A method for calculating the stability of high and steep slopes

Abstract

The present invention relates to a method for calculating the stability of a steep slope, comprising the following steps: equating the failure surface of the steep slope to a two-segment linear shape, and equating the sliding body to a first triangular wedge and a second triangular wedge connected to each other; analyzing the force applied to the second triangular wedge and calculating the force applied to the second triangle; calculating the normal static equilibrium and tangential static equilibrium of the bottom surface of the second triangular wedge based on the force applied to the second triangular wedge; and calculating the stability coefficient of the steep slope based on the slope safety factor, the force applied to the second triangular wedge, the normal static equilibrium, and the tangential static equilibrium. This calculation method improves the problem of the limit equilibrium method causing the calculation results of the steep slope stability to be too large or too small, and can effectively solve existing problems in the evaluation of steep slope models. The calculation results are more consistent with the actual stability of the slope and are more accurate. Furthermore, this method can also calculate the stability coefficient of the steep slope under different groundwater levels.

Description

Technical Field

[0001] The present invention belongs to the technical field of geological disaster risk analysis, and in particular relates to a method for calculating the stability of a high and steep slope. Background Art

[0002] Slope stability calculation is a classic geotechnical engineering problem, encompassing numerous engineering fields. Slope instability is not only related to rainfall, earthquakes, and human activities, but is also influenced by factors such as slope gradient and height. Reasonable and accurate slope stability calculation results are crucial for slope risk assessment and prevention. Currently, the most commonly used slope stability calculation methods are primarily limit equilibrium methods, such as the Fellenius method, the Bishop method, and the Janbu method. Other methods include limit analysis, reliability analysis, and numerical methods. Of these, limit equilibrium methods have been the most extensively studied and widely used. However, the stability calculation results obtained using limit equilibrium methods for high and steep slopes differ from actual conditions. Generally, soil slopes exceeding 20 meters in height are considered high slopes. The presence of large slope angles further reduces the stability of high and steep slopes. Currently, there are few stability calculation methods specifically designed for high and steep slopes. In practice, general slope calculation methods are often used, primarily using the strip method with various simplifying assumptions.

[0003] Using the limit equilibrium principle, the strip method can solve slope stability analysis for complex geometries, various soil types, and pore water pressure conditions. In practical applications, the strip method has evolved in various forms, all of which share two basic assumptions: slope stability is assumed to be a planar stability problem; and the sliding surface is assumed to be a circular arc, with the sliding body on the arc being a rigid body. Under these conditions, the safety factors calculated using the Bishop and Janbu methods for slopes with a height of 40 meters and a slope gradient greater than 40 degrees without groundwater are both less than 1. However, in practice, many stable high and steep slopes have heights and slope gradients within the instability range calculated using the strip method. Therefore, the classic strip method has significant limitations when calculating the stability of high and steep slopes without groundwater within this range. Furthermore, the slope safety factors calculated using the classic strip method are primarily concentrated in the range of 0.8 to 1.4, especially for smaller slopes, where the actual slope stability may differ significantly from the actual situation. For high and steep slopes involving groundwater, the strip method produces results that are completely unstable. This is inconsistent with the actual conditions of some soil slopes, particularly in the stability assessment of loess slopes. In such high and steep loess slopes, the gradient and height of the "limit state slope" far exceed the applicable range of the strip method.

[0004] In summary, when existing methods are applied, the stability calculation results of low-steep slopes are often too high, and the stability calculation results of high-steep slopes are often too low, which is inconsistent with the actual situation and makes it difficult to guide disaster prevention and mitigation work on high-steep slopes. Summary of the Invention

[0005] In order to solve the above problems existing in the prior art, the present invention provides a method for calculating the stability of steep slopes. The technical problem to be solved by the present invention is achieved through the following technical solutions:

[0006] An embodiment of the present invention provides a method for calculating the stability of a high and steep slope, comprising the steps of:

[0007] The failure surface of the steep slope is equivalent to a double-segment linear shape, and the sliding body of the steep slope is equivalent to the first triangular wedge and the second triangular wedge connected;

[0008] Analyze the force applied to the second triangular wedge and calculate the force applied to the second triangle;

[0009] Calculate the normal static equilibrium and tangential static equilibrium of the bottom surface of the second triangular wedge based on the forces acting on the second triangular wedge;

[0010] The stability coefficient of the high and steep slope is calculated by combining the slope safety factor, the force applied to the second triangular wedge, the normal static balance, and the tangential static balance.

