point for stability analysis, the fitting analysis of the two indicators according to the logarithmic relationship yields good results. The fitting relationship is as follows:

[0232] Safety factor: F = 2.7747 - 0.279·ln(n) n ≤ 100R 2 =0.9348

[0233] Damage variable: D C =0.2065+0.0603·ln(n)n≤100R 2 =0.9946

[0234] By using the fitted relationship between the safety factor and the cumulative damage variable, and eliminating the time parameter using the elimination method, the linear relationship between the two parameters can be obtained:

[0235] D C =0.806-0.216F 1≤F<3.73 (35)

[0236] The value of the safety factor in equation (35) needs to take into account regional characteristics and calculation conditions. The upper limit of the safety factor is determined by the minimum value of the damage variable, and the upper limit of the cumulative damage can also be determined by the minimum value of the safety factor, i.e., 0 < D. C ≤0.52.

[0237] Based on the numerical calculation results of the safety factor in Table 1, when n = 0, F max =2.94, substituting into equation (35) to calculate D c0 =0.17, so the comparative analysis mainly considers process damage, and the influence of initial damage can be appropriately weakened. That is, the initial damage is omitted in equation (35). At the same time, considering the range of damage values, the expression after adjusting the coefficient is:

[0238] D n =0.636-0.116F 1≤F≤5.48 (36)

[0239] The above formula describes the relationship between cumulative damage and the stability safety factor.

[0240] The relationship between cumulative damage variables and the stability safety factor can be defined as D C =AB·F, thus establishing a connection between the cumulative damage calculation method based on wave electrical characteristics and the traditional stability analysis method, and conducting stability evaluation accordingly.

[0241] Considering that the safety factor of a first-order slope is greater than or equal to 1.35, the threshold values ​​of damage variables for slope stability can be determined according to equations (35) and (36), which are very close to the cumulative damage threshold values ​​for a calculation period of n=100 in Table 2. Therefore, considering the initial damage situation of the slope, based on the theoretical relationship of equation (36) and combined with the safety factor values ​​under general working conditions in Table 3, the upper limit range of damage variable values ​​for judging the slope stability level is shown in Table 4 below.

[0242] When performing slope stability analysis based on damage variables, the initial damage condition and slope grade can be combined, and the slope stability can be judged according to the range of damage variable values ​​in Table 4.

[0243] Table 3. Safety Factor Values

[0244]

[0245] Table 4 Upper Limit of Damage Variable Values

[0246]

[0247] In the description of this specification, references to terms such as "an embodiment," "example," "specific example," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0248] The preferred embodiments of the present invention disclosed above are merely illustrative of the invention. These preferred embodiments do not exhaustively describe all details, nor do they limit the invention to the specific implementations described. Clearly, many modifications and variations can be made based on the content of this specification. This specification selects and specifically describes these embodiments to better explain the principles and practical applications of the invention, thereby enabling those skilled in the art to better understand and utilize the invention. The invention is limited only by the claims and their full scope and equivalents.

Claims

1. A method for evaluating the stability of reservoir bank rock slopes based on the wave electrical properties of rock masses, characterized in that, The steps are as follows: S1: Predicting macroscopic mechanical parameters of rock mass based on in-situ wave electrical testing; S2: The MC strength criterion is selected for material treatment, and the soil and rock materials are regarded as ideal elastic-plastic materials. The strength reduction method is used to calculate the slope stability. S3: Since the damage within the slope rock mass is a gradual process, the degree of damage is a dynamic variable. Now, assume that the measured rock mass damage at a certain moment is the initial damage. From this moment onward, the damage that accumulates within the rock mass after each dry-saturation cycle is the cumulative damage, which is the concept of cumulative damage related to the time factor, denoted as D. c ; S4: Numerical calculation of the comprehensive safety factor and cumulative damage analysis to evaluate the stability of the bank slope; Determine the calculation model for cumulative damage variables jointly characterized by wave and electrical parameters: ； In the formula, ; , These are the correction factors mentioned earlier, representing correction factors that take into account test error and those that take into account time accumulation, respectively. The initial damage variable; The rock mass integrity coefficient. ,in, The measured wave velocity of the rock mass Measured P-wave velocity of the rock block; The initial porosity, , Let be the resistivity of the saturated solution. The resistivity of the initial unsaturated rock. The initial saturation; The longitudinal wave velocity (m / s) represents the velocity of the undamaged rock. is the measured sound wave value (m / s) at a certain sampling time; n is a time parameter with a period of one year; Slope stability calculations using the strength reduction method can be performed under cyclic saturation. Wave velocity or resistivity at a specific moment can be measured using acoustic or resistivity testing techniques, allowing for the calculation of instantaneous damage at that moment. The rock mass integrity coefficient, a physical index reflecting rock mass quality and strength, is incorporated into process damage analysis based on an integrity coefficient defined by acoustic velocity. : ； In the formula: Measured wave velocity of the rock mass; Measured P-wave velocity of the rock block; The better the rock integrity, The larger the value of , the better. The value can be selected by combining the range of measured P-wave velocity, joint number, RQD, and other indicators of the rock sample. The larger the value of , the slower the accumulation rate of process damage.

