A method for obtaining a structural plane shear strength degradation model considering both seismic abrasion and relative motion speed

Abstract

The application discloses a method for obtaining a structural surface shear strength degradation model considering vibration wear and relative motion speed simultaneously. In view of the fact that the current structural surface strength vibration degradation model has important defects, i.e. exaggerating the influence degree of vibration wear effect influence coefficient and relative motion speed effect influence coefficient on structural surface strength vibration degradation, the application improves the above model based on Barton criterion, and thus proposes a rock mass structural surface shear strength degradation model considering vibration wear and relative motion speed simultaneously, and adopts parameter sensitivity analysis to study the influence law of the peak value of seismic wave, the basic friction angle and roughness coefficient of the structural surface, the influence parameters m and P0 of the structural surface shear strength degradation factor on the slope seismic stability, so as to provide a beneficial reference for the slope seismic stability analysis.

Description

Technical Field

[0001] This invention belongs to the field of rock slope stability analysis technology, specifically relating to a method for obtaining a structural surface shear strength degradation model that simultaneously considers vibration wear and relative motion velocity. Background Technology

[0002] The stability of rock slopes under earthquake loading has been a focus of research and significant progress has been made. The methods have evolved from the initial quasi-static, quasi-dynamic, and Newmark slider displacement methods to dynamic time history analysis methods (including finite element method, meshless method, discrete element method and its coupling methods). The impact of rock mass structural damage during earthquakes, such as the vibration degradation effect of structural surface strength, on the dynamic stability and permanent displacement of slopes has been gradually considered, and fruitful research results have been achieved.

[0003] Although many scholars agree that the impact of earthquake-induced structural surface strength degradation on rock slope stability and permanent displacement should be considered, certain disagreements remain on some important issues due to differences in research methods and focuses. Therefore, it is essential to conduct an in-depth analysis of the current research status, further clarify key issues, and address shortcomings. Current research methods on the structural surface strength characteristics under earthquake loading mainly include two aspects: theoretical research and experimental research.

[0004] Because theoretical models often require many assumptions, the theoretical calculations may not perfectly match the actual measurements. Therefore, many scholars have attempted to establish corresponding degradation models by fitting experimental results from an experimental perspective. Jafari et al. studied the relationship between shear displacement, shear cycles, loading period, stress amplitude, and shear strength through cyclic shear tests, thus establishing a shear strength degradation model. Liu Xinrong et al. also studied the influence of loading cycles, loading rate, and amplitude on the cyclic shear characteristics of structural surfaces through cyclic shear tests, attributing the influence of cyclic loading on structural surfaces to contact effects and damage effects. Subsequently, other scholars have also studied the strength degradation effect of structural surfaces under cyclic shear from the perspective of two different effects. For example, Ni Weida et al. attributed the strength degradation effect of structural surfaces under earthquakes to vibration wear effects and relative velocity effects, and proposed corresponding strength degradation models.

[0005] Current research indicates that while there is a consensus on the vibration degradation effect on structural surface strength, further research is needed to more accurately and reasonably describe its degradation law. The strength degradation criterion proposed by Ni Weida et al. has two problems: ① it exaggerates the influence of vibration wear; ② it exaggerates the influence of relative motion velocity. Therefore, this application aims to improve the strength degradation criterion proposed by Ni Weida et al. to address these issues and propose a more realistic model for the vibration degradation of structural surface strength. Summary of the Invention

[0006] To address the aforementioned problems, this invention proposes a method for obtaining a structural surface shear strength degradation model that simultaneously considers vibration wear and relative motion velocity.

[0007] For the following structural plane shear strength degradation model:

[0008] (6)

[0009] τ(t) is the shear strength of the structural surface, σ n The normal stress acting on the structural surface, The basic friction angle of the structural surface is JRC, and JCS is the surface roughness coefficient and the rock wall compressive strength, respectively; vibration wear influence coefficient η(t):

[0010] (7)

[0011] In the formula: δ(t) is the convergent value of the vibration wear influence coefficient η(t); a is an undetermined coefficient; k(t) is the number of cyclic shearing cycles; the convergent value δ(t) of the vibration wear influence coefficient η(t) is:

[0012] (8)

[0013] In the formula: R0 is the convergence value of δ(t); b is an undetermined coefficient; J(t) is the cyclic shear amplitude; substituting equation (8) into equation (7) yields the vibration wear influence coefficient η(t):

[0014] (9)

[0015] The relative motion velocity influence coefficient γ(t):

[0016] (10)

[0017] In the formula: m is an undetermined coefficient determined by the experiment; P0 is the decay convergence value of γ(t), determined by the experiment; V(t) is the relative motion velocity between the sliding body and the slope at time t; Substituting equations (9) to (10) into equation (6) yields the structural surface shear strength degradation model that simultaneously considers vibration wear and relative motion velocity.