[0011] In one embodiment of the present invention, when the high and steep slope is a high and steep slope without groundwater, the force acting on the second triangular wedge includes the active earth pressure thrust exerted by the first triangular wedge on the second triangular wedge.

[0012] In one embodiment of the present invention, the active earth pressure thrust is:

[0013]

[0014] Among them, E a is the total active earth pressure, γ is the soil density, h1 is the height of the first triangular wedge, H is the height of the slope, θ is the angle between the bottom of the second triangular wedge and the ground, θ = α - π / 4 + φ / 2, α is the angle between the steep slope surface and the ground, K a is the active earth pressure coefficient, c and φ are indicators of soil shear strength.

[0015] In one embodiment of the present invention, calculating the normal static equilibrium and the tangential static equilibrium of the bottom surface of the second triangular wedge in combination with the forces acting on the second triangular wedge includes:

[0016] The active earth pressure thrust is used to calculate the normal static equilibrium of the bottom surface of the second triangular wedge:

[0017] NW BCD cosθ-Ea sinθ=0

[0018] Where N is the normal stress on the shear surface of the bottom surface of the second triangular wedge, W BCD is the weight of the first triangular wedge, E a is the total active earth pressure, θ is the angle between the bottom surface of the second triangular wedge and the ground;

[0019] The tangential static equilibrium of the bottom surface of the second triangular wedge is calculated using the active earth pressure thrust:

[0020] SW BCD sinθ-E a cosθ=0

[0021] Where S is the shear stress on the shear surface of the bottom surface of the second triangular wedge.

[0022] In one embodiment of the present invention, the stability coefficient of the high and steep slope is calculated by combining the slope safety factor, the force on the second triangular wedge, the normal static balance, and the tangential static balance, including:

[0023] The slope safety factor is:

[0024]

[0025] Where N is the normal stress on the shear surface of the bottom surface of the second triangular wedge, c and φ are the shear strength indices of the soil, b2 is the length of the bottom surface of the first triangular wedge, and S is the shear stress on the shear surface of the bottom surface of the second triangular wedge;

[0026] The stability coefficient of the steep slope is calculated by combining the slope safety factor, the active earth pressure thrust, the normal static balance and the tangential static balance:

[0027]

[0028] Where h1 is the height of the first triangular wedge, h2 is the height of the bottom of the second triangular wedge, γ is the soil density, θ is the angle between the bottom of the second triangular wedge and the ground, θ = α - π / 4 + φ / 2, E a is the total active earth pressure, c and φ are the shear strength indicators of the soil.

[0029] In one embodiment of the present invention, when the high and steep slope is a high and steep slope with groundwater, the forces acting on the second triangular wedge include: the active earth pressure thrust exerted by the first triangular wedge on the second triangular wedge, the hydrostatic pressure, and the total pore water pressure at the bottom surface of the second triangular wedge, wherein the active earth pressure thrust and the hydrostatic pressure form the total active earth pressure.

[0030] In one embodiment of the present invention, the total active earth pressure is:

[0031]

[0032] Among them, E a is the total active earth pressure, γ is the soil density, H is the slope height, h1 is the height of the first triangular wedge, θ is the angle between the bottom of the second triangular wedge and the ground, θ=α-π / 4+φ / 2, α is the angle between the steep slope and the ground, K a is the active earth pressure coefficient, c and φ are soil shear strength indices, h w is the height of the groundwater level, and h2 is the height of the bottom surface of the second triangular wedge.

