Method for analyzing stability of rock slope with parallel rock stratum and slope surface

Abstract

The invention discloses a method for analyzing the stability of a rock slope with a rock stratum parallel to a slope surface, and belongs to the field of mechanical analysis of slope stability of geological engineering and geotechnical engineering. The method comprises the following steps: taking the ith unit body, which is x away from the top end, in the jth soft rock stratum of the slope to carry out stress analysis; for all the unit bodies of the slope, iterative calculation is conducted from the first unit body of the first layer, the stability coefficient of each unit body is obtained, and then the overall stability coefficient or the critical excavation height of the slope is determined. By the adoption of the stability analysis method for the rock slope with the rock stratum and the slope face parallel, quantitative analysis of the stability of the rock slope with the rock stratum and the slope face parallel can be carried out, the excavation height of the rock slope with the rock stratum and the slope face parallel is reasonably determined, and back calculation solving of key mechanical property parameters of the rock slope with the rock stratum and the slope face parallel is achieved.

Description

Technical Field

[0001] The invention relates to the field of mechanical analysis of slope stability in geological engineering and geotechnical engineering, and in particular to a method for analyzing the stability of a rock slope in which a rock layer is parallel to a slope surface. Background Art

[0002] In mountainous areas where sedimentary rocks and metamorphic rocks are widely distributed at home and abroad, rock slopes with rock layers parallel to the slope surface can sometimes be seen. Under the action of excavation and natural environmental degradation, the physical and mechanical properties of the slope rock layers will deteriorate, and such rock slopes with rock layers parallel to the slope surface will be deformed and damaged, threatening the safety of engineering facilities or residents at the foot of the slope. Therefore, it is necessary to carry out targeted stability analysis on slopes with rock layers parallel to the slope surface.

[0003] For a long time, technicians in this field have conducted systematic and in-depth research on soil slopes, and have formed soil slope analysis methods mainly based on the Swedish arc method, the Swedish arc strip method, and the Bishop strip method. However, rock slopes are different from soil slopes and often have specific rock formations, which not only complicates the stability analysis of rock slopes, but also makes it difficult to apply the commonly used methods for soil slope analysis to rock slopes with specific rock formations. For special slopes where the rock layer is parallel to the slope surface, it is difficult to conduct stability analysis using the commonly used methods for soil slope analysis.

[0004] Therefore, it is urgent to propose a rock slope stability analysis method in which the rock layer is parallel to the slope surface to solve the stability analysis problem of special rock slopes, and then serve the reasonable reinforcement design of rock slopes. Summary of the invention

[0005] The purpose of the present invention is to provide a stability analysis method for a rock slope with a rock layer parallel to the slope surface, which can carry out quantitative stability analysis of the rock slope with a rock layer parallel to the slope surface, reasonably determine the excavation height of the rock slope with a rock layer parallel to the slope surface, and realize the inverse calculation and solution of key mechanical property parameters of the rock slope with a rock layer parallel to the slope surface.

[0006] To achieve the above-mentioned purpose, the present invention provides a method for analyzing the stability of a rock slope in which the rock layer is parallel to the slope surface, including taking the i-th unit body at a distance x from the top in the j-th soft rock layer of the slope for force analysis; for the i-th unit body, the forces along the directions parallel to the rock layer and perpendicular to the rock layer meet the equilibrium conditions, and all forces act on the center o of the unit body.

[0007] Preferably, according to the force balance condition parallel to the rock formation direction, it can be obtained:

[0008] W j,ix sinθ+F j,ix +f j,idx =F j,ix +△F j,ix+f j,iux (1);

[0009] Among them, W j,ix is the gravity of the i-th unit in the j-th soft rock layer of the slope, which is x away from the top; θ is the angle between the soft rock layer and the horizontal plane; F j,ix It is the force between the upper end surface of the i-th unit body with a distance x from the top in the j-th soft rock layer of the slope and the adjacent unit body;

[0010] f j,idx is the sliding force of the i-th unit at a distance x from the top in the j-th soft rock layer of the slope under the action of the overlying adjacent unit; △F j,ix is the increment of the force between the upper and lower end faces of the ith unit with a distance x from the top and the adjacent units in the jth soft rock layer of the slope; f j,iux

[0011] It is the anti-sliding force exerted by the underlying adjacent unit on the i-th unit at a distance x from the top in the j-th soft rock layer of the slope.

