A method for determining a sliding surface of a non-penetrating interlayer rock slope

Abstract

The application discloses a kind of containing non-through interlayer rock slope slip surface determination method, belong to geotechnical engineering and geological disaster prevention and control technical field, including by step 1, determine the basic parameters of rock slope and the parameter of non-through interlayer of slope;Step 2, establish the geometric model of rock slope, analyze the potential sliding surface of slope;Step 3, the sliding block is divided into three parts.Step 4, establish the expression of interaction force by solving balance equation;Step 5, by derivation and let derivative equal to zero, determine the inclination of lower slide surface and upper slide surface, and then the projection length in horizontal direction can be determined.The method of the application can effectively determine the slip surface of the non-through interlayer rock slope, provide a scientific basis for the design and stability analysis of slope engineering, only need to clarify the most common geotechnical parameters, the slip surface of non-through interlayer rock slope can be determined, the process is simple, and the prediction result is reliable.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of geotechnical engineering and geological disaster prevention and control, and particularly relates to a method for determining a sliding surface of a rock slope containing a non-penetrating interlayer. BACKGROUND

[0002] The stability of rock slope is a research hotspot in geotechnical engineering, geological engineering, water conservancy engineering and the like. In nature and human engineering activities, the instability of rock slope can cause serious economic loss and environmental damage, and even threaten the safety of human life, so it is of great significance to study the stability of rock slope. Finding a potential sliding surface is one of the core steps of slope stability analysis. However, the existing method for determining the sliding surface of rock slope containing a non-penetrating interlayer still has some defects. The existing method for determining the sliding surface does not systematically calculate the sliding surface in blocks and independently calculate the stability coefficients of each part, and analyze and search the potential sliding surface. Therefore, a method for determining the sliding surface of rock slope containing a non-penetrating interlayer is proposed. The present application provides a new theoretical tool and analysis method for the field of rock slope stability analysis, which helps to improve the accuracy of the determination of the sliding surface and the reliability of the engineering application. SUMMARY

[0003] The technical problem to be solved by the present application is to provide a method for determining the sliding surface of rock slope containing a non-penetrating interlayer, which can determine the inclination and length of the sliding surface and represent the position of the potential sliding surface by the inclination of the sliding surface, based on the rock mass cohesion c1, friction angle interlayer cohesion c2, internal friction angle rock mass specific gravity γ, slope angle α, slope height h, and interlayer inclination θ2. The method is simple and practical, and can provide a reference for determining the sliding surface of the slope in actual engineering, predict the occurrence of landslide, and minimize the loss.

[0004] In order to solve the above technical problem, the method for determining the sliding surface of rock slope containing a non-penetrating interlayer comprises the following steps:

[0005] S1, based on historical data, geological data investigation report and field measurement analysis, the basic parameters of rock slope and the geological parameters of weak interlayer of the slope are obtained, and according to Mohr-Coulomb failure criterion, the stability coefficient expression of three sliding blocks is as follows:

[0006]

[0007]

[0008] Among them, Fs1, F S2 and F S3 are the stability coefficients of the lower, middle and upper three sliding blocks, c1, c2 represents the cohesion and internal friction angle of the rock mass. Let l1, l2, and l3 represent the cohesion and internal friction angle of the interlayer, respectively, and l1, l2, and l3 represent the sliding surface lengths of the lower, middle, and upper sliders, respectively. Let θ1, θ2, and θ3 represent the inclination angles of the lower, middle, and upper sliding surfaces, respectively.

[0009] S2. Based on the equilibrium equations, derive the expressions for the interaction forces F1, F2, P1, and P2;

[0010] S3. Solving for the minimum values ​​of Fs1 and Fs3 and combining them with the slope parameters, we can obtain θ1, θ3, x1 and x3; where θ1 is the tilt angle of the lower slider, θ3 is the tilt angle of the upper slider, x1 is the horizontal projection length of the lower sliding surface, and x3 is the horizontal projection length of the upper sliding surface.

[0011] Because this invention uses rigorous mathematical formulas to solve for the slip surface of rock slopes containing non-penetrating interlayers, it provides an accurate reference for preventing the instability of such slopes. Therefore, the advantages of this invention are: it proposes a simple and practical method for determining the slip surface of rock slopes containing non-penetrating interlayers, and the parameters involved are easily determined.