[0033] In one embodiment of the present invention, the total pore water pressure is:

[0034]

[0035] Among them, r w is the water density, h w is the height of the groundwater level, h2 is the height of the bottom of the second triangular wedge, θ is the angle between the bottom of the second triangular wedge and the ground, θ=α-π / 4+φ / 2, H is the height of the slope, h1 is the height of the first triangular wedge,

[0036] In one embodiment of the present invention, calculating the normal static equilibrium and the tangential static equilibrium of the bottom surface of the second triangular wedge in combination with the forces acting on the second triangular wedge includes:

[0037] The total active earth pressure is used to calculate the normal static equilibrium of the bottom surface of the second triangular wedge:

[0038] NW BCD cosθ-E a sinθ=0

[0039] Where N is the normal stress on the shear surface of the bottom surface of the second triangular wedge, is the weight of the first triangular wedge, γ satis the saturated weight of soil, E a is the total active earth pressure, θ is the angle between the bottom surface of the second triangular wedge and the ground;

[0040] The total active earth pressure is used to calculate the tangential static equilibrium of the bottom surface of the second triangular wedge:

[0041] SW BCD sinθ-E a cosθ=0

[0042] Where S is the shear stress on the shear surface of the bottom surface of the second triangular wedge.

[0043] In one embodiment of the present invention, the stability coefficient of the high and steep slope is calculated by combining the slope safety factor, the force on the second triangular wedge, the normal static balance, and the tangential static balance, including:

[0044] The slope safety factor is:

[0045]

[0046] Where N is the normal stress on the shear surface of the bottom surface of the second triangular wedge, c and φ are the shear strength indices of the soil, b2 is the length of the bottom surface of the first triangular wedge, S is the shear stress on the shear surface of the bottom surface of the second triangular wedge, and u is the total pore water pressure at the bottom surface of the second triangular wedge;

[0047] The stability coefficient of the high and steep slope is calculated by combining the slope safety factor, the total active earth pressure, the normal static balance, and the tangential static balance:

[0048]

[0049] Where h2 is the height of the bottom of the second triangular wedge, θ is the angle between the bottom of the second triangular wedge and the ground, θ = α - π / 4 + φ / 2, E a is the total active earth pressure, u is the total pore water pressure at the bottom of the second triangular wedge, c and φ are the shear strength indices of the soil, W BCD is the weight of the first triangular wedge, h w >h2.

[0050] Compared with the prior art, the present invention has the following beneficial effects:

[0051] The calculation method of the present invention takes into account the typical characteristics of the failure surface of high and steep slopes as a two-segment linear shape, simplifies the sliding body into two triangular wedges, and analyzes the stress conditions of high and steep slopes. A stability calculation method for high and steep slopes is provided, and the problem of the limit equilibrium method being too large (low-steep slopes) or too small (high-steep slopes) in calculating the stability of high and steep slopes is improved. The method can better solve the existing problems in the evaluation of high and steep slope models, and the calculation results are more consistent with the actual stability of the slopes and more accurate. At the same time, the method can also calculate the stability coefficient of high and steep slopes under the action of different groundwater levels, thereby effectively guiding the disaster prevention and mitigation work of high and steep slopes. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 A schematic flow chart of a method for calculating the stability of a high and steep slope provided by an embodiment of the present invention;

[0053] Figure 2 A schematic diagram of a high and steep slope model without groundwater provided by an embodiment of the present invention;

[0054] Figure 3 A schematic diagram of a high and steep slope model with groundwater provided by an embodiment of the present invention;

[0055] Figure 4 A comparison chart of the safety factor calculation results of steep slopes calculated using different methods provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0056] The present invention will be further described in detail below with reference to specific examples, but the embodiments of the present invention are not limited thereto.

[0057] Example 1

[0058] See Figure 1 , Figure 1 A flowchart of a method for calculating the stability of a high-steep slope provided by an embodiment of the present invention is provided. This embodiment uses a high-steep slope without groundwater as an example to illustrate the method for calculating the stability of a high-steep slope. The method for calculating the stability of a high-steep slope includes the following steps:

[0059] S1. The failure surface of the steep slope is equivalent to a double-segment linear shape, and the sliding body of the steep slope is equivalent to a first triangular wedge and a second triangular wedge connected to each other.

[0060] See Figure 2 , Figure 2 A schematic diagram of a high and steep slope model without groundwater provided in an embodiment of the present invention.

[0061] Specifically, according to the typical profile of soil landslide, the slope rupture surface is considered to be a double-segment linear shape, and the sliding body is equivalent to Figure 2The two adjacent triangular wedges shown in , namely the first triangular wedge BCD and the second triangular wedge ABD.

[0062] S2. Analyze the force applied to the second triangular wedge and calculate the force applied to the second triangle.

