A Stability Calculation Method for Shallow Soil Landslide

Abstract

The present invention discloses a method for calculating the stability of a shallow soil landslide, comprising: constructing an improved infinite slope model with a certain increment of slope angle based on a Taylor infinite slope model; calculating the effective anti-sliding force and sliding force of a soil strip unit based on the improved infinite slope model; calculating the safety factor of a shallow soil layer using the effective anti-sliding force and sliding force of a soil strip unit; and deriving the stability factor of a shallow soil landslide according to the calculation formula of the safety factor of a shallow soil layer. The present invention constructs an improved infinite slope model with a certain increment to derive and calculate the stability factor of a shallow soil landslide, thereby correcting the deficiency and error of the previous infinite slope model that the calculation result increases with the increase of the slope when the slope is large, making the calculation result more consistent with the actual situation and more accurate, thereby improving the accuracy of predicting shallow soil landslides induced by rainfall.

Description

Technical Field

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

[0002] Slope stability calculation is a classic geotechnical engineering problem involving many engineering fields. Slope instability is not only related to rainfall, earthquakes and human activities, but also affected by factors such as slope gradient and height. Reasonable and accurate slope stability calculation results are an important support for slope risk assessment and prevention and control. Rainfall-induced landslides are mainly caused by the saturation of soil at a certain depth within the slope due to rainfall, and the reduction of the effective strength of the saturated soil, resulting in slope instability. A large number of studies have shown that rainfall-induced landslides are mostly shallow landslides with small sliding body thickness, and the ratio of sliding body thickness to slope length is small. Such landslides occur suddenly, with insufficient deformation signs and are widely distributed.

[0003] Based on this, researchers obtained a stability calculation model for rainfall-induced landslides based on Taylor's infinite slope model. Figure 1 , Figure 1 is the existing Taylor infinite slope model. Based on this model, the calculation expression of landslide safety factor can be obtained as follows:

[0004]

[0005] Where: γ sat is the saturated weight of sliding zone soil; w is the water density; h w is the depth of saturated zone; α is the slope angle; b is the bottom width of soil strip unit; c′ and φ′ are the effective shear strength indexes of sliding zone soil.

[0006] Considering several groups of slope calculation parameters, see Table 1, the existing Taylor method is used to calculate the safety factor. The results are as follows Figure 2 shown.

[0007] Table 1 Slope characteristics and geotechnical parameters of sliding zone soil

[0008]

[0009] According to the above calculation formula of landslide safety factor and Figure 2 It can be seen that for non-cohesive soil slopes, the safety factor is independent of the saturated zone depth. As the slope gradient increases, the safety factor of the non-cohesive soil slope decreases. For cohesive soil slopes, when the slope is less than 35 degrees, the safety factor decreases as the slope increases; when the slope is greater than 50 degrees, the safety factor "increases" as the slope increases, and the greater the slope, the greater the "increase" of the safety factor. When the slope is between 35 and 50 degrees, the safety factor curve is asymptotically horizontal.

[0010] However, for a given slope, whether it is a cohesive soil slope or a non-cohesive soil slope, the increase in slope gradient will inevitably lead to a decrease in the safety factor. Obviously, when the slope gradient is large, the calculation results obtained by the existing Taylor infinite slope model are quite different from the actual situation, and cannot meet the prediction of rainfall-induced shallow soil landslides, and thus it is difficult to guide the disaster prevention and mitigation work of high and steep slopes. Summary of the invention

[0011] In order to solve the above problems existing in the prior art, the present invention provides a method for calculating the stability of shallow soil landslides. The technical problem to be solved by the present invention is achieved through the following technical solutions:

[0012] A soil shallow landslide stability calculation method, comprising:

[0013] Step 1: Based on Taylor infinite slope model, an improved infinite slope model with a certain increment of slope angle is constructed;

[0014] Step 2: Calculate the effective anti-sliding force and sliding force of the soil strip unit based on the improved infinite slope model;

[0015] Step 3: Calculate the safety factor of the shallow soil layer using the effective anti-sliding force and sliding force of the soil strip unit;

[0016] Step 4: Derivation of the stability coefficient of the shallow soil landslide according to the calculation formula of the safety coefficient of the shallow soil layer.