2. The method for evaluating the stability of reservoir bank rock slopes based on the wave electrical properties of rock mass according to claim 1, characterized in that, After determining the rock mass integrity coefficient and structural plane type, the parameters of rock blocks and rock mass are converted based on laboratory tests. The relationship between the deformation modulus of rock mass and rock block: ； Therefore, the strength conversion relationship between rock mass and rock block can be obtained: ； Based on the relationship between resistivity and porosity in the Archie formula, and considering the water saturation of the pores, the correction factor k1 can be calculated based on the measured resistivity, i.e.: ； Based on the GSI scoring standard, the conversion relationship between rock mass and rock block parameters is obtained, namely the generalized HB strength criterion: ； ； ； ； ； GSI stands for Geological Strength Index. The elastic modulus of the rock mass; is the elastic modulus of the rock block; D is the construction disturbance factor, which is taken as 0-1 according to the on-site construction conditions. , are the Hoek-Brown constants for the rock mass and rock block, respectively; s and a are characteristic parameters of the rock mass. and These are the maximum and minimum effective stresses at failure; It represents the uniaxial compressive strength of the rock block.

3. The method for evaluating the stability of reservoir bank rock slopes based on the wave electrical properties of rock mass according to claim 1, characterized in that, Considering the characteristics of the rock mass, an equation describing dynamic damage is established, and a cumulative damage calculation model related to the time factor n is proposed, namely... The calculation formula is as follows: ； ； In the formula: To account for the correction factor for test error; A correction factor is added to account for the cumulative effect over time; The initial damage variable; is the rock mass integrity coefficient; n is a time parameter with a period of one year; It is the process damage variable in the nth cycle; This represents the incremental damage over the process from n to n+1 cycles, used to reflect the dynamic evolution of damage. Under the action of the dry-saturation cycle, all indicators of the rock are in a dynamic state of change. Taking a certain moment when the rock mass is working normally as the starting point, that is... Since acoustic testing can be performed under undisturbed conditions, the initial damage variable of the rock mass can be calculated using the wave velocity expression as follows: ； In the formula: The measured value of the sound wave in m / s at a certain sampling time; The longitudinal wave velocity of the undamaged rock is m / s; The initial damage value can also be determined by other methods. The relationship between the damage factor and porosity of rocks with initial damage is shown in the following formula: ； Therefore, we can conclude that: ； Correction coefficient Determination: Based on the reduction of sound wave velocity by the internal pores of the rock, and using the initial porosity at a certain moment as the basis for calculation, a correction factor was defined. : ； in, To determine the rock porosity, a correction coefficient is further obtained by fitting the data. The range of values ​​for: 。 4. The method for evaluating the stability of reservoir bank rock slopes based on the wave electrical properties of rock mass according to claim 3, characterized in that, The formula for calculating porosity can be obtained using the Archie formula: ； in, Represents the resistivity of a saturated solution. Represents the resistivity of unsaturated rocks. Indicates saturation.

5. The method for evaluating the stability of reservoir bank rock slopes based on the wave electrical properties of rock mass according to claim 1, characterized in that, For cyclically saturated sandstone, the main factors influencing cumulative damage are porosity and saturation, which can be reflected by wave-electric properties. First, using porosity changes as a link, the damage variation law is analyzed, and the wave velocity of the solid matrix of the rock material is calculated using the Gassmann equation. ； In the formula: The bulk modulus of the rock matrix; The shear modulus of the matrix; This represents the matrix density.