[0063] Specifically, there is no relative displacement between the first triangular wedge BCD and the second triangular wedge ABD. The first triangular wedge BCD forms an active earth pressure zone, exerting an active thrust on the second triangular wedge ABD. Therefore, when the steep slope is a steep slope without groundwater, the force acting on the second triangular wedge ABD includes the active earth pressure thrust exerted by the first triangular wedge BCD on the second triangular wedge ABD.

[0064] According to Rankine's earth pressure theory, the thrust of the active earth pressure on the second triangular wedge ABD is:

[0065]

[0066] Among them, E a is the total active earth pressure, γ is the soil density, h1 is the height of the first triangular wedge, H is the height of the slope, θ is the angle between the bottom of the second triangular wedge and the ground, θ = α - π / 4 + φ / 2, α is the angle between the steep slope surface and the ground, K a is the active earth pressure coefficient, c and φ are indicators of soil shear strength.

[0067] S3. Calculate the normal static equilibrium and tangential static equilibrium of the bottom surface of the second triangular wedge based on the forces acting on the second triangular wedge.

[0068] Specifically, consider the second triangular wedge ABD as a retaining wall, subject to the earth pressure exerted by the first triangular wedge BCD, and thus in a passive stress state. When the entire sliding mass is in a state of ultimate equilibrium, the anti-sliding force comes from the shear strength of the soil at the bottom of the second triangular wedge ABD. The sliding force comprises the earth pressure exerted by the first triangular wedge BCD on the second triangular wedge ABD and the component of the second triangular wedge ABD's own weight in the sliding direction.

[0069] Therefore, the active earth pressure thrust is used to calculate the normal static equilibrium of the bottom surface of the second triangular wedge:

[0070] NW BCD cosθ-E a sinθ=0 (2)

[0071] Where N is the normal stress on the shear surface of the bottom surface of the second triangular wedge, W BCD is the weight of the first triangular wedge, and h2 is the height of the base of the second triangular wedge.

[0072] The tangential static equilibrium of the bottom surface of the second triangular wedge is calculated using the active earth pressure thrust:

[0073] SW BCD sinθ-E a cosθ=0 (3)

[0074] Where S is the shear stress on the shear surface of the bottom surface of the second triangular wedge.

[0075] S4. Calculate the stability coefficient of the high and steep slope based on the slope safety factor, the force applied to the second triangular wedge, the normal static balance, and the tangential static balance.

[0076] First, the slope safety factor is:

[0077]

[0078] Wherein, b2 is the length of the base of the first triangular wedge.

[0079] Then, the stability coefficient of the high and steep slope is calculated by combining the slope safety factor, the active earth pressure thrust, the normal static balance and the tangential static balance.

[0080] Specifically, the stability coefficient of the steep slope is calculated by combining formulas (2), (3), and (4):

[0081]

[0082] Among them, θ=α-π / 4+φ / 2, E a Calculated according to formula (1).

[0083] Furthermore, after obtaining the stability coefficient of the steep slope, the stability of the steep slope is determined based on the stability coefficient. In a specific embodiment, when the stability coefficient is less than 1, the steep slope is unstable; when the stability coefficient is between 1.1 and 1.15, the steep slope is unstable; and when the stability coefficient is greater than 1.2, the steep slope is stable.

[0084] In this embodiment, the slope stability calculation results differ significantly from the actual situation, making them unable to meet the requirements for predicting the instability of high and steep slopes. Considering the typical characteristic of the high and steep slope failure surface as a double-segment linear shape, the sliding wedges are simplified to the Rankine earth pressure. Based on the equilibrium condition and the strength failure criterion, the double wedge analysis method and the limit equilibrium method are used to analyze the stress conditions of the high and steep slopes. A stability calculation method for high and steep slopes is proposed, and a high and steep slope stability calculation formula is constructed. This improves the problem of the limit equilibrium method's overestimation (low-steep slopes) or underestimation (high-steep slopes) in calculating the stability of high and steep slopes. This embodiment can effectively solve the existing problem of high and steep slope model evaluation, and the calculation results are more consistent with the actual stability of the slopes. The calculation results are more accurate, thereby effectively guiding disaster prevention and mitigation work on high and steep slopes.