[0017] In one embodiment of the present invention, in step 2, calculating the effective anti-sliding force of the soil strip unit based on the improved infinite slope model includes:

[0018] 21) Calculate the deadweight of the soil strip unit according to the following formula:

[0019] W = γ sat h w (b+Δb)cos(α+Δα)

[0020] Among them, γ sat is the saturated weight of sliding zone soil, h w is the saturated zone depth, α is the slope angle, b is the bottom width of the soil strip unit, Δα is the slope angle increment, and Δb is the increment of the bottom width of the soil strip unit;

[0021] 22) Based on the stress conditions of the soil strip unit in the improved infinite slope model, the effective anti-sliding force and sliding force of the soil strip unit are calculated according to the deadweight of the soil strip unit.

[0022] In one embodiment of the present invention, in step 22), calculating the effective anti-sliding force of the soil strip unit according to the deadweight of the soil strip unit includes:

[0023] The effective normal stress of the soil strip unit is calculated according to the deadweight of the soil strip unit, and the calculation formula is:

[0024] N′=W·cos(α+Δα)-γ w h w (b+Δb)cos 2 (α+Δα)

[0025] =γ sat h w (b+Δb)cos 2 (α+Δα)-γ w h w (b+Δb)cos 2 (α+Δα)

[0026] The effective anti-sliding force of the soil strip unit is calculated according to the effective normal stress, and the calculation formula is:

[0027] T f =N′·tanφ'+c′(b+Δb)

[0028] =[γ sat h w (b+Δb)cos 2 (α+Δα)-γ w h w (b+Δb)cos 2 (α+Δα)]tanφ'+c′(b+Δb)

[0029] Based on the influence of the slope angle increment on the cohesive strength and pore water pressure, the effective anti-sliding force is corrected to obtain the corrected effective anti-sliding force, and its calculation formula is:

[0030] T f =[γ sat h w (b+Δb)cos 2 (α+Δα)-γ w h w bcos 2 (α+Δα)]tanφ'+c′b

[0031] Among them, γ w is the water density, c′ and φ′ are the effective shear strength indicators of sliding zone soil.

[0032] In one embodiment of the present invention, in step 22), the sliding force of the soil strip unit is calculated according to the following formula:

[0033]

[0034] In one embodiment of the present invention, step 3 comprises:

[0035] The effective anti-sliding force T of the soil strip unit f The ratio of the sliding force S is taken as the safety factor of the shallow soil layer, and assuming that the unit area of ​​the soil strip remains unchanged, the calculation formula of the safety factor of the shallow soil layer is derived as follows:

[0036]

[0037] In one embodiment of the present invention, step 4 comprises:

[0038] 41) For the calculation formula of safety factor of shallow soil, let α = α 1 , α+Δα=α 2 , then the calculation formula of the safety factor of the shallow soil layer can be expressed as:

[0039]

[0040] Among them, m α =cosα 2 / cosα 1 ;

[0041] 42) Define c′secα 1 Assume that α is the reference cohesive strength. 1 = 0 to ensure that the reference cohesive strength corresponding to any slope angle is equal, and let α 2 =α, then the calculation formula of the stability coefficient of shallow soil landslide can be simplified as:

[0042]

[0043] Beneficial effects of the present invention:

[0044] 1. The present invention constructs an improved infinite slope model with a certain increment to derive and calculate the stability coefficient of shallow soil landslides, which corrects the shortcomings and errors of the previous infinite slope model when the slope is large, that is, the calculation result increases with the increase of the slope, so that the calculation result is more consistent with the actual situation and more accurate, and improves the accuracy of predicting shallow soil landslides induced by rainfall;

[0045] 2. The soil shallow landslide stability calculation method provided by the present invention can also use the constructed improved infinite slope model with a certain increment to calculate the critical sliding depth under different slopes.

[0046] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 It is a schematic diagram of the existing Taylor infinite slope model;

[0048] Figure 2 It is the calculation result of safety factor corresponding to different parameters of the existing Taylor infinite slope model;

[0049] Figure 3 It is a schematic flow chart of a method for calculating the stability of a shallow soil landslide provided by an embodiment of the present invention;

[0050] Figure 4 is a schematic diagram of an improved infinite slope model provided by an embodiment of the present invention;

[0051] Figure 5 It is a comparison chart of the calculation results of the landslide stability coefficient of the cohesionless soil slope using the traditional Taylor infinite slope model and the method of the present invention;

[0052] Figure 6 It is a comparison chart of the calculation results of the landslide stability coefficient of the cohesive soil slope using the traditional Taylor infinite slope model and the method of the present invention; DETAILED DESCRIPTION

[0053] The present invention is further described in detail below with reference to specific embodiments, but the embodiments of the present invention are not limited thereto.