[0012] Compared with the prior art, the beneficial effects of the present invention are:

[0013] 1. By comprehensively considering the specific physical and mechanical properties of the soil and rock mass and the geometric characteristics of the slope, and combining the Mohr-Coulomb failure criterion, this invention can more accurately assess landslide risk and improve the scientificity and accuracy of prediction.

[0014] 2. This invention proposes a detailed geometric model for rock slopes containing non-penetrating weak interlayers. This model considers the physical properties of the rock mass, the geometric layout of the weak interlayers and their impact on slope stability, thus providing a more accurate theoretical basis for determining the slope slip surface.

[0015] 3. By dividing the sliding surface into three parts—lower, middle, and upper—and calculating the stability coefficient of each part separately, this invention provides a more detailed and systematic stability analysis method, which helps to more accurately assess the stability of slopes.

[0016] 4. This invention obtains the inclination angles θ1 and θ3 of the sliding surface by solving an optimization problem, providing an accurate method for determining the potential sliding surface of a slope, which helps to improve the accuracy and safety of slope engineering design. Attached Figure Description

[0017] The accompanying drawings of this invention are described below:

[0018] Figure 1 This is a two-dimensional model diagram of the slope according to the present invention;

[0019] Figure 2 Flow chart for the method of determining the slip surface;

[0020] Figure 3 Analysis diagram for the slope geometry mathematical model;

[0021] Figure 4 Analysis diagram for the lower sliding block geometry mathematical model;

[0022] Figure 5 Analysis diagram for the upper sliding block geometry mathematical model;

[0023] Figure 6 Schematic diagram for the numerical simulation boundary condition;

[0024] Figure 7 Discrete element model diagram for the numerical simulation;

[0025] Figure 8 Stability analysis result diagram for the numerical simulation;

[0026] Figure 9 Slope failure result schematic diagram for the numerical simulation; DETAILED DESCRIPTION

[0027] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative work fall within the scope of protection of the present application.

[0028] EMBODIMENT

[0029] Please refer to Figures 1-9 The present application provides a technical solution comprising the following steps:

[0030] The present application will be further described in combination with the drawings:

[0031] S1, a representative non-penetrating interlayer rock slope is selected as the analysis object, such as Figure 1 As shown, the specific parameters of the slope are determined, that is, the rock mass cohesion c1, internal friction angle Interlayer cohesion c2, internal friction angle The rock mass weight γ, slope angle α, rock slope height h, interlayer dip angle θ2, the red line is the potential sliding surface when the slope fails as a whole, and the blue line represents the interlayer with a dip angle of θ2. When the slope fails locally, the potential sliding surface develops along the interlayer. The projection lengths of the lower and upper sliding surfaces in the horizontal direction are x1 and x3, and the dip angles of the lower and upper sliding surfaces are θ1 and θ3, respectively. The projection lengths of the lower and upper sliding surfaces in the vertical direction are h4 and h3, respectively. Other parameters such as h1, h2, and x4 are related to the position of the interlayer and can be obtained through geological information.

[0032] S2, according to the Mohr-Coulomb failure criterion:

[0033]

[0034]

[0035] The stability coefficients of the three sliding blocks are obtained.

[0036] wherein G1, G2 and G3 are the weights of the lower, middle and upper sliding blocks, respectively. F1 is the thrust of the middle sliding block on the lower sliding block, and F2 is the pull of the middle sliding block on the upper sliding block. P1 is the vertical force of the middle sliding block on the lower sliding block, and P2 is the vertical force of the middle sliding block on the upper sliding block. The anti-sliding forces of the rock mass on the lower, middle and upper sliding blocks are f1, f2 and f3, respectively. The support forces of the rock mass on the lower, middle and upper sliding blocks are F N1 , F N2 and F N3 , respectively. l1, l2 and l3 are the lengths of the sliding surfaces of the lower, middle and upper sliding blocks, respectively. O is the midpoint of the weak interlayer. O1 and O2 are the positions of the points of action of the mutual forces between the three sliding blocks. c1, is the cohesion and friction angle of the rock mass, and c2, is the cohesion and friction angle of the interlayer.