[0012] Preferably, according to the force balance condition perpendicular to the rock formation direction, it can be obtained:

[0013] W j,ix cosθ+N j-1,ix =N j,ix (2);

[0014] Among them, N j-1,ix N is the normal force exerted on the i-th unit at a distance x from the top in the j-th soft rock layer of the slope by the overlying adjacent unit; j,ix It is the normal force exerted on the i-th unit at a distance x from the top in the j-th soft rock layer of the slope by the underlying adjacent unit.

[0015] Preferably, for the f j,idx For , it is assumed that the Mohr-Coulomb strength criterion is satisfied, namely:

[0016]

[0017] Where △x is the length of the unit cell; c is the friction angle between the contact surface of the ith unit with a distance x from the top in the jth soft rock layer of the slope and the overlying adjacent unit; j,idx It is the cohesion between the contact surface between the ith unit cell at a distance x from the top in the jth soft rock layer of the slope and the overlying adjacent unit cell.

[0018] Preferably, for the f j,iux For , it is assumed that the Mohr-Coulomb strength criterion is satisfied, namely:

[0019]

[0020] in, c is the friction angle between the contact surface of the ith unit with a distance x from the top in the jth soft rock layer of the slope and the underlying adjacent unit; j,iux It is the cohesion between the contact surface between the ith unit at a distance x from the top in the jth soft rock layer of the slope and the underlying adjacent unit.

[0021] Preferably, the W j,ix The following relations are satisfied:

[0022] W j,ix =ρ j g j △x (5);

[0023] Among them, ρ j is the density of the jth soft rock layer of the slope; g is the acceleration of gravity; D j is the thickness of the jth soft rock layer of the slope.

[0024] Preferably, for the i-th unit with a distance x from the top in the j-th soft rock layer of the slope, there is a stability coefficient K j,ix Satisfy the following formula:

[0025] K j,ix =(F j,ix +△F j,ix ) / (D j σ j.ix ) (6);

[0026] Among them, σ j.ix is the uniaxial compressive strength of the i-th unit at a distance x from the top in the j-th soft rock layer of the slope;

[0027] For the slope as a whole, its stability coefficient K satisfies:

[0028] K=MAX(K j,ix ), (j=1,2,…,m; i=1,2,…,n) (7);

[0029] Among them, MAX(K j,ix ) means K j,ix The larger the maximum value, the more unsafe the slope is.

[0030] Preferably, if the slope as a whole is in a critical failure state, there is an arbitrary unit body that just undergoes compression failure, and K should satisfy:

[0031] K = 1 (8);

[0032] If the slope is in a state of overall destruction, and any unit cell has undergone compression failure, then K should satisfy:

[0033] K>1 (9);

[0034] If the slope remains stable as a whole, no unit will be crushed, and K should satisfy:

[0035] K<1 (10);

[0036] For all units of the slope, iterative calculations are performed starting from the first unit of the first layer. When other relevant parameters are known, the stability coefficient of each unit is obtained, and then the overall stability coefficient of the slope or the critical excavation height is determined;

[0037] If it is known that similar slopes have been damaged, the key mechanical property parameters of the slope can be calculated based on equations (1)-(8) based on other parameters determined through experiments.

[0038] Therefore, the present invention adopts the above-mentioned method for analyzing the stability of rock slopes with parallel rock layers and slope surfaces, which can carry out quantitative analysis of the stability of rock slopes with parallel rock layers and slope surfaces, reasonably determine the excavation height of rock slopes with parallel rock layers and slope surfaces, and realize the inverse calculation and solution of key mechanical property parameters of rock slopes with parallel rock layers and slope surfaces.

