Method for determining slip crack surface of rock slope containing non-through interlayer

Abstract

The invention discloses a slip crack surface determination method for a rock slope containing a non-through interlayer, and belongs to the technical field of geotechnical engineering and geological disaster prevention and control, and the slip crack surface determination method comprises the following steps: step 1, determining basic parameters of the rock slope and parameters of the non-through interlayer of the slope; 2, establishing a geometric model of the rock slope, and analyzing a potential sliding surface of the slope; and step 3, dividing the sliding block into three parts. And 4, establishing an equilibrium equation, and solving to obtain an expression of the interaction force. And step 5, determining the inclination angle of the lower sliding surface and the upper sliding surface through derivation and making the derivative equal to zero, and further determining the projection length in the horizontal direction. According to the method, the slip crack surface containing the non-through interlayer rock slope can be effectively determined, a scientific basis is provided for design and stability analysis of slope engineering, the slip crack surface of the non-through interlayer rock slope can be determined only by determining the most common rock-soil body parameters, the process is simple, and the prediction result is reliable.

Description

Technical Field

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

[0002] The stability of rock slopes is a hot topic in geotechnical engineering, geological engineering, water conservancy engineering and other engineering projects. In nature and human engineering activities, the instability of rock slopes may lead to serious economic losses and environmental damage, and even threaten human life safety. Therefore, it is of great significance to study the stability of rock slopes. Finding potential sliding surfaces is one of the core steps in slope stability analysis. However, the existing sliding surface determination method technology for rock slopes with non-penetrating interlayers still has certain defects. The existing sliding surface determination method does not systematically divide the sliding surface into blocks, and independently calculate the stability coefficient of each part, and analyze and search for potential sliding surfaces. To this end, a sliding surface determination method for rock slopes with non-penetrating interlayers is proposed. It provides new theoretical tools and analysis methods for the field of rock slope stability analysis, which helps to improve the accuracy of sliding surface determination and the reliability of engineering applications. Summary of the invention

[0003] The technical problem to be solved by the present invention is to provide a method for determining the sliding surface of a rock slope with a non-penetrating interlayer, which can meet the requirements of knowing the rock mass cohesion c1, friction angle Interlayer cohesion c2, internal friction angle The rock mass γ, slope angle α, slope height h, and interlayer inclination θ2 can be used to determine the inclination and length of the sliding surface, and the inclination of the sliding surface can be used to characterize the position of the potential sliding surface. 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 landslides, and minimize losses.

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

[0005] S1. Based on historical data, geological data survey reports and field measurement analysis, the basic parameters of the rock slope and the geological parameters of the weak interlayer of the slope are obtained. According to the Mohr-Coulomb failure criterion, the stability coefficient expressions of the three sliding blocks are as follows:

[0006]

[0007]

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

[0009] S2. Based on the equilibrium equation, find the expressions of the interaction forces F1, F2, P1 and P2;

[0010] S3. Solve the minimum values ​​of Fs1 and Fs3 and combine them with the slope parameters to obtain θ1, θ3, x1 and x3; among them, θ1 is the inclination angle of the lower sliding block, θ3 is the inclination angle of the upper sliding block, x1 is the horizontal projection length of the lower sliding surface, and x3 is the horizontal projection length of the upper sliding surface.

[0011] Since the present invention is derived based on rigorous mathematical formulas, the sliding surface of the rock slope containing non-penetrating interlayers is solved, and an accurate reference is provided for preventing the instability of the rock slope containing non-penetrating interlayers. Therefore, the advantages of the present invention are: a simple and practical method for determining the sliding of the rock slope containing non-penetrating interlayers is proposed, and the parameters involved are easy to determine.

[0012] Compared with the prior art, the present invention has the following beneficial effects:

[0013] 1. The present invention comprehensively considers the specific physical and mechanical properties of the rock and soil mass and the geometric characteristics of the slope, and combines the Mohr-Coulomb failure criterion. This method can more accurately assess the landslide risk and improve the scientificity and accuracy of the prediction.

[0014] 2. The present invention proposes a detailed geometric model for rock slopes with non-penetrating weak interlayers. The model takes into account the physical properties of the rock mass, the geometric layout of the weak interlayers and their influence on the stability of the slope, thus providing a more accurate theoretical basis for determining the sliding surface of the slope;

[0015] 3. The present invention provides a more detailed and systematic stability analysis method by dividing the sliding surface into three parts: lower, middle and upper parts, and calculating the stability coefficient of each part respectively, which helps to more accurately evaluate the stability of the slope;

[0016] 4. The present invention obtains the inclination angles θ1 and θ3 of the sliding surface by solving the optimization problem, which provides an accurate method for determining the potential sliding surface of the slope and helps to improve the accuracy and safety of slope engineering design. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] The accompanying drawings of the present invention are as follows:

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

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

[0020] Figure 3 It is the analysis diagram of the slope geometric mathematical model;

[0021] Figure 4 This is the analysis diagram of the geometric mathematical model of the lower slider;

[0022] Figure 5 It is the analysis diagram of the geometric mathematical model of the upper slider;

[0023] Figure 6 Schematic diagram of boundary conditions for numerical simulation;

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

[0025] Figure 8 This is the result diagram of numerical simulation stability analysis;

[0026] Fig. 9 This is a schematic diagram of the numerical simulation results of slope failure; DETAILED DESCRIPTION

[0027] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0028] Example

[0029] See also Figure 1-9 As shown, the present invention provides a technical solution: comprising the following steps:

[0030] The present invention will be further described with reference to the accompanying drawings:

[0031] S1. Select a representative rock slope with non-penetrating interlayers as the analysis object, such as Figure 1 As shown in the figure, the specific parameters of the slope are determined, including the rock mass cohesion c1, internal friction angle Interlayer cohesion c2, internal friction angle Rock mass γ, slope angle α, rock slope height h, interlayer inclination θ2, the red line is the potential slip surface in the case of overall slope failure, and the blue line represents the interlayer, whose inclination is θ2. In the event of local failure, the potential slip surface develops along the interlayer. The horizontal projection lengths of the lower and upper slip surfaces are x1 and x3, respectively, and the inclination angles of the lower and upper slip surfaces are θ1 and θ3, respectively. The vertical projection lengths of the lower and upper slip surfaces 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] Get the stability coefficient of the three-part slider.

[0036] Among them, G1, G2 and G3 are the deadweights of the lower, middle and upper sliders respectively. F1 is the thrust of the middle slider on the lower slider, and F2 is the pull of the middle slider on the upper slider. P1 is the vertical force of the middle slider on the lower slider, and P2 is the vertical force of the middle slider on the upper slider. The anti-sliding force of the rock mass on the lower, middle and upper sliders is f1, f2 and f3 respectively. The supporting force of the rock mass on the lower, middle and upper sliders is F N1 、F N2 and F N3 l1, l2 and l3 are the lengths of the sliding surfaces of the lower, middle and upper sliders respectively. O is the midpoint of the weak interlayer. O1 and O2 are the locations of the points of action of the interaction forces between the three sliders respectively. c1, is the cohesion and friction angle of the rock mass, c2, are the cohesion and friction angle of the interlayer.

[0037] S3, the thrust F1 of the middle slider on the lower slider, the vertical force P1 of the middle slider on the lower slider, the pulling force F2 of the middle slider on the upper slider and the vertical force P2 of the middle slider on the upper slider can be determined by the following equilibrium equations.

[0038]

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

[0040]

[0041]

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

[0043] S5, stability factor F S1 It can be expressed as a function of θ1 and some slope parameters, namely:

[0044]

[0045] Take F S1 Taking the derivative of θ1 and setting it equal to 0, we get:

[0046]

[0047] The inclination angle of the sliding surface θ1 is expressed according to the slope parameters as follows:

[0048]

[0049] Once the slope parameter θ1 is determined, θ1 can be easily calculated. Similarly, the stability factor F S3 It can be expressed as a function of θ3 and some slope parameters, namely:

[0050]

[0051] Take F S3 Taking the derivative of θ3 and setting it equal to 0, we get:

[0052]

[0053] The inclination angle of the upper sliding surface θ3 is expressed according to the slope parameters as follows:

[0054]

[0055] Once the slope parameters of θ3 are determined, θ3 can be easily calculated. Stability factor F S2 It can be expressed as a function of θ1 and θ3, that is:

[0056]

[0057] Once θ1 and θ3 are determined,

[0058]

[0059] The detailed expressions of Fs1, Fs2 and Fs3 are:

[0060]

[0061] in,

[0062]

[0063]

[0064] in,

[0065]

[0066] The slope geometry model is as follows Figure 1 As shown, the slope stability is analyzed using discrete element software, and the size of the model is designed to be 908×250×700 (mm). The slope angle and height of the slope are 60° and 700 mm respectively. The inclination angle and length of the interlayer are θ2=38° and l2=0.6 m respectively. The weight of the model slope rock and soil is γ=22.416 kN / m 3 , cohesion c1 = 16.79 kPa, internal friction angle Interlayer cohesion c2 = 0 kPa, internal friction angle

[0067] S1, Assume that 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 of Fs1, Fs2 and Fs3. S2, use θ1, θ3 to represent the slider parameters:

[0070]

[0071] S3, according to the formula:

[0072]

[0073]

[0074] The interaction forces F1, F2, P1 and P2 were 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 inclination angles of the lower and upper slip surfaces were determined to be 8.74° and 87.36°.