[0018] The beneficial effects of this invention are:

[0019] (1) In view of the important shortcomings of the current structural surface strength vibration degradation model, namely, the influence of vibration wear effect coefficient and relative motion velocity effect coefficient on the structural surface strength vibration degradation, the above model was improved based on the Barton criterion, and a new structural surface shear strength degradation model was proposed.

[0020] (2) A seismic stability analysis model for planar sliding rock slopes considering structural surface strength degradation was proposed. Parameter sensitivity analysis was used to study the influence of peak ground acceleration, basic friction angle and roughness coefficient of the structural surface, and the parameters m and P0 of the structural surface shear strength degradation factor on the seismic stability of the slope. These findings can provide a useful reference for the seismic stability analysis of slopes. Attached Figure Description

[0021] Figure 1 This invention provides a calculation model for the seismic stability of planar sliding rock slopes.

[0022] Figure 2 This is the seismic wave acceleration time history curve of the present invention.

[0023] Figure 3 This invention describes the variation of the slope seismic stability coefficient over time.

[0024] Figure 4 This describes the variation of the influence coefficients η and γ of this invention over time.

[0025] Figure 5 This invention describes the influence of peak ground acceleration on slope seismic stability in an embodiment of the present invention.

[0026] Figure 6 This invention relates to the influence of the basic friction angle of the structural surface on the seismic stability of the slope in an embodiment of the invention.

[0027] Figure 7 This describes the influence of the structural plane JRC on the seismic stability of the slope in an embodiment of the present invention.

[0028] Figure 8 This is the influence law of m on the seismic stability of slope in an embodiment of the present invention.

[0029] Figure 9 This is the influence law of P0 on slope seismic stability in an embodiment of the present invention. Detailed Implementation

[0030] Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0031] The construction process of the seismic stability analysis model for planar sliding rock slopes that considers the strength degradation of rough structural surfaces in this invention is as follows.

[0032] 1. Seismic stability of planar sliding rock slopes based on Barton's criterion

[0033] Currently, there are three main types of commonly used structural shear strength criteria:

[0034] (1) Classical MC criterion applicable to flat structural surfaces

[0035] (1)

[0036] In the formula: τ and σ n These represent the shear strength of the structural surface and the normal stress acting on the structural surface, respectively; c and These are the surface cohesion and friction angle, respectively.

[0037] (2) Applicable to Patton's criterion with obvious shear dilatation.

[0038] (2)

[0039] In the formula: δ is the basic friction angle of the structural surface. n This is the shear dilatation angle; the other parameters are the same as before.

[0040] (3) Barton's criterion applicable to cohesive and rough structural surfaces

[0041] (3)

[0042] In the formula: JRC and JCS are the surface roughness coefficient and the rock wall compressive strength, respectively, and the other parameters are the same as before.

[0043] Since rock mass structural surfaces are typically discontinuous surfaces formed by geological tectonic processes, their cohesion is usually very small and negligible. Natural rock mass structural surfaces are often uneven and have a certain degree of roughness; when subjected to shear forces, they often exhibit dilatation. Therefore, the Patton criterion and the Barton criterion are essentially consistent. However, because the main parameters of the Barton criterion, such as JRC and JCS, are easy to measure in practice, it has been widely used in actual engineering. Therefore, this application uses this criterion to study the seismic stability of planar sliding rock slopes.

[0044] Figure 1 For a planar sliding rock slope with a continuous structural plane, considering only gravity, the static stability coefficient F0 of block ABC based on the Barton strength criterion is:

[0045] (4)

[0046] In the formula: α is the angle between the structural plane AB and the horizontal plane; the other parameters are the same as before.