[0054] Embodiment 1

[0055] In view of the large difference between the slope stability calculation result and the actual situation, which cannot meet the prediction of rainfall-induced shallow soil landslides, this embodiment modifies the problem that the currently commonly used calculation value based on the infinite slope model is too large when the slope is greater than 35°. Firstly, for the existing infinite slope stability calculation method, considering the influence of slope control factors and different differential unit forms, Taylor's infinite slope model is improved, and a rainfall-induced landslide slope stability calculation method based on the improved infinite slope model (RISM) is proposed, which corrects the problem that the infinite slope model calculates the result of the slope with a larger slope and the actual difference is too large.

[0056] For details, see Figure 3 , Figure 3 The present invention provides a schematic flow chart of a method for calculating the stability of a shallow soil landslide, which includes:

[0057] Step 1: Based on the Taylor infinite slope model, an improved infinite slope model with a certain increment of slope angle is constructed.

[0058] Specifically, based on the existing Taylor infinite slope model, the slope angle α is increased by Δα, and the saturated zone depth h is maintained. w unchanged, and obtain Figure 4The improved infinite slope model shown in Figure 1. Where b represents the bottom width of the soil strip unit under the original infinite slope model, and Δb represents the increment of the bottom width of the soil strip unit under the improved infinite slope model; to a certain extent, b and Δb can also reflect the bottom area of ​​the soil strip unit and the increment of the bottom area caused by Δα. u and Δu b Represents the pore water pressure and its increment.

[0059] Step 2: Calculate the effective anti-sliding force and sliding force of the soil strip unit based on the improved infinite slope model.

[0060] 21) Calculate the self-weight of soil strip unit:

[0061] Specifically, when the slope increases Δα, the saturated zone depth h w If the value of the soil strip unit is constant, the expression of the self-weight of the soil strip unit is:

[0062] W = γ sat h w (b+Δb)cos(α+Δα) (1)

[0063] Among them, γ sat is the saturated weight of sliding zone soil, h w is the depth of the saturated zone.

[0064] It should be noted that the increase in the depth of the saturated zone caused by rainfall is an external factor that affects the stability of the slope. The slope gradient belongs to the nature of the slope itself and is an internal factor. In the calculation of the safety factor of the slope with different slopes, external factors should be controlled, and attention should be paid to controlling the properties of the soil strip unit to remain unchanged before and after the slope changes.

[0065] Formula (1) keeps the weight of the soil strip unit W unchanged. It also shows that although the change of slope has no effect on the weight of the differential unit, it causes the unit bottom area b to change, which in turn causes the cohesive strength and pore water pressure of the bottom surface of the soil strip unit to change.

[0066] It can be understood that for cohesionless soil slopes, only the pore water pressure value at the bottom of the soil strip unit is changed.

[0067] 22) Based on the stress conditions of the soil strip unit in the improved infinite slope model, the effective anti-sliding force and sliding force of the soil strip unit are calculated according to the self-weight of the soil strip unit.

[0068] a) Calculate the effective anti-sliding force of the soil strip unit.

[0069] First, the effective normal stress of the soil strip unit is calculated according to the self-weight of the soil strip unit. The calculation formula is:

[0070]

[0071] Among them, γ wIt is water heavy.

[0072] Then, the effective anti-sliding force of the soil strip unit is calculated according to the effective normal stress, and the calculation formula is:

[0073]

[0074] Among them, c′ and φ′ are both indicators of the effective shear strength of sliding zone soil.

[0075] Finally, the effective anti-sliding force is corrected based on the influence of slope angle increment on cohesive strength and pore water pressure.

[0076] Specifically, analogous to the classic inclined plate slider model, the change in slope only affects the component values ​​of each force in the system in the normal and tangential directions of the sliding surface. Therefore, when analyzing the stability of slopes with different slopes α, the changes in cohesive strength and pore water pressure caused by Δα should be removed. Among them, the cohesive strength and pore water pressure caused by Δα are:

[0077] ΔC=c′Δb (4)

[0078] Δu b =γ w h w Δbcos 2 (α+Δα) (5)

[0079] Combining formulas (3), (4) and (5), we can obtain the corrected effective anti-slip force calculation formula:

[0080] T f =[γ sat h w (b+Δb)cos 2 (α+Δα)-γ w h w bcos 2 (α+Δα)]tanφ'+c′b (6)

[0081] b) Calculate the sliding force of the soil strip unit.