[0078] S5. According to the formula:

[0079]

[0080] The stability factor Fs2 was determined to be 0.681.

[0081] S6. According to Figure 8 According to the numerical simulation analysis results, the slope stability coefficient is 0.69, which indicates that the slope of this embodiment is damaged along the interlayer.

[0082] S7. According to Fig. 9 From the numerical simulation results of block displacement, we can get the inclination angle θ1 of the lower sliding surface to be 8.4°, and the inclination angle θ3 of the upper sliding surface to be 84.3°.

[0083] S8. Comparison of the method of the present invention and the numerical simulation results is shown in Table 1:

[0084] Table 1 Comparison of calculation results of the embodiments

[0085]

[0086]

[0087] As can be seen from Table 1, the calculation results of the method of the present invention are close to the results obtained by numerical simulation, indicating that the method of the present invention is reliable in application.

[0088] In this example, specifically: In S3, if the basic parameters representing the rock sample are known, the rock mass cohesion c1, the internal friction angle Interlayer cohesion c2, internal friction angle The rock mass γ, slope angle α; the deadweight of the lower, middle and upper sliders G1, G2 and G3, the vertical force P1 of the middle slider on the lower slider, and the vertical force P2 of the middle slider on the upper slider; based on the limit equilibrium method and the definition of the stability coefficient, the slope failure complies with the Mohr-Coulomb failure criterion, and the stability coefficients of the three sliders can be expressed as:

[0089]

[0090] In this example, specifically: S4, according to the equilibrium equation, can be used to find the expressions of the interaction forces F1, F2, P1 and P2:

[0091] The equilibrium equation is expressed as:

[0092]

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

[0094]

[0095] In this example, specifically: in S5, the corresponding θ1, θ3, x1 and x3 when the slope slips are:

[0096] According to F S1 The relationship between θ1 and F S3 The relationship between θ3 and F is determined by taking the derivative S1 The minimum value of the corresponding sliding crack surface inclination angle θ1 and F S3 The expression of the upper sliding surface inclination angle θ3 corresponding to the minimum value of is:

[0097]

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

[0099]

[0100]

[0101] This formula solves the problem of difficulty in determining the sliding surface of a rock slope with non-penetrating interlayers.

[0102] Working principle: The specific parameters of the slope and its interlayer are determined by survey reports and other information. This method analyzes the potential sliding surface of the slope by establishing a geometric model of the rock slope and considering the influence of weak interlayers on the stability of the slope. First, the slider is divided into three parts, and the stability coefficients Fs1, Fs2 and Fs3 of the lower, middle and upper sliders 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 thrust F1, tension F2, vertical forces P1 and P2 are solved. Further, by taking the derivative and setting the derivative equal to zero, the inclination angles θ1 and θ3 of the sliding surface and the upper sliding surface are determined. Once the slope parameters are determined, θ1 and θ3 can be easily calculated, and then the projection lengths x1 and x3 in the horizontal direction are obtained. This method describes in detail the derivation process of F1, P1, F2 and P2, and provides specific calculation results of Fs1, Fs2 and Fs3. The method of the present invention can effectively determine the sliding surface of the rock slope containing non-penetrating weak interlayers, and provide a scientific basis for the design and stability analysis of slope engineering. Although the embodiments of the present invention have been shown and described, it can be understood by those of ordinary skill 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 invention, and the scope of the present invention is defined by the appended claims and their equivalents.

[0103] The present invention and its embodiments are described above, and such description is not restrictive. The drawings show only one embodiment of the present invention, and the actual structure is not limited thereto. In short, if ordinary technicians in the field are inspired by it, without departing from the purpose of the invention, they can design a structure and embodiment similar to the technical solution without creativity, which should belong to the protection scope of the present invention.

Claims

1. A method for determining the sliding surface of a rock slope containing non-penetrating interlayers, characterized in that: The steps include: 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-penetrating interlayer of the slope are obtained; including the rock mass cohesion c1, the internal friction angle Interlayer cohesion c2, internal friction angle Rock mass γ, slope angle α, slope height h, interlayer dip angle θ2; S2. Establish a geometric model of the rock slope and analyze the potential sliding surface of the slope; S3. A plane analysis model is established with the basic parameters of the rock slope obtained in the above way, and the slider is divided into three parts: lower, middle and upper. According to the Mohr-Coulomb failure criterion, the stability coefficients Fs1, Fs2 and Fs3 of the three sliders are expressed by functions; S4. Based on the equilibrium equation, find the expressions of the interaction forces F1, F2, P1 and P2; S5. Analytical solution of sliding surface: By solving the minimum values ​​of Fs1 and Fs3 and combining them with the slope parameters, θ1, θ3, x1 and x3 can be obtained; among which θ1 is the inclination angle of the lower sliding block, θ3 is the inclination angle of the upper sliding block, x1 is the horizontal projection length of the lower sliding surface, and x3 is the horizontal projection length of the upper sliding surface.