[0047] This study only considers horizontal seismic forces. Therefore, it is assumed that the slope is subjected to a horizontal seismic wave with acceleration ζ(t)·g (ζ(t) is the seismic acceleration coefficient that varies with time, t is time, and g is the gravitational acceleration, i.e., the seismic wave intensity varies with time) at the center of block ABC. Then its seismic stability coefficient F d for:

[0048] (5)

[0049] Since ζ(t) varies with time, the seismic stability coefficient F of the slope is... d It is also a function of the earthquake action time t.

[0050] 2. Degradation Model of Shear Strength of Structural Surfaces

[0051] From the perspective of earthquake load characteristics, it is both a dynamic load and a cyclic load. Therefore, its impact on the stability of rock slopes is mainly reflected in two aspects: first, it subjectes the slope to dynamic seismic inertial forces that change in real time; second, it subjects the rock mass structural surfaces to cyclic shearing action, leading to varying degrees of degradation or reduction in the shear strength of the structural surfaces. As mentioned earlier, the impact of these two important characteristics of earthquakes on the degradation of structural surface strength is mainly manifested in vibration wear and relative motion velocity. Vibration wear is caused by the cyclic shearing action of the seismic load, which causes repeated shearing on the upper and lower surfaces of the structural surface, resulting in erosion, climbing, and wear effects. This makes the structural surface smoother and flatter, ultimately reducing its shear strength. Therefore, it can be considered that the cyclic shearing action mainly reduces the roughness coefficient (JRC) of the structural surface. The relative motion velocity is mainly due to the velocity effect. Under the influence of gravity, the frictional force generated by the relative motion between the upper and lower surfaces of the structure is static friction. However, since seismic loads are dynamic loads, the frictional force generated by the relative motion between the upper and lower surfaces of the structure caused by an earthquake is dynamic friction. Studies show that the coefficient of dynamic friction is generally lower than the coefficient of static friction; therefore, the existence and magnitude of relative motion velocity also lead to a decrease in the shear strength of the structural surface. In summary, both of these factors contribute to a decrease in the shear strength of the structural surface, and their mechanisms of influence can be considered independent.

[0052] Therefore, this application proposes the following structural shear strength degradation model:

[0053] (6)

[0054] The calculation methods for η(t) and γ(t) are discussed below. First, the vibration wear influence coefficient η(t) is discussed, which is related not only to the number of cyclic shearing cycles but also to the amplitude of the cyclic shearing cycle; therefore, it can be represented by a negative exponential function:

[0055] (7)

[0056] In the formula: δ(t) is the convergence value of the vibration wear influence coefficient; a is an undetermined coefficient; k(t) is the number of cyclic shearing.

[0057] Meanwhile, the convergence value δ(t) is also related to the cyclic shear amplitude, that is:

[0058] (8)

[0059] In the formula: R0 is the convergence value of δ(t); b is the coefficient to be determined; J(t) is the cyclic shear amplitude.

[0060] Substituting equation (8) into equation (7), we can obtain the vibration wear influence coefficient η(t) as follows:

[0061] (9)

[0062] In the formula: a, b and R0 are experimental parameters.

[0063] Secondly, the influence coefficient of relative motion velocity γ(t) is discussed. Since the degree of structural strength degradation decreases exponentially with the absolute value of the relative motion velocity between blocks, that is:

[0064] (10)

[0065] In the formula: m is an undetermined coefficient that can be determined by experiment; P0 is the decay convergence value of γ(t), which is also determined by experiment; V(t) is the relative velocity between the sliding body and the slope at time t.

[0066] Therefore, by substituting equations (9) to (10) into equation (6), we can obtain the structural surface shear strength degradation model.

