A stability analysis method for super-giant landslides considering the influence of earth curvature

Abstract

The present invention discloses a super-giant landslide stability analysis method considering the influence of earth curvature factors, comprising the following steps: S1. Determine the criteria for super-giant landslide stability analysis and data characterizing the analysis results: Based on the Franius stability safety factor criterion, soil slope stability analysis is performed and the interaction force between soil strips is considered, and finally the safety factor K is required to characterize the analysis results; S2. According to the Franius stability safety factor criterion described in step S1, when the soil strip is in equilibrium, the tangential force formula at the sliding surface of the soil strip is obtained; the normal stress of the soil strip is obtained from the vertical force balance of the soil strip; when the sliding soil body is in overall equilibrium, the algebraic sum of the moment of force on each soil strip to the center of the sliding surface is zero to obtain the sum of the tangential forces of each soil strip; S3. According to the result obtained in step S2, the safety factor K is obtained according to the effective stress method. The simplified Bishop method considering the influence of earth curvature of the present invention has a reduced safety factor in the calculation of long landslides, which is more in line with the actual landslide situation.

Description

Technical Field

[0001] The invention relates to the field of slope stability calculation, and in particular to a super-giant landslide stability analysis method taking into account the influence of earth curvature factors. Background Art

[0002] In 1927, Franius proposed a stability safety factor, which is equal to the ratio of the maximum shear strength that the soil can provide to the shear stress value of the soil required to maintain slope stability. If the Coulomb strength criterion is adopted, the stability safety factor is related to the shear strength of each point in the soil, the effective stress level, and the shear stress level required to maintain stability. This definition is called the Franius stability safety factor criterion.

[0003] Based on this criterion, Bishop proposed a method to calculate the stability safety factor K in 1955 by considering the inter-strip force. He believed that when the slope is in a stable state (i.e. K>1), the shear stress τ of any soil strip i on the sliding arc surface is i Should be less than its shear strength S i , its stability safety factor K is S i With τ i ratio.

[0004] Since the simplified Bishop method assumes that the gravity of each soil strip is vertically downward, however, there are many long landslides in many places on the earth, some of which are tens of kilometers or even hundreds of kilometers long, such as submarine landslides. In this case, when studying the stability of landslides by the simplified Bishop method, due to the gravity of the soil block W i There is a certain angle with the vertical downward assumption of the Bishop method, and it is necessary to take into account that it is affected by the curvature of the earth. Summary of the invention

[0005] The purpose of the present invention is to overcome the deficiencies of the prior art and provide a super-giant landslide stability analysis method taking into account the influence of the earth's curvature factor.

[0006] The objective of the present invention is achieved through the following technical solution: A super giant landslide stability analysis method considering the influence of earth curvature factors comprises the following steps:

[0007] S1. Determination of criteria for stability analysis of mega-landslides and data for characterizing analysis results:

[0008] Based on the Franius stability safety factor criterion, the slope stability analysis is carried out and the interaction force between soil strips is considered. Finally, the safety factor K is needed to characterize the analysis results.

[0009] S2. According to the Franius stability safety factor criterion described in step S1, when the soil strip is in equilibrium, the vertical force balance equation is analyzed for each soil strip to obtain the tangential force at the sliding surface of the soil strip; the normal stress of the soil strip is obtained from the vertical force balance of the soil strip; when the sliding soil body is in overall equilibrium, the algebraic sum of the moments of the forces on each soil strip about the center of the sliding surface is zero, and the overall equilibrium equation is calculated; according to the overall equilibrium of the landslide, the horizontal force effect of gravity on the sliding block under the influence of the earth's curvature is obtained, and the complete stability coefficient of the landslide is derived under this condition;

[0010] S3. According to the result obtained in step S2, the safety factor K is obtained according to the effective stress method. At this time, the converted formula is:

[0011]

[0012] in

[0013] In the formula, c i , ——soil cohesion and internal friction angle, °;

[0014] Q i ——lateral force on the soil strip, kN;

[0015] e i ——The moment arm of the lateral force about the center O, m;

[0016] θ i ——The angle between the gravity direction of the soil strip and the vertical direction, °;

[0017] R——radius of the earth, km;

[0018] α i ——the angle between the normal direction of the soil strip sliding surface and the vertical direction, °;

[0019] W i ——Gravity acting on the soil strip, kN.

[0020] According to the converted formula, pre-set the coefficient K and substitute it to find m i Then inversely calculate the K value, and repeat this process until the true safety factor is calculated.

[0021] When the soil strip is in a balanced state in step S2, the gravity W of the soil strip pointing to the center of the earth is considered. i There is an angle θ between the vertical force of the soil strip i , so the vertical force of the soil strip is W i cosθ i ; From this, the vertical force equilibrium equation of the soil strip is obtained, and the relationship between the tangential force and the normal stress is obtained:

[0022] Wi cosθ i -T i sinα i -N i cosα i =0

[0023] Where: T i is the tangential force at the sliding surface of the soil strip; N i is the normal pressure; thus, the normal stress of the soil strip is obtained from the vertical force balance of the soil strip.