[0085] Example 2

[0086] Based on the first embodiment, this embodiment takes a steep slope with groundwater as an example to illustrate a method for calculating the stability of a steep slope. The method includes the following steps:

[0087] S1. The failure surface of the steep slope is equivalent to a double-segment linear shape, and the sliding body of the steep slope is equivalent to a first triangular wedge and a second triangular wedge connected to each other.

[0088] See Figure 3 , Figure 3 A schematic diagram of a high and steep slope model with groundwater provided in an embodiment of the present invention.

[0089] Specifically, according to the typical profile of soil landslide, the slope rupture surface is considered to be a double-segment linear shape, and the sliding body is equivalent to Figure 2 The two connected triangular wedges shown in FIG are the first triangular wedge BCD and the second triangular wedge ABD. At the same time, assuming that the water surface line EF is parallel to the AD surface, the groundwater level line is simplified to a double-segment line form.

[0090] S2. Analyze the force applied to the second triangular wedge and calculate the force applied to the second triangle.

[0091] Specifically, when the high and steep slope is a high and steep slope with groundwater, the forces acting on the second triangular wedge ABD include: the active earth pressure thrust exerted by the first triangular wedge BCD on the second triangular wedge ABD, the hydrostatic pressure, and the total pore water pressure at the bottom surface of the second triangular wedge ABD.

[0092] First, calculate the active earth pressure thrust and hydrostatic pressure exerted by the first triangular wedge BCD on the second triangular wedge ABD respectively to obtain the total active earth pressure:

[0093]

[0094] Among them, E a is the total active earth pressure, γ is the soil density, H is the slope height, h1 is the height of the first triangular wedge, θ is the angle between the bottom of the second triangular wedge and the ground, θ=α-π / 4+φ / 2, α is the angle between the steep slope and the ground, K a is the active earth pressure coefficient, c and φ are soil shear strength indices, γ w is the water density, h w is the height of the groundwater level, and h2 is the height of the bottom surface of the second triangular wedge.

[0095] Then, the total pore water pressure at the bottom of the second triangular wedge ABD is calculated.

[0096] Specifically, the water surface line function above the AD surface is:

[0097]

[0098] Where x is the distance from the foot of the slope, x1 is the x coordinate value of point E, and x D is the x-coordinate value of point B.

[0099] Integrating formula (7) yields:

[0100]

[0101] Solving the integral (8) yields the total pore water pressure at the bottom surface of the second triangular wedge ABD, i.e., surface AD:

[0102]

[0103] S3. Calculate the normal static equilibrium and tangential static equilibrium of the bottom surface of the second triangular wedge based on the forces acting on the second triangular wedge.

[0104] First, the total active earth pressure is used to calculate the normal static equilibrium of the bottom surface of the second triangular wedge ABD:

[0105] NW BCD cosθ-E a sinθ=0 (10)

[0106] Where N is the normal stress on the shear surface of the bottom surface of the second triangular wedge, W BCD is the deadweight of the first triangular wedge;

[0107]

[0108] Among them, γ sat Saturated weight of soil.

[0109] Then, the total active earth pressure is used to calculate the tangential static equilibrium of the bottom surface of the second triangular wedge:

[0110] SW BCD sinθ-E a cosθ=0 (12)

[0111] Where S is the shear stress on the shear surface of the bottom surface of the second triangular wedge.

[0112] S4. Calculate the stability coefficient of the high and steep slope based on the slope safety factor, the force applied to the second triangular wedge, the normal static balance, and the tangential static balance.

[0113] First, the slope safety factor is:

[0114]

[0115] Wherein, b2 is the length of the base of the first triangular wedge.

[0116] Then, the stability coefficient of the high and steep slope is calculated by combining the slope safety factor, the total active earth pressure, the normal static balance and the tangential static balance.

[0117] Specifically, by combining equations (10), (11), and (12), the stability coefficient of the steep slope is calculated as:

[0118]

[0119] Among them, h is required w >h2,W BCD Given by formula (11); E a is given by formula (6); u is given by formula (9).

[0120] Based on Rankine's earth pressure theory, this embodiment uses the double wedge analysis method and the limit equilibrium method to analyze the stress conditions of high and steep slopes, construct a formula for calculating the stability of high and steep slopes, and proposes a new solution and architecture for calculating high and steep slopes under the action of groundwater. The stability coefficient of high and steep slopes under different groundwater levels can be calculated. The calculation results are more consistent with the actual stability of the slope and more accurate, thereby effectively guiding disaster prevention and mitigation work on high and steep slopes.