[0067] 3. Seismic stability of planar sliding rock slopes considering structural surface strength degradation

[0068] The structural shear strength degradation model shown in equation (6) is compared with the seismic stability coefficient F shown in equation (5). dBy combining these factors, the seismic stability coefficient F of a planar sliding rock slope, considering the degradation of structural surface strength, can be obtained. dt for

[0069] (11)

[0070] It can be seen that Equation (11) is the slope seismic stability coefficient expressed by the JRC of the structural surface. It should be noted that although the Barton criterion takes into account the roughness of the structural surface well and provides 10 typical profiles to determine the JRC value of the structural surface, it still has two main problems: ① The determination of JRC is highly subjective. The current determination method mainly relies on the 10 typical profiles given by Barton. However, the structural surfaces in actual engineering vary greatly. Therefore, if only human field identification is used to compare with typical profiles, the results will vary from person to person and produce a large subjective error. ② In actual problems, there may be a situation where JRC>20, which obviously contradicts the application conditions of the Barton criterion. Therefore, the fractal dimension ψ is used to quantitatively characterize the roughness of the crack and establish its functional relationship with JRC, that is:

[0071] (12)

[0072] For a two-dimensional planar structural surface, ψ = 1~2. When ψ = 1, the corresponding structural surface is flat and without roughness. However, as ψ increases, the roughness of the structural surface increases. Therefore, it is proposed to use the fractal dimension ψ to quantitatively characterize the crack roughness. Substituting equation (12) into equation (11) will yield the formula for calculating the slope seismic stability coefficient expressed by the fractal dimension ψ of the structural surface.

[0073] Meanwhile, since earthquakes are dynamic loads, the dynamic stability coefficient F of slopes under earthquake action is... dt Since the stability coefficient is dynamic and changes over time rather than being a constant, it is impossible to provide a general index to evaluate the seismic stability of slopes. Therefore, the minimum average safety factor method is used to calculate the overall stability coefficient F of the slope under seismic loading. z for:

[0074] (13)

[0075] In the formula: F0 is the static stability coefficient, (F dt ) min The minimum value of the time history curve of the dynamic stability coefficient is calculated by equations (4) and (11), respectively.

[0076] 4. Example

[0077] by Figure 1Taking the planar sliding rock slope shown as an example, for ease of theoretical calculation, a sinusoidal wave with an acceleration time history curve of a(t) = λsin(2πft) is used as the input seismic wave, where a(t) is the seismic wave acceleration that varies with time, with amplitude λ = 0.1g, frequency f = 2Hz, and duration t = 10s. The resulting seismic wave acceleration curve is shown below. Figure 2 (Take g = 10 m / s) 2 ), the earthquake acceleration coefficient ζ(t) = 0.1sin(4πt).

[0078] Drawing on the research findings of Ni Weida et al. and considering the actual situation of this embodiment, the calculation parameters are shown in Table 1.

[0079] Table 1 Calculation Parameter Table

[0080]

[0081] Based on the above calculation conditions, the seismic stability coefficient of the planar sliding rock slope can be calculated using the method of this application (e.g., Figure 3 ) and the time-varying patterns of influence coefficients η and γ (e.g. Figure 4 It can be seen that: ① Since seismic waves are sinusoidal waves, their direction of action varies, thus the slope stability coefficient also exhibits a time-varying pattern. This is significantly different from the conclusion that the stability coefficient calculated using the quasi-static method is a constant value. ② By comparing the impact of structural surface strength degradation on the slope stability coefficient, it can be seen that when vibration degradation is not considered, although the slope stability coefficient changes periodically with time, its amplitude remains constant. This is because although the magnitude of the vibration coefficient changes due to different seismic wave directions, the maximum and minimum stability coefficients remain unchanged at 2.52 and 1.52, respectively, because the structural surface strength remains constant. However, when structural surface strength degradation is considered, with the action of seismic waves, on the one hand, the cyclic shearing and abrasion of the seismic waves causes the structural surface protrusions to be sheared off, reducing the structural surface strength; on the other hand, the velocity effect generated by the dynamic load characteristics of the seismic waves causes the structural surface friction coefficient to change from static friction to dynamic friction, thus reducing the shear strength of the structural surface. Due to the effects of these two aspects, the slope seismic stability coefficient gradually decreases with the duration of the seismic action. During the first seismic wave cycle, the maximum and minimum stability coefficients were 2.08 and 1.15, respectively. However, when the seismic wave action ended at 10 seconds, the maximum and minimum stability coefficients were 1.92 and 1.06, respectively, representing a decrease of 7.69% and 6.0%. This indicates that when considering the structural surface strength vibration degradation, the slope seismic stability coefficient gradually decreases, which is consistent with actual laws. ③ To give the overall stability coefficient of the slope under seismic action, equation (13) is used for calculation. From equation (4), the static stability coefficient of the slope F0 = 1.91 can be obtained, and from... Figure 3 We can obtain (F) dt ) min =1.06, from which the overall stability coefficient F of the slope under seismic loading can be obtained. z =1.36. This indicates that the slope was generally stable under the action of this seismic wave. ④ To compare with the method of Ni Weida et al., Figure 3 The calculation results of the method by Ni Weida et al. are also presented. It can be seen that the slope seismic stability coefficients calculated by the method in this paper at different times are all greater than the corresponding calculation results of the method by Ni Weida et al. This is because the method by Ni Weida et al. exaggerates the influence of relative motion velocity, thus leading to an underestimation of the slope seismic stability coefficient. Here, the overall slope stability coefficient F is taken as... z By comparison, it can also be obtained from equation (13) that the F of the method of Ni Weida et al. z =1.29, and as mentioned above, the overall slope stability coefficient F obtained by the method in this application is... z =1.36, which shows that the calculation results of Ni Weida et al.'s method are too low. ⑤ From Figure 4 The variation patterns of the vibration wear influence coefficient η and the relative velocity influence coefficient γ over time show that η decreases approximately linearly with the duration of seismic wave action, gradually decreasing from an initial value of 1 to 0.907, a decrease of 9.3%. This indicates that the cyclic shearing action of the earthquake causes reciprocating vibration wear on the structural surface, reducing the surface roughness and ultimately leading to a decrease in its shear strength. γ also shows a gradual decreasing trend with the increase of seismic wave action time, with its maximum and minimum values ​​decreasing from the initial 1 and 0.6947 to 0.9994 and 0.6921, respectively, a decrease of 0.06% and 0.26%, indicating a relatively small decrease. As shown in equation (10), the decrease is significantly related to the relative velocity between the sliding body and the slope, as well as parameters such as m and P0.