[0037] S3, the thrust F1 of the middle sliding block on the lower sliding block, the vertical force P1 of the middle sliding block on the lower sliding block, the pull F2 of the middle sliding block on the upper sliding block, and the vertical force P2 of the middle sliding block on the upper sliding block can be determined by the following balance equations.

[0038]

[0039] S4, the expressions of F1, P1, F2 and P2 can be expressed as:

[0040]

[0041]

[0042] wherein G1, F N1 , F1 and the distance from F1 to O1 are defined as LO1G1 , L O1FN1 , L O1f1 . The distances from G3, F N3 and f3 to O2 are L O2G3 , L O2FN3 , L O2f3 .

[0043] S5, the stability factor F S1 can be expressed as a function of θ1 and some slope parameters, i.e.:

[0044]

[0045] Taking the derivative of F S1 with respect to θ1 and setting it equal to zero gives:

[0046]

[0047] The dip angle of the lower slide surface θ1 is expressed in terms of the slope parameters as:

[0048]

[0049] Once the slope parameters for θ1 are determined, θ1 can be easily calculated. Similarly, the stability factor F S3 can be expressed as a function of θ3 and some slope parameters, i.e.:

[0050]

[0051] Taking the derivative of F S3 with respect to θ3 and setting it equal to zero gives:

[0052]

[0053] The dip angle of the upper slide surface θ3 is expressed in terms of the slope parameters as:

[0054]

[0055] Once the slope parameters for θ3 are determined, θ3 can be easily calculated. The stability factor F S2 can be expressed as a function of θ1 and θ3, i.e.:

[0056]

[0057] Once θ1 and θ3 are determined,

[0058]

[0059] The detailed expressions for F s1, F

[0060] s2, and F s3 are:

[0061] in,

[0062]

[0063]

[0064] in,

[0065]

[0066] Slope geometric model such as Figure 1 As shown, discrete element method (DEM) software was used to analyze the slope stability. The model dimensions were designed to be 908×250×700 (mm). The slope angle and height were 60° and 700 mm, respectively. The dip angle and length of the interlayer were θ2=38° and l2=0.6m, respectively. The unit weight of the soil and rock in the model slope was γ=22.416kN / m. 3 Cohesion c1 = 16.79 kPa, internal friction angle Interlayer cohesion c2=0kPa, internal friction angle

[0067] S1. Assuming the inclination angles of the sliding surfaces of the lower and upper sliders are θ1 and θ3, according to the formula:

[0068]

[0069] Find the expressions for Fs1, Fs2, and Fs3. S2. Characterize the slider parameters using θ1 and θ3:

[0070]

[0071] S3. According to the formula:

[0072]

[0073]

[0074] The interaction forces F1, F2, P1, and P2 are determined to be 348.580 kN, 14.744 kN, 187.990 kN, and 24.093 kN, respectively.

[0075] S4. According to the formula:

[0076]

[0077] The dip angles of the lower and upper slip surfaces were determined to be 8.74° and 87.36°, respectively.

[0078] S5. According to the formula:

[0079]

[0080] The stability coefficient Fs2 is determined as 0.681.

[0081] S6, according to Figure 8 The numerical simulation analysis result shows that the slope stability coefficient is 0.69, and it is judged that the slope of the embodiment is damaged along the interlayer.

[0082] S7, according to Figure 9 The numerical simulation block displacement result shows that the lower sliding surface inclination angle θ1 is 8.4°, and the upper sliding surface inclination angle θ3 is 84.3°.

[0083] S8, the method of the application and the numerical simulation result are compared in Table 1:

[0084] Table 1 compares the calculation results of the embodiment

[0085]

[0086]

[0087] As shown in Table 1, the calculation results of the method of the application are close to the results obtained by numerical simulation, indicating that the method of the application is reliable in application.