[0039] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 It is a schematic diagram of analyzing the stability of a rock slope in which the rock layer is parallel to the slope surface according to an embodiment of a method for analyzing the stability of a rock slope in which the rock layer is parallel to the slope surface of the present invention;

[0041] Figure 2 This is an example diagram of a rock slope with two rock layers parallel to the slope surface according to an embodiment of a method for analyzing stability of a rock slope with rock layers parallel to the slope surface of the present invention. DETAILED DESCRIPTION

[0042] The technical solution of the present invention is further described below through the accompanying drawings and embodiments.

[0043] Unless otherwise defined, technical or scientific terms used in the present invention shall have the common meanings understood by one having ordinary skills in the field to which the present invention belongs.

[0044] Embodiment 1

[0045] The present invention provides a method for analyzing the stability of a rock slope in which the rock layer is parallel to the slope surface. Figure 1 As shown, Figure 1It is a schematic diagram of the stability analysis of a rock slope in which the rock layer is parallel to the slope surface. It is assumed that a series of parallel weak rock layers are distributed in the horizontal direction from the slope surface to the inside of the slope. The i-th unit body with a distance x from the top in the j-th soft rock layer of the slope is taken for force analysis. For the i-th unit body, the forces along the directions parallel to the rock layer and perpendicular to the rock layer meet the equilibrium conditions, and all forces act on the center o of the unit body.

[0046] According to the force balance condition parallel to the rock formation direction, we can get:

[0047] W j , ix sinθ+F j,ix +f j,idx =F j,ix +△F j,ix +f j,iux (1);

[0048] Among them, W j,ix is the gravity of the i-th unit in the j-th soft rock layer of the slope, which is x away from the top; θ is the angle between the soft rock layer and the horizontal plane; F j,ix is the force between the upper end face of the i-th unit body and the adjacent unit body in the j-th soft rock layer of the slope, which is x away from the top; f j,idx is the sliding force of the i-th unit at a distance x from the top in the j-th soft rock layer of the slope under the action of the overlying adjacent unit; △F j,ix is the increment of the force between the upper and lower end faces of the ith unit with a distance x from the top and the adjacent units in the jth soft rock layer of the slope; f j,iux It is the anti-sliding force exerted by the underlying adjacent unit on the i-th unit at a distance x from the top in the j-th soft rock layer of the slope.

[0049] According to the force balance condition perpendicular to the rock formation, we can get:

[0050] W j,ix cosθ+N j-1,ix =N j,ix (2);

[0051] Among them, N j-1,ix N is the normal force exerted on the i-th unit at a distance x from the top in the j-th soft rock layer of the slope by the overlying adjacent unit; j,ix It is the normal force exerted on the i-th unit at a distance x from the top in the j-th soft rock layer of the slope by the underlying adjacent unit.

[0052] For f j,idx For , it is assumed that the Mohr-Coulomb strength criterion is satisfied, namely:

[0053]

[0054] Where △x is the length of the unit cell; c is the friction angle between the contact surface of the ith unit with a distance x from the top in the jth soft rock layer of the slope and the overlying adjacent unit; j,idx It is the cohesion between the contact surface between the ith unit cell at a distance x from the top in the jth soft rock layer of the slope and the overlying adjacent unit cell.

[0055] For f j,iux For , it is assumed that the Mohr-Coulomb strength criterion is satisfied, namely:

[0056]

[0057] in, c is the friction angle between the contact surface of the ith unit with a distance x from the top in the jth soft rock layer of the slope and the underlying adjacent unit; j,iux It is the cohesion between the contact surface between the ith unit at a distance x from the top in the jth soft rock layer of the slope and the underlying adjacent unit.

[0058] W j,ix The following relations are satisfied:

[0059] W j,ix =ρ j g j △x (5);

[0060] Among them, ρ j is the density of the jth soft rock layer of the slope; g is the acceleration of gravity; D j is the thickness of the jth soft rock layer of the slope.