[0121] Example 3

[0122] Based on the first and second embodiments, this embodiment uses the high and steep slope stability calculation method, the Bishop method, and the Janbu method to respectively calculate the high and steep slope stability coefficient to illustrate the effect of the high and steep slope stability calculation method.

[0123] Specifically, there is a high and steep clay soil slope. The Bishop method and Janbu method are used to calculate the slope safety factor under the conditions of groundwater and no groundwater respectively, and the results are compared with the high and steep slope stability calculation method proposed in this embodiment. The parameters required for the calculation are shown in Table 2. The calculation results are as follows: Figure 4 As shown, Figure 4 A comparison chart of the safety factor calculation results of steep slopes calculated using different methods provided in an embodiment of the present invention. Figure 4 (a) is a high and steep slope without groundwater. Figure 4 (b) is a high and steep slope with groundwater.

[0124] Table 2 Slope characteristics and geotechnical parameters of sliding zone soil

[0125]

[0126] Figure 4 In (a), the range of working conditions that can cause slope instability is a slope gradient of less than 45 degrees and a slope height of less than 50 meters, which is inconsistent with some actual stable slopes. In addition, all the calculation results of the Bishop method and the Janbu method are too concentrated and cannot well reflect the stability differences of slopes under different working conditions. For the same slope working condition, the calculation results of the Bishop method and the Janbu method are basically the same. Overall, the safety factor obtained by the high-steep slope calculation method proposed in this embodiment not only reflects the differences in slope stability caused by factors such as slope gradient and slope height, but also conforms to the actual stability of the slope.

[0127] Figure 4 In (b), for the relatively "most stable" slope parameters in Table 2 (slope height 30m, slope gradient 25 degrees, groundwater level 9m), the calculation results obtained by the Bishop method and the Janbu method are both destructive. However, the slope in this working condition is actually stable. This shows that strip-based methods such as the Bishop method and the Janbu method have limitations in calculating the stability of high and steep slopes. The high and steep slope calculation method proposed in this embodiment, when establishing the model, specifically considers the impact of large slope angles (greater than 35°) and large slope heights (greater than 15m) on slope stability. Therefore, the calculation results of the high and steep slope calculation method proposed in this embodiment are consistent with the actual stability of high and steep slopes.

[0128] Furthermore, the development trends of the safety factor curves of slopes with a slope gradient greater than 40 degrees obtained by the high and steep slope calculation method proposed in this embodiment, the Bishop method, and the Janbu method are almost the same, which shows that the high and steep slope calculation method proposed in this embodiment is consistent with other methods.

[0129] The above is a further detailed description of the present invention in conjunction with specific preferred embodiments, and the specific implementation of the present invention should not be considered to be limited to these descriptions. For those skilled in the art of the present invention, without departing from the concept of the present invention, several simple deductions or substitutions can be made, which should be considered to fall within the scope of protection of the present invention.