[0082] Specifically, in this embodiment, the sliding force of the soil strip unit is calculated according to the following formula:

[0083]

[0084] Step 3: Calculate the safety factor of the shallow soil layer using the effective anti-sliding force and sliding force of the soil strip unit.

[0085] In this embodiment, the effective anti-sliding force T of the soil strip unit is f The ratio of the sliding force S to the shallow layer safety factor of the soil is taken as the safety factor of the shallow layer of the soil, and assuming that the unit area of ​​the soil strip remains unchanged, the calculation formula of the safety factor of the shallow layer of the soil is derived.

[0086] Specifically, assuming that the unit area of ​​the soil strip remains unchanged, that is:

[0087] h w (b+Δb)cos(α+Δα)=h w bcosα (8)

[0088] By combining formulas (7) and (8), we can get the calculation formula of the safety factor of the shallow soil layer:

[0089]

[0090] Step 4: Derive the stability coefficient of shallow soil landslide based on the calculation formula of the safety factor of shallow soil.

[0091] 41) According to the calculation formula (9) of the safety factor of shallow soil, let α = α 1 , α+Δα=α 2 , then the calculation formula of the safety factor of the shallow soil layer can be expressed as:

[0092]

[0093] Among them, m α =cosα 2 / cosα 1 .

[0094] 42) Define c′secα 1 Assume that α is the reference cohesive strength. 1 =0 to ensure that the reference cohesive strength corresponding to any slope angle is equal, and the simplified calculation formula for the stability coefficient of shallow soil landslide is obtained.

[0095] Specifically, for the convenience of analysis, c′secα in formula (10) is 1 The term is defined as the reference cohesive strength. 1 The value of α 1 Monotonically changes, so to make the reference cohesion strength corresponding to any slope angle equal, it is only necessary to satisfy α 1 Less than or equal to all target slope angles α 2 ,Right now:

[0096] α 1 =min{α 2},α 2 ∈α (11)

[0097] The stability coefficient of shallow soil landslide can be expressed as:

[0098]

[0099] Let α2 =α, the final calculation formula of the stability coefficient of shallow soil landslide is:

[0100]

[0101] By using the above formula (13), the stability coefficient of a shallow landslide of a certain soil type can be calculated, and then the stability of the shallow landslide of the soil type can be judged. When the K value is greater than 1, it means that the slope is in a stable state, and the larger the K value, the more stable the slope; when the K value is less than 1, it means that the slope is unstable and there is a risk of landslide.

[0102] The present invention constructs an improved infinite slope model with a certain increment to derive and calculate the stability coefficient of shallow soil landslides, thereby correcting the shortcomings and errors of the previous infinite slope model when the slope is large, that is, the calculation result increases with the increase of the slope, so that the calculation result is more consistent with the actual situation and more accurate, and the accuracy of predicting rainfall-induced shallow soil landslides is improved.

[0103] In addition, the present invention can also use the constructed improved infinite slope model with a certain increment to calculate the critical sliding depth under different slopes. Specifically, the landslide stability coefficient K value can be set to 1, and the critical sliding depth can be obtained by reverse calculation.

[0104] Embodiment 2

[0105] The method of the present invention is compared with the traditional calculation method of Taylor infinite slope model to illustrate the beneficial effects of the present invention.

[0106] Specifically, for a certain soil slope, shallow sliding failure may occur under the action of rainfall. Considering the slope soil as cohesionless soil and cohesive soil, the Taylor method is used to calculate the slope safety factor, and compared with the landslide stability calculation of the improved infinite slope model newly constructed in the present invention. The parameters required for the calculation are shown in Table 2.

[0107] Table 2 Slope characteristics and geotechnical parameters of sliding zone soil

[0108]

[0109] The calculation results are shown in Figure 5-6 ,in, Figure 5 It is a comparison chart of the calculation results of the landslide stability coefficient of the cohesionless soil slope using the traditional Taylor infinite slope model and the method of the present invention; Figure 6 It is a comparison chart of the calculation results of the landslide stability coefficient of the cohesive soil slope using the traditional Taylor infinite slope model and the method of the present invention.