[0061] For the i-th unit with a distance x from the top in the j-th soft rock layer of the slope, there is a stability coefficient K j,ix Satisfy the following formula:

[0062] K j,ix =(F j,ix +△F j,ix ) / (D j σ j.ix ) (6);

[0063] Among them, σ j.ix is the uniaxial compressive strength of the i-th unit at a distance x from the top in the j-th soft rock layer of the slope;

[0064] For the slope as a whole, its stability coefficient K satisfies:

[0065] K=MAX(K j,ix ), (j=1,2,…,m; i=1,2,…,n) (7);

[0066] Among them, MAX(K j,ix ) means K j,ix The larger the maximum value, the more unsafe the slope is.

[0067] If the slope as a whole is in a critical failure state, there is an arbitrary unit body that just happens to be compressively damaged, and K should satisfy:

[0068] K = 1 (8);

[0069] If the slope is in a state of overall destruction, and any unit cell has undergone compression failure, then K should satisfy:

[0070] K>1 (9);

[0071] If the slope remains stable as a whole, no unit will be crushed, and K should satisfy:

[0072] K<1 (10);

[0073] For all units of the slope, iterative calculations are performed starting from the first unit of the first layer. When other relevant parameters are known, the stability coefficient of each unit is obtained, and then the overall stability coefficient of the slope or the critical excavation height is determined;

[0074] If it is known that similar slopes have been damaged, the key mechanical property parameters of the slope can be calculated based on equations (1)-(8) based on other parameters determined through experiments.

[0075] Embodiment 2

[0076] like Figure 2 As shown, Figure 2 The rock slope has two rock layers parallel to the slope surface. The angle θ between the rock layer and the horizontal plane is 45°. The density and thickness of the two rock layers are both 2.4g / cm 3The cohesion and friction angle of the contact surface between the first and second rock layers are 0 and 25° respectively, the cohesion and friction angle of the contact surface between the second rock layer and the underlying rock layer (not shown in the figure) are 0 and 30° respectively, the unit length of the two rock layers is set to 2m, the uniaxial compressive strength of the first and second rock layers are 5MPa and 10MPa respectively, and there are 8 units in total (the part less than 1 unit can be ignored and not analyzed). The stability coefficient of each unit is calculated according to formulas (1)-(6) as shown in Table 1 below. It can be seen that the stability coefficient of the third and fourth units of the first rock layer will be destroyed because it is greater than 1. According to the destruction of the third and fourth units of the first rock layer, assuming that the first rock layer was covered by other excavated rock masses in the early stage, it can be inferred that the excavation height of the overlying rock mass on the first rock layer should not expose the third unit of the first rock layer, and the critical excavation height of the overlying rock mass on the first rock layer can be determined. According to equations (7) and (9), the overall stability coefficient of the slope is 1.45, and the slope will be unstable and will cause destruction. It should be noted that the smaller the length of the unit, the more accurate the specific position of the unstable unit is, that is, the more accurate the critical excavation height of the rock slope is.

[0077] Table 1 Stability coefficients of each unit of rock slope with two rock layers parallel to the slope surface

[0078]

[0079]

[0080] Therefore, the present invention adopts the above-mentioned method for analyzing the stability of rock slopes with parallel rock layers and slope surfaces, which can carry out quantitative analysis of the stability of rock slopes with parallel rock layers and slope surfaces, reasonably determine the excavation height of rock slopes with parallel rock layers and slope surfaces, and realize the inverse calculation and solution of key mechanical property parameters of rock slopes with parallel rock layers and slope surfaces.

[0081] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A method for analyzing the stability of a rock slope in which the rock layer is parallel to the slope surface, characterized in that: It includes taking the i-th unit body at a distance x from the top in the j-th soft rock layer of the slope for force analysis; for the i-th unit body, the forces along the directions parallel to the rock layer and perpendicular to the rock layer meet the equilibrium conditions, and all forces act at the center o of the unit body.