[0088] In the present example, specifically: in the S3, if the basic parameters of the rock sample, the rock mass cohesion c1, the internal friction angle The interlayer cohesion c2, the internal friction angle The rock mass gravity γ, the slope angle α, the self-weight G1, G2 and G3 of the lower, middle and upper sliding blocks, the vertical force P1 of the middle sliding block on the lower sliding block, and the vertical force P2 of the middle sliding block on the upper sliding block; based on the limit equilibrium method, according to the stability coefficient definition, the slope failure complies with the Mohr-Coulomb failure criterion, and the stability coefficients of the three sliding blocks can be expressed as:

[0089]

[0090] In the present example, specifically: in the S4, according to the balance equation, the expressions of the interaction forces F1, F2, P1 and P2 can be obtained:

[0091] The balance equation is expressed as:

[0092]

[0093] According to Figure 4 , Figure 5 The expressions of F1, F2, P1 and P2 are obtained according to the geometric relationship and Mohr-Coulomb criterion:

[0094]

[0095] In this example, specifically: in the S5, the corresponding θ1, θ3, x1 and x3 of the slope slip:

[0096] According to F S1 The relationship between θ1 and F S3 The relationship between θ3 and F, the minimum value of F S1 The expression of the lower sliding surface inclination angle θ1 and the minimum value of F S3 The expression of the upper sliding surface inclination angle θ3 corresponding to the minimum value of F

[0097]

[0098] According to the geometric relationship between the sliding surface inclination angle and the horizontal projection, the expressions of x1 and x3 are obtained as follows:

[0099]

[0100]

[0101] The formula solves the problem that the sliding surface determination method of the rock slope containing a non-penetrating interlayer is difficult to determine.

[0102] Working principle: Through the survey report and other data, the specific parameters of the slope and its interlayer are determined. This method establishes a geometric model of the rock slope, analyzes the potential sliding surface of the slope, and considers the influence of the weak interlayer on the stability of the slope. First, the sliding block is divided into three parts, and the stability coefficients Fs1, Fs2 and Fs3 of the lower, middle and upper sliding blocks are calculated respectively. The stability coefficient is defined as the ratio of the anti-sliding force to the sliding force acting on the potential sliding surface. Through the Mohr-Coulomb criterion, combined with the cohesion and friction angle of the rock mass and the weak interlayer, and the length of the sliding surface, the force balance equation is established, and the expressions of the thrust F1, the tension F2, the vertical force P1 and P2 are obtained. Further, by taking the derivative and setting the derivative equal to zero, the inclination angles θ1 and θ3 of the lower and upper sliding surfaces are determined. Once the slope parameters are determined, θ1 and θ3 can be easily calculated, and the projection lengths x1 and x3 in the horizontal direction are obtained. This method describes the derivation process of F1, P1, F2 and P2 in detail, and provides specific calculation results of Fs1, Fs2 and Fs3. The method of the present application can effectively determine the sliding surface of the rock slope containing a non-penetrating weak interlayer, and provide a scientific basis for the design and stability analysis of slope engineering. Although embodiments of the present application have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and variations can be made to these embodiments without departing from the principles and spirit of the present application, and the scope of the present application is defined by the appended claims and their equivalents.

[0103] The above describes the present application and its embodiments, which are not limited, and the drawings only show one of the embodiments of the present application, and the actual structure is not limited thereto. In general, if a person skilled in the art is inspired thereby, without departing from the purpose of the present application, without creative design, similar structure and embodiments of the technical solution are not creative, and should belong to the protection scope of the present application.