[0082] 5. Parameter sensitivity analysis

[0083] As can be seen from equation (11), there are many calculation parameters that affect the seismic stability of slopes. In order to explore the influence of each calculation parameter, parameter sensitivity analysis is used to study its influence on the seismic stability of slopes. In the process of parameter sensitivity analysis, only one parameter is changed each time.

[0084] (1) Seismic wave parameters

[0085] Since the peak ground acceleration of seismic waves has a significant impact on slope stability, this paper focuses on discussing its influence.

[0086] First, the peak ground acceleration coefficients λ are taken as 0.05g, 0.1g, 0.15g, and 0.2g, respectively. The corresponding slope seismic stability coefficients are as follows: Figure 5 . Figure 5 (a) shows the variation of the slope seismic stability coefficient over time. Figure 5 (b) shows the variation of the slope seismic stability coefficient with peak ground acceleration (PGA). It can be seen that: ① From the perspective of the range of slope stability coefficient variation, as the PGA increases, the upper and lower limits of the slope stability coefficient gradually widen. When λ increases from 0.05g to 0.1g, 0.15g, and 0.2g respectively, the range of slope stability coefficient changes from 1.36~1.96 to 1.06~2.08, 0.89~2.27, and 0.77~2.57. This indicates that as the PGA increases, the seismic wave intensity increases, and therefore, as the direction of seismic wave action changes, the range of slope stability coefficient also widens. ② From the perspective of the trend of the overall slope stability coefficient variation, when λ increases from 0.05g to 0.1g, 0.15g, and 0.2g respectively, the overall slope stability coefficient F... z The slope stability coefficient decreased from 1.55 to 1.36, 1.25, and 1.17 respectively, indicating that the slope stability coefficient gradually decreased with the increase of peak ground acceleration, which is consistent with the basic law of slope seismic stability change. Furthermore, the rate of decrease was 12.42%, 7.77%, and 6.38% respectively, showing a gradually decreasing rate of reduction.

[0087] (2) Structural surface parameters

[0088] This section mainly discusses the basic friction angle of structural surfaces. The influence of roughness coefficient JRC on slope seismic stability.