2. The method for analyzing the stability of a rock slope in which the rock layer is parallel to the slope surface according to claim 1, characterized in that: According to the force balance condition parallel to the rock formation direction, we can get: W j,ix sinθ+F j,ix +f j,idx =F j,ix +△F j,ix +f j,iux (1); Among them, W j,ix is the gravity of the i-th unit in the j-th soft rock layer of the slope, which is x away from the top; θ is the angle between the soft rock layer and the horizontal plane; F j,ix is the force between the upper end face of the i-th unit body and the adjacent unit body in the j-th soft rock layer of the slope, which is x away from the top; f j,idx is the sliding force of the i-th unit at a distance x from the top in the j-th soft rock layer of the slope under the action of the overlying adjacent unit; △F j,ix is the increment of the force between the upper and lower end faces of the ith unit with a distance x from the top and the adjacent units in the jth soft rock layer of the slope; f j,iux It is the anti-sliding force exerted by the underlying adjacent unit on the i-th unit at a distance x from the top in the j-th soft rock layer of the slope.

3. The method for analyzing the stability of a rock slope in which the rock layer is parallel to the slope surface according to claim 1, characterized in that: According to the force balance condition perpendicular to the rock formation, we can get: W j,ix cosθ+N j-1,ix =N j,ix (2); Among them, N j-1,ix N is the normal force exerted on the i-th unit at a distance x from the top in the j-th soft rock layer of the slope by the overlying adjacent unit; j,ix It is the normal force exerted on the i-th unit at a distance x from the top in the j-th soft rock layer of the slope by the underlying adjacent unit.

4. The method for analyzing the stability of a rock slope in which the rock layer is parallel to the slope surface according to claim 2, characterized in that: For the f j,idx For , it is assumed that the Mohr-Coulomb strength criterion is satisfied, namely: Where △x is the length of the unit cell; c is the friction angle between the contact surface of the ith unit with a distance x from the top in the jth soft rock layer of the slope and the overlying adjacent unit; j,idx It is the cohesion between the contact surface between the ith unit cell at a distance x from the top in the jth soft rock layer of the slope and the overlying adjacent unit cell.

5. The method for analyzing the stability of a rock slope in which the rock layer is parallel to the slope surface according to claim 2, characterized in that: For the f j,iux For , it is assumed that the Mohr-Coulomb strength criterion is satisfied, namely: in, c is the friction angle between the contact surface of the ith unit with a distance x from the top in the jth soft rock layer of the slope and the underlying adjacent unit; j,iux It is the cohesion between the contact surface between the ith unit at a distance x from the top in the jth soft rock layer of the slope and the underlying adjacent unit.

6. The method for analyzing the stability of a rock slope in which the rock layer is parallel to the slope surface according to claim 2, characterized in that: The W j,ix The following relations are satisfied: IN j,ix =ρ j gD j △x (5); Among them, ρ j is the density of the jth soft rock layer of the slope; g is the acceleration of gravity; D j is the thickness of the jth soft rock layer of the slope.

7. The method for analyzing the stability of a rock slope in which the rock layer is parallel to the slope surface according to claim 1, characterized in that: For the i-th unit with a distance x from the top in the j-th soft rock layer of the slope, there is a stability coefficient K j,ix Satisfy the following formula: K j，ix =(F j，ix +ΔF j，ix ) / (D j σ j.ix ) (6); Among them, σ j.ix is the uniaxial compressive strength of the i-th unit at a distance x from the top in the j-th soft rock layer of the slope; For the slope as a whole, its stability coefficient K satisfies: K=MAX(K j，ix ),(j=1,2,......,m;i=1,2,......,n) (7); Among them, MAX(K j，ix ) means K j，ix The larger the maximum value, the more unsafe the slope is.

8. The method for analyzing the stability of a rock slope in which the rock layer is parallel to the slope surface according to claim 7, characterized in that: If the slope as a whole is in a critical failure state, there is an arbitrary unit body that just happens to be compressed and destroyed, then K should satisfy: K＝1 (8)； If the slope is in a state of overall destruction, and any unit cell has undergone compression failure, then K should satisfy: K＞1 (9)； If the slope remains stable as a whole, no unit will be crushed, and K should satisfy: K＜1 (10)； For all units of the slope, iterative calculations are performed starting from the first unit of the first layer. When other relevant parameters are known, the stability coefficient of each unit is obtained, and then the overall stability coefficient of the slope or the critical excavation height is determined; If it is known that similar slopes have been damaged, the key mechanical property parameters of the slope can be calculated based on equations (1)-(8) based on other parameters determined through experiments.

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