6. The method for evaluating the stability of reservoir bank rock slopes based on the wave electrical properties of rock mass according to claim 5, characterized in that, By fitting the logarithmic relationship, the variation of matrix wave velocity with porosity is obtained, satisfying the following equation: ； In the formula: A and B are constants related to the characteristics of the rock sample; In practical engineering, rock masses are often in an unsaturated state. Considering the good stability of acoustic wave testing, the damage variation law during the process can be analyzed based on this empirical formula, thus obtaining the dynamic relationship of acoustic wave velocity: ； ； In the formula: The velocity of sound under n cycles is m / s; Wave velocity under dry conditions; The wave speed under saturation; Dynamic porosity; Dynamic water saturation; , To account for the constant terms of wave velocity in solution and wave velocity in air: ； ； The wave velocity of rock in a dry state depends on the physical and mechanical properties of the matrix and the porosity. The wave velocity in a saturated state also needs to consider the type of pore solution. Based on the Wyllie time-averaged equation and combined with a microstructure equivalent model, the analysis is conducted as follows: It is assumed that the pores are entirely filled with air under dry conditions, and the saturation level... Under saturated conditions, it is assumed that the pores are filled with water. : ； ； In the formula: Indicates the speed of sound waves in the air. m / s; This represents the speed of sound waves in water. m / s.

7. The method for evaluating the stability of reservoir bank rock slopes based on the wave electrical properties of rock mass according to claim 6, characterized in that, Calculation based on wave velocity variation patterns under different cycle numbers Further analysis of damage increment The variation of the time parameter n Finally, considering the time effect, a correction factor is used. Corrections were made for the incremental damage during the process, taking into account the effects of porosity and saturation, to obtain the results for different cycle periods. Calculation formula: ； ； in, It is the process damage variable in the nth cycle; This represents the incremental damage over the process from n to n+1 cycles. Calculation: First, calculate the damage increment: 。 8. The method for evaluating the stability of reservoir bank rock slopes based on the wave electrical properties of rock mass according to claim 7, characterized in that, when At that time, and Substitute get: ； The porosity of the rock mass is relatively low under normal working conditions. To simplify calculations, it is assumed that... Minimum value, ignoring higher-order minima. Simplified to: ； Combination Sure The product of and porosity can be considered a higher-order infinitesimal, which can be ignored, and further simplified to: ； Similarly, it can be calculated : ； Will and Substitution After calculation and simplification, higher-order local minima are omitted. Item, obtained: ； Since the porosity varies with n according to a logarithmic relationship, we assume that: ； In the formula: A and B are fitting coefficients, and A>0, B>0; Substitution have to: ； The time parameter n is a variable parameter, while all other parameters are available. The lossless wave velocity is related to the rock material type; if the rock damage is low, the lossless wave velocity and the matrix wave velocity can be approximated as equal. If the degree of damage is high ,So When performing cumulative damage calculations, it is assumed that the constant term in the denominator is removed. ,Pick The increased damage increment is simplified as follows: ； It is related to the time parameter and reflects the dynamic change pattern of damage increment.

9. The method for evaluating the stability of reservoir bank rock slopes based on the wave electrical properties of rock mass according to claim 7, characterized in that, when At that time, and Substitution calculate: ； Similarly, we do not consider higher-order minima. , omitted The product term is: ； Simplified Calculation formula and resemblance, The calculation formula is also consistent with Similarly, it can be seen that the formula for calculating damage increment can be uniformly used. This indicates; however, when n=1, it is determined by... Calculated This is inconsistent with reality, due to the characteristic point relationships in the logarithmic fitting relationship; based on this, we define: under no loading condition, when the damage increment is less than the initial damage, based on Only by studying cumulative damage can the formula be meaningful; therefore, when calculating the damage increment, take... ; After fitting, the variation of damage increment with time parameters satisfies the power function relationship well: ； In the formula: A and B are fitting coefficients, and 0 <A<1、B> 1; To determine the correction factor First, analyze the relative rate of change of damage increment. The relative rate of change is related to the time parameter. The magnitude of the fitting coefficient in the general formula is taken as... : ； Based on the relative rate of change of damage increment, a correction factor considering the accumulation over time is defined: ； when The time represents the test moment. The damage at this moment can be directly determined from the initial damage, meaning the initial damage can be directly determined using wave-electric testing methods; and conducting... When calculating the cumulative damage afterward, it can be determined Therefore, it can be determined ; Thus, a calculation model for cumulative damage variables that can be jointly characterized by wave-electric parameters was determined: ； in, , .

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