[0089] First, determine the basic friction angle of the structural surface. The slope seismic stability coefficients for angles of 10°, 20°, 30°, and 40° are as follows: Figure 6 . Figure 6 (a) shows the variation of the slope seismic stability coefficient over time. Figure 6 (b) shows the variation of the slope seismic stability coefficient with the fundamental friction angle of the structural surface. It can be seen that: ① From the perspective of the variation range of the slope stability coefficient, as the fundamental friction angle of the structural surface increases, the overall trend of the slope stability coefficient is increasing, and its upper and lower limits are gradually widening. When the angle of inclination increases from 10° to 20°, 30°, and 40°, the range of slope stability coefficient changes from 0.73~1.44 to 1.06~2.08, 1.51~2.95, and 2.19~4.33, respectively. This indicates that as the basic friction angle of the structural surface increases, the shear strength of the slope increases, and its resistance to sliding improves, thus widening the range of slope stability coefficient. ② From the trend of the overall slope stability coefficient, when... The overall slope stability coefficient F for angles of 10°, 20°, 30° and 40° respectively. z The coefficients increase from 1.14 to 1.36, 1.65, and 2.09 respectively, indicating that the slope stability coefficient gradually increases with the increase of the basic friction angle of the structural surface, which is consistent with current theoretical results. Furthermore, the rate of increase is 18.77%, 21.55%, and 26.79% respectively, showing a gradually increasing rate of increase.

[0090] Secondly, the influence of the surface roughness coefficient (JRC) on slope stability is studied. Since the JRC in this application is calculated using the fractal dimension of the surface, the fractal dimension of the surface is given first, and then the corresponding JRC is obtained through inverse calculation. Therefore, the JRC obtained through inverse calculation is usually not an integer. Because the fractal dimension of a typical surface is between 1.00 and 1.08, we take fractal dimensions of 1.01, 1.03, 1.05, and 1.07, respectively. Correspondingly, the JRC values ​​are 6.24, 11.64, 15.56, and 18.83, and the corresponding slope seismic stability coefficients are as follows: Figure 7 . Figure 7 (a) shows the variation of the slope seismic stability coefficient over time. Figure 7 (b) shows the variation of the slope seismic stability coefficient with the structural plane JRC. It can be seen that: ① From the perspective of the range of slope stability coefficient variation, as the structural plane JRC increases, the overall trend of the slope stability coefficient is increasing, and its upper and lower limits gradually widen. When JRC increases from 6.24 to 11.64, 15.56, and 18.83 respectively, the range of slope stability coefficient changes from 1.06~2.08 to 1.95~4.11, 3.36~8.12, and 6.91~28.44. This indicates that as the structural plane JRC increases, the slope shear strength increases, and the resistance to sliding improves; therefore, the range of slope stability coefficient also widens. ② From the perspective of the trend of the overall slope stability coefficient variation, when JRC increases from 6.24 to 11.64, 15.56, and 18.83 respectively, the overall slope stability coefficient F... z The coefficients increased from 1.36 to 1.94, 2.85, and 5.16 respectively, meaning that the slope stability coefficient gradually increases with the increase of the structural surface JRC, which is consistent with current theoretical results. Furthermore, the increase rates were 42.62%, 47.34%, and 80.89% respectively, indicating a gradually increasing rate of increase. ③ From Figure 7As shown in (a), the slope stability coefficient changes rapidly with increasing JRC as the seismic wave action time increases. For example, when JRC=18.83, the slope stability coefficient decreases rapidly from the initial 26.91 as the seismic wave action time increases, and the decrease is relatively large in the initial stage. It is believed that since this application considers the structural surface strength degradation caused by seismic action, for rough structural surfaces, the strength degradation is mainly caused by vibration wear of the structural surface. In the initial stage, the vibration wear of the structural surface is very significant, and therefore the stability decrease is also the most significant. This is consistent with the research conclusions of other scholars.

[0091] (3) Parameters affecting the shear strength degradation factor of structural surfaces

[0092] In this application, the parameters influencing the shear strength degradation factor of the structural surface include five parameters: a, b, R0, m, and P0, all of which have a certain influence on the seismic stability of the slope. Theoretical analysis and trial calculations revealed that m and P0 have a relatively large impact on the calculation results; therefore, this paper focuses on discussing their influence on the seismic stability of the slope.