2. A method for determining a sliding surface of a rock slope containing non-penetrating interlayers according to claim 1, characterized in that: The failure mode of the rock slope containing non-penetrating interlayers in S2 is plane sliding failure, and the sliding block is divided into three parts: lower, middle and upper.

3. A method for determining a sliding surface of a rock slope containing non-penetrating interlayers according to claim 1, characterized in that: In S3, if the basic parameters representing the rock sample are known, the rock mass cohesion c1, the internal friction angle Interlayer cohesion c2, internal friction angle The rock mass γ, slope angle α; the deadweight of the lower, middle and upper sliders G1, G2 and G3, the vertical force P1 of the middle slider on the lower slider, and the vertical force P2 of the middle slider on the upper slider; based on the limit equilibrium method and the definition of the stability coefficient, the slope failure complies with the Mohr-Coulomb failure criterion, and the stability coefficients of the three sliders can be expressed as:

4. A method for determining a sliding surface of a rock slope containing non-penetrating interlayers according to claim 1, characterized in that: In S3, the thrust F1 of the middle slider on the lower slider, the vertical force P1 of the middle slider on the lower slider, the pulling force F2 of the middle slider on the upper slider and the vertical force P2 of the middle slider on the upper slider can be determined by the following equilibrium equations: The specific calculation process is as follows: F1+F N1 sinθ1=f1cosθ1, G1+P1=F N1 cosθ1+f1sinθ1, F N1 L O1FN1 =G1L O1G1 +f1L O1f1 , the anti-slip force f1 can be expressed as: The coordinates of the lower end point of the interlayer can be expressed as: x j =x4, and j =x4tanα-h1, Assume that the coordinates of the shear outlet are (x i , x i tanα), according to the geometric relationship, we can get: x i +x1=x4, y i +h4=x4tanα-h1, h4=x1tanθ1, The expression of x1 is: As shown in Figure 1, the weight of the lower slider G1 is: And the length l1 of the lower sliding surface can be expressed as: The expression of f1 is: F N1 The expression is: The expression of P1 is: The expression of F1 is: According to the equilibrium equation for the upper slider, we have: F2+F N3 sinθ3=f3cosθ3, G3+P2=F N3 cosθ3+f3sinθ3, <h2 style=";text-align:left;direction:ltr">G3L<h2 style=";text-align:left;direction:ltr"> O2G3 <h2 style=";text-align:left;direction:ltr"> =F<h2 style=";text-align:left;direction:ltr"> N3 <h2 style=";text-align:left;direction:ltr"> L<h2 style=";text-align:left;direction:ltr"> O2FN3 <h2 style=";text-align:left;direction:ltr"> +f3L<h2 style=";text-align:left;direction:ltr"> O2f3 <h2 style=";text-align:left;direction:ltr"> , The anti-slip force f3 is expressed as: As shown in Figure 1, the upper slider's deadweight G3 is expressed as: And the length l3 of the upper sliding surface can be expressed as: The expression of f3 is: F N3 The expression is: The expression of P2 is: The expression of F2 is: So the expressions for calculating F1, F2, P1 and P2 are: Among them, G1, F N1 , F1 and the distance from F1 to O1 are defined as L O1G1 , L O1FN1 , L O1f1 ; From G3, F N3 and the distances from f3 to O2 are L O2G3 , L O2FN3 , L O2f3 .

5. A method for determining a sliding surface of a rock slope containing non-penetrating interlayers according to claim 1, characterized in that: In S5, the specific calculation steps of θ1, θ3, x1 and x3 are: Stability factor F S1 It can be expressed as a function of θ1 and some slope parameters, namely: Take F S1 Taking the derivative of θ1 and setting it equal to 0, we get: The inclination angle of the sliding surface θ1 is expressed according to the slope parameters as follows: Once the slope parameters of θ1 are determined, the result of θ1 can be obtained; similarly, the stability factor F S3 It can be expressed as a function of θ3 and some slope parameters, namely: Take F S3 Taking the derivative of θ3 and setting it equal to 0, we get: The inclination angle θ3 of the upper sliding surface is expressed according to the slope parameters as follows: Once the slope parameters of θ3 are determined, the result of θ3 can be obtained; Stability factor F S2 It can be expressed as a function of θ1 and θ3, that is: Once θ1 and θ3 are determined, x1 and x3 can be easily calculated: The detailed expressions of Fs1, Fs2 and Fs3 are as follows: in, in,

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