[0110] from Figure 5It can be seen that when the slope exceeds 35 degrees, the safety factor curve obtained by the Taylor method tends to be horizontal, which does not conform to the development law of slope stability with the change of slope. The result curve obtained by the shallow landslide stability calculation model newly constructed by the present invention becomes steeper after the slope exceeds 35 degrees, which is consistent with the practical understanding that "the steeper the slope, the faster the slope stability is lost".

[0111] from Figure 6 It can be seen that as the slope increases, the safety factor curve obtained by the Taylor method shows a "warping" phenomenon, and the curve shape is symmetrical at a slope of 35 degrees. When the slope is between 35 and 55 degrees, the safety factor curve tends to the horizontal line; when the slope exceeds 65 degrees, the increase in the "warping" of the curve becomes larger, that is, the steeper the slope, the faster the safety factor increases. The result curve obtained by the shallow landslide stability calculation model newly constructed by the present invention maintains consistency with the calculation results of the Taylor method at low angles, and then as the slope increases, the curve reduction increases, and the larger the slope, the faster the safety factor decreases, which is consistent with the actual stability development law of the slope.

[0112] The above contents are further detailed descriptions of the present invention in combination with specific preferred embodiments, and it cannot be determined that the specific implementation of the present invention is limited to these descriptions. For ordinary technicians in the technical field to which the present invention belongs, several simple deductions or substitutions can be made without departing from the concept of the present invention, which should be regarded as falling within the protection scope of the present invention.

Claims

1. A method for calculating the stability of shallow soil landslides, characterized in that: include: Step 1: Based on Taylor infinite slope model, an improved infinite slope model with a certain increment of slope angle is constructed; Step 2: Calculate the effective anti-sliding force and sliding force of the soil strip unit based on the improved infinite slope model; Step 3: Calculate the safety factor of the shallow soil layer using the effective anti-sliding force and sliding force of the soil strip unit; Step 4: deriving the stability coefficient of the shallow soil landslide according to the calculation formula of the safety coefficient of the shallow soil layer; Wherein, in step 2, calculating the effective anti-sliding force of the soil strip unit based on the improved infinite slope model includes: 21) Calculate the deadweight of the soil strip unit according to the following formula: W=γ sat h w (b+Δb)cos(α+Δα); Where W is the deadweight of the soil strip unit, γ sat is the saturated weight of sliding zone soil, h w is the saturated zone depth, α is the slope angle, b is the bottom width of the soil strip unit, Δα is the slope angle increment, and Δb is the increment of the bottom width of the soil strip unit; 22) Based on the stress conditions of the soil strip unit in the improved infinite slope model, the effective anti-sliding force and sliding force of the soil strip unit are calculated according to the deadweight of the soil strip unit, including: The effective normal stress of the soil strip unit is calculated according to the deadweight of the soil strip unit, and the calculation formula is: Where N′ is the effective normal stress of the soil strip unit, γ w It is water weight; The effective anti-sliding force of the soil strip unit is calculated according to the effective normal stress, and the calculation formula is: Where, T f is the effective anti-sliding force of the soil strip unit, c′ and φ′ are both indicators of the effective shear strength of the sliding zone soil; Based on the influence of the slope angle increment on the cohesive strength and pore water pressure, the effective anti-sliding force is corrected to obtain the corrected effective anti-sliding force, which is calculated as follows: T f =[γ sat h w (b+Δb)cos 2 (a+Dα)-γ w h w because 2 (α+Δα)]tanφ'+c′b; The calculation formula of the sliding force of the soil strip unit is: Where S is the sliding force of the soil strip unit; Step 3 specifically includes: The effective anti-sliding force T of the soil strip unit f The ratio of the sliding force S is taken as the safety factor of the shallow soil layer, and assuming that the unit area of ​​the soil strip remains unchanged, the calculation formula of the safety factor of the shallow soil layer is derived as follows: Where K is the safety factor of the shallow soil layer; Step 4 specifically includes: 41) For the calculation formula of the safety factor of the shallow soil layer, let α = α1, α + Δα = α2, then the calculation formula of the safety factor K of the shallow soil layer can be expressed as: In the formula, m α =cosα2 / cosα1; 42) Define c′secα1 as the reference cohesion strength, set α1 = 0 to ensure that the reference cohesion strength corresponding to any slope angle is equal, and set α2 = α, then the calculation formula of the stability coefficient of shallow soil landslide can be simplified to:

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