Claims

1. A method for determining the slip surface of a rock slope containing non-penetrating interlayers, characterized in that, Includes the following steps: S1. Based on the geological survey report and field measurement analysis, the basic parameters of the rock slope and the geological parameters of the non-continuous interlayers of the slope were obtained; including rock mass cohesion. c 1. Angle of friction within the rock mass φ 1. Interlayer cohesion c 2. Angle of friction within the interlayer φ 2. Rock mass γ slope angle α slope height h interlayer dip angle θ 2; S2. Establish a geometric model of the rock slope and analyze the potential sliding surface of the slope; S3. Using the basic parameters of the rock slope obtained above, establish a planar analysis model, divide the slider into three parts: lower, middle, and upper. Based on the Mohr-Coulomb failure criterion, express the stability coefficient of the three sliders using a function. F s1、 F s2 and F s3; S4. Determine the interaction forces based on the equilibrium equations. F 1. F 2. P 1 and P The expression for 2; where F 1 represents the pushing force of the middle slider on the lower slider. F 2 represents the pulling force of the middle slider on the upper slider. P 1 represents the vertical force exerted by the middle slider on the lower slider. P 2 represents the vertical force exerted by the middle slider on the upper slider; S5. Solving the analytical solution for the slip surface. F s1、 F The minimum value of s3 can be obtained by combining it with slope parameters. θ 1. θ 3, x 1 and x 3; in, θ 1 represents the tilt angle of the sliding block. θ 3 The tilt angle of the upper slider. x 1 represents the horizontal projection length of the lower sliding surface. x 3 represents the horizontal projection length of the upper sliding surface; In S5, θ 1. θ 3, x 1 and x 3. The specific calculation steps are as follows: Stability coefficient of the lower slider It can be expressed as a pair θ 1 and some slope parameters are functions, namely: ， Pick right θ Taking the derivative of 1 and setting it to 0, we get: ， Slide θ The inclination angle of 1 is expressed according to the slope parameters as follows: ， Once determined θ The slope parameters of 1 can be obtained. θ The result of 1; similarly, the stability coefficient of the upper slider. It can be expressed as a pair θ 3 and some slope parameters are functions, namely: ， Pick F S3 right θ Taking the derivative of 3 and setting it to 0, we get: ， Inclination of the upper surface θ 3. Based on the slope parameters, it can be expressed as follows: ， Once determined θ The slope parameters of 3 can be obtained. θ The result of 3; Stability coefficient of the intermediate slider It can be expressed as a pair θ 1 and θ A function of 3, namely: ， Once determined θ 1 and θ 3, x 1 and x 3 can be easily calculated: ， ， The above F s1、 F s2、 F The detailed expression for s3 is: ， in, , l 1 represents the length of the lower sliding surface; ， ， in, ， ， 。 2. The method for determining the slip surface of a rock slope containing non-penetrating interlayers as described in claim 1, characterized in that: The failure mode of the non-penetrating interlayered rock slope in S2 is planar sliding failure, which divides the slider into three parts: lower, middle and upper.

3. The method for determining the slip surface of a rock slope containing non-penetrating interlayers as described in claim 1, characterized in that: In S3, if the basic parameter representing the rock sample, rock mass cohesion, is known... c 1. Angle of internal friction φ 1. Interlayer cohesion c 2. Angle of internal friction φ 2. Rock mass γ slope angle α The weight of the lower, middle, and upper sliders G 1. G 2 and G 3. The vertical force exerted by the middle slider on the lower slider P 1. Vertical force exerted by the middle slider on the upper slider P 2. Based on the limit equilibrium method and according to the definition of the stability coefficient, the slope failure follows the Mohr-Coulomb failure criterion, and the stability coefficients of the three sliders can be expressed as: ， ， ， in, l 1. l 2 and l 3 represents the length of the sliding surface corresponding to the lower, middle, and upper sliders, respectively.

4. The method for determining the slip surface of a rock slope containing non-penetrating interlayers as described in claim 1, characterized in that: In S4, the pushing force of the middle slider on the lower slider F 1. The vertical force exerted by the middle slider on the lower slider P 1. The pulling force of the middle slider on the upper slider F 2. The vertical force exerted by the middle slider on the upper slider P 2 can be determined by the following equilibrium equations. ， The specific calculation process is as follows: ， ， ， Anti-skid force f 1 can be represented as: ， The coordinates of the lower endpoint of the interlayer can be expressed as: ， ， Assume the coordinates of the shear exit of the glide slope are ( x i , y i According to geometric relationships, we can obtain: ， ， ， ， x The expression for 1 is: ， As can be seen from the two-dimensional model diagram of the slope, the lower slider S The weight of 1 is: ， And the length of the lower sliding surface l 1 can be represented as: ， f The expression for 1 is: ， The supporting force of the rock mass on the lower slider is F N1 , F N1 The expression is: ， P The expression for 1 is: ， F The expression for 1 is: ， According to the equilibrium equations for the upper slider, we have: ， ， ， Anti-skid force f The expression for 3 is: ， The weight of the upper slider G The expression for 3 is: ， And the length of the upper sliding surface l 3 can be represented as: ， f The expression for 3 is: ， The supporting force of the rock mass on the upper slider is F N3， F N3 The expression is: ， P The expression for 2 is: ， F The expression for 2 is: ， Therefore, the calculation is... F 1, F 2, P 1 and P The expression for 2 is: ， ， ， ， in G 1 to O The distance of 1 is defined as L O1G1 ;from G 3 to O The distance of 2 is L O2G3 .

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