Claims

1. A method for calculating the stability of a high and steep slope, characterized in that: Including steps: The failure surface of the steep slope is equivalent to a two-segment linear shape, and the sliding body of the steep slope is equivalent to a first triangular wedge and a second triangular wedge connected to each other; when the steep slope is a steep slope without groundwater, the force acting on the second triangular wedge includes the active earth pressure thrust exerted by the first triangular wedge on the second triangular wedge; when the steep slope is a steep slope with groundwater, the force acting on the second triangular wedge includes the active earth pressure thrust exerted by the first triangular wedge on the second triangular wedge, the hydrostatic pressure, and the total pore water pressure at the bottom surface of the second triangular wedge, wherein the active earth pressure thrust and the hydrostatic pressure form the total active earth pressure; Analyze the force applied to the second triangular wedge and calculate the force applied to the second triangle; The normal static equilibrium and tangential static equilibrium of the bottom surface of the second triangular wedge are calculated based on the force applied to the second triangular wedge. When the high and steep slope is a high and steep slope without groundwater, the normal static equilibrium and tangential static equilibrium of the bottom surface of the second triangular wedge are calculated using the active earth pressure thrust. When the high and steep slope is a high and steep slope with groundwater, the normal static equilibrium and tangential static equilibrium of the bottom surface of the second triangular wedge are calculated using the active earth pressure. Calculating the normal static equilibrium of the bottom surface of the second triangular wedge includes: N-W BCD cosθ-E a sinθ=0 Where N is the normal stress on the shear surface of the bottom surface of the second triangular wedge, W BCD is the weight of the first triangular wedge, E a is the total active earth pressure, θ is the angle between the bottom surface of the second triangular wedge and the ground; when the steep slope is a steep slope without groundwater, When the steep slope is a steep slope with groundwater, γ sat is the saturated weight of soil, H is the slope height, h w is the height of groundwater level; Calculate the tangential static equilibrium of the base of the second triangular wedge: S-W BCD sinθ-E a cosθ=0 Where S is the shear stress on the shear surface of the bottom surface of the second triangular wedge; Calculating the stability coefficient of the high and steep slope by combining the slope safety factor, the force applied to the second triangular wedge, the normal static balance, and the tangential static balance; When the high and steep slope is a high and steep slope without groundwater, the slope safety factor is: Where N is the normal stress on the shear surface of the bottom surface of the second triangular wedge, c and φ are the shear strength indices of the soil, b2 is the length of the bottom surface of the first triangular wedge, and S is the shear stress on the shear surface of the bottom surface of the second triangular wedge; The stability coefficient of the steep slope is calculated by combining the slope safety factor, the active earth pressure thrust, the normal static balance and the tangential static balance: Where h1 is the height of the first triangular wedge, h2 is the height of the bottom of the second triangular wedge, γ is the soil density, θ is the angle between the bottom of the second triangular wedge and the ground, θ = α - π / 4 + φ / 2, E a is the total active earth pressure, c and φ are the shear strength indices of the soil; When the steep slope is a steep slope with groundwater, the slope safety factor is: Where N is the normal stress on the shear surface of the bottom surface of the second triangular wedge, c and φ are the shear strength indices of the soil, b2 is the length of the bottom surface of the first triangular wedge, S is the shear stress on the shear surface of the bottom surface of the second triangular wedge, and u is the total pore water pressure at the bottom surface of the second triangular wedge; The stability coefficient of the high and steep slope is calculated by combining the slope safety factor, the total active earth pressure, the normal static balance, and the tangential static balance: Where h2 is the height of the bottom of the second triangular wedge, θ is the angle between the bottom of the second triangular wedge and the ground, θ = α - π / 4 + φ / 2, E a is the total active earth pressure, u is the total pore water pressure at the bottom of the second triangular wedge, c and φ are the shear strength indices of the soil, W BCD is the weight of the first triangular wedge, h w >h2.

2. The method for calculating the stability of a high and steep slope according to claim 1, characterized in that: When the high and steep slope is a high and steep slope without groundwater, the active earth pressure thrust is: Among them, E a is the total active earth pressure, γ is the soil density, h1 is the height of the first triangular wedge, H is the height of the slope, θ is the angle between the bottom of the second triangular wedge and the ground, θ = α - π / 4 + φ / 2, α is the angle between the steep slope surface and the ground, K a is the active earth pressure coefficient, c and φ are indicators of soil shear strength.

3. The method for calculating the stability of a high and steep slope according to claim 1, characterized in that: When the steep slope is a steep slope with groundwater, the total active earth pressure is: Among them, E a is the total active earth pressure, γ is the soil density, H is the slope height, h1 is the height of the first triangular wedge, θ is the angle between the bottom of the second triangular wedge and the ground, θ=α-π / 4+φ / 2, α is the angle between the steep slope and the ground, K a is the active earth pressure coefficient, c and φ are soil shear strength indices, h w is the height of the groundwater level, and h2 is the height of the bottom surface of the second triangular wedge.

4. The method for calculating the stability of a high and steep slope according to claim 1, characterized in that: When the steep slope is a steep slope with groundwater, the total pore water pressure is: Among them, r w is the water density, h w is the height of the groundwater level, h2 is the height of the bottom of the second triangular wedge, θ is the angle between the bottom of the second triangular wedge and the ground, θ=α-π / 4+φ / 2, H is the height of the slope, h1 is the height of the first triangular wedge,

Images