[0093] First, the influence of m on slope stability is studied. Here, m is taken as 10, 15, 20, and 25, and the corresponding slope seismic stability coefficients are as follows: Figure 8 . Figure 8 (a) shows the variation of the slope seismic stability coefficient over time. Figure 8 (b) shows the variation of the slope seismic stability coefficient with m. It can be seen that: ① From the perspective of the range of the slope stability coefficient, as m increases, the overall trend of the slope stability coefficient is decreasing, and its upper and lower limits gradually narrow. When m increases from 10 to 15, 20, and 25 respectively, the range of the slope stability coefficient changes from 1.06~2.08 to 0.99~1.94, 0.95~1.83, and 0.93~1.75. This indicates that as m increases, the range of the slope stability coefficient also narrows, and the stability gradually decreases. ② From the perspective of the trend of the overall slope stability coefficient, when m increases from 10 to 15, 20, and 25 respectively, the overall slope stability coefficient F... z The slope stability coefficient decreased from 1.36 to 1.31, 1.29, and 1.27 respectively, meaning that the slope stability coefficient gradually decreased as m increased. Furthermore, the rate of decrease was 3.35%, 1.98%, and 1.01% respectively, indicating that the rate of decrease gradually decreased.

[0094] Secondly, the influence of P0 on slope stability is studied. Here, P0 is set to 0.2, 0.4, 0.6, and 0.8, and the corresponding slope seismic stability coefficients are as follows: Figure 9 . Figure 9(a) shows the variation of the slope seismic stability coefficient over time. Figure 9 (b) shows the variation of the slope seismic stability coefficient with P0. It can be seen that: ① From the perspective of the range of change of the slope stability coefficient, as P0 increases, the overall trend of the slope stability coefficient is increasing, and its upper and lower limits are gradually narrowing. When P0 increases from 0.2 to 0.4, 0.6, and 0.8 respectively, the range of change of the slope stability coefficient changes from 0.60~1.65 to 0.83~1.87, 1.06~2.08, and 1.29~2.29. This indicates that as P0 increases, the range of change of the slope stability coefficient also narrows, but the stability gradually increases. ② From the perspective of the trend of change of the overall slope stability coefficient, when P0 increases from 0.2 to 0.4, 0.6, and 0.8 respectively, the overall slope stability coefficient F... z The coefficients increase from 1.06 to 1.21, 1.36, and 1.51 respectively, meaning that the slope stability coefficient gradually increases with the increase of P0. Furthermore, the rate of increase is 14.12%, 12.38%, and 11.01% respectively, indicating that the rate of increase gradually decreases, but the magnitude is not large, and the increase is approximately linear.

[0095] In summary, the study found that as the peak ground acceleration (PGA) and velocity (m) of the seismic wave increase, the seismic stability of the slope decreases, while the basic friction angle of the structural surface, the roughness coefficient, and P0 have the opposite effect on the seismic stability of the slope. These findings can provide a useful reference for the analysis of slope seismic stability.

[0096] Although the above embodiments have been shown and described, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Any changes, modifications, substitutions and variations made to the above embodiments by those skilled in the art are within the protection scope of the present invention.

Claims

1. A method for obtaining a structural surface shear strength degradation model that simultaneously considers vibration wear and relative motion velocity, characterized in that, For the following structural plane shear strength degradation model: （6） τ(t) is the shear strength of the structural surface, σ n The normal stress acting on the structural surface, JRC and JCS are the basic friction angle of the structural surface, respectively, and the roughness coefficient of the structural surface and the compressive strength of the rock wall. Vibration wear influence coefficient η(t): （7） In the formula: δ(t) is the convergence value of the vibration wear influence coefficient η(t); a is an undetermined coefficient; k(t) is the number of cyclic shearing cycles; The convergence value δ(t) of the vibration wear influence coefficient η(t): （8） In the formula: R0 is the convergence value of δ(t); b is the coefficient to be determined; J(t) is the cyclic shear amplitude; Substituting equation (8) into equation (7), we obtain the vibration wear influence coefficient η(t) as follows: （9） The relative motion velocity influence coefficient γ(t): （10） In the formula: m is an undetermined coefficient determined by experiments; P0 is the decay convergence value of γ(t), determined by experiments; V(t) is the relative velocity between the sliding body and the slope at time t; Substituting equations (9) to (10) into equation (6) yields a structural surface shear strength degradation model that simultaneously considers vibration wear and relative motion velocity.

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