[0024] In step S2, the soil strip is directed toward the center of the earth by gravity W i , there is a lateral component of the soil strip gravity W i sinθ i , the algebraic sum of the moments of the forces on each soil strip about the center of the sliding surface is zero, thus the overall equilibrium equation of the soil is obtained:

[0025] ∑W i cosθ i Rsinα i -∑T i R+∑(Q i +W i sinθ i ) i =0

[0026] In the formula, Q i Indicates the lateral force on the soil strip, unit kN; θ i It represents the angle between the gravity direction of the soil strip and the vertical direction, in degrees; e i It represents the force arm of the lateral force to the center of the circle O, in m; thus, the tangential force T is obtained. i Relationship with safety factor K;

[0027] According to the tangential force T i The relationship between it and the safety factor K is used to derive the safety factor K.

[0028] In step S2, the influence of gravity on the horizontal force of the slider as a whole under the influence of the earth's curvature is determined as follows:

[0029] Suppose the soil block is divided into 2i blocks, with the i-th block separating the left and right sides. From the first block, W i The angles with the vertical downward are θ 1 ,θ 2 ,…,θ 2i-1 ,θ 2i ; From this, we can know that at this time, the horizontal force produced by gravity on the slider as a whole under the influence of the earth's curvature is:

[0030]

[0031] When finally finding K, we use an iterative calculation method. First, assume that K = 1 and find m i Then substitute it to find the K value; if K≠1 at this time, use the new K value to find the next m i and K value, and iterates repeatedly until the K before the last iteration is very close to the K after the calculated iteration. At this time, the slope safety factor K obtained by the iteration is used as the final stability analysis result; the K before the iteration and the K after the calculated iteration are very close means that the difference between the two is less than the set threshold.

[0032] The beneficial effect of the present invention is that the simplified Bishop method taking into account the influence of the earth curvature has a lower safety factor in the calculation of long landslides, which is more in line with the actual landslide situation. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 It is a schematic diagram of the soil mass gravity W of a long landslide under the influence of the earth's curvature of the present invention;

[0034] Figure 2 It is a diagram of the Bishop method calculation taking into account the curvature of the earth according to the present invention. DETAILED DESCRIPTION

[0035] The technical solution of the present invention is further described in detail below in conjunction with the accompanying drawings, but the protection scope of the present invention is not limited to the following.

[0036] S1. Determination of criteria for stability analysis of mega-landslides and data for characterizing analysis results:

[0037] Based on the Franius stability safety factor criterion, the slope stability analysis is carried out and the interaction force between soil strips is considered. Finally, the safety factor K is needed to characterize the analysis results.

[0038] S2. According to the Franius stability safety factor criterion described in step S1, when the soil strip is in equilibrium, the vertical force balance equation is analyzed for each soil strip to obtain the tangential force at the sliding surface of the soil strip; the normal stress of the soil strip is obtained from the vertical force balance of the soil strip; when the sliding soil body is in overall equilibrium, the algebraic sum of the moments of the forces on each soil strip about the center of the sliding surface is zero, and the overall equilibrium equation is calculated; according to the overall equilibrium of the landslide, the horizontal force effect of gravity on the sliding block under the influence of the earth's curvature is obtained, and the complete stability coefficient of the landslide is derived under this condition;

[0039] S3. According to the result obtained in step S2, the safety factor K is obtained according to the effective stress method. At this time, the converted formula is:

[0040]

[0041] in

[0042] In the formula, c i , ——soil cohesion and internal friction angle, °;

[0043] Q i ——lateral force on the soil strip, kN;

[0044] e i ——The moment arm of the lateral force about the center O, m;

[0045] θ i ——The angle between the gravity direction of the soil strip and the vertical direction, °;

[0046] R——radius of the earth, km;

[0047] α i ——the angle between the normal direction of the soil strip sliding surface and the vertical direction, °;

[0048] W i ——Gravity acting on the soil strip, kN.

[0049] According to the converted formula, pre-set the coefficient K and substitute it to find m i Then inversely calculate the K value, and repeat this process until the true safety factor is calculated.

[0050] In this application, the simplified Bishop method is used to study the stability of landslides. i There is a certain angle with the vertical downward assumed by the Bishop method, and it is necessary to consider that it is affected by the curvature of the earth. Figure 1 As shown, O r is the center of the earth, and R is the radius of the earth.

[0051] Based on the simplified Bishop method, the calculation is given as follows: Figure 2 shown.

[0052] Based on this criterion, a method for calculating the stability safety factor K considering the inter-strip force is proposed. When the soil slope is in a stable state (i.e. K>1), the shear stress τ of any soil strip i on the sliding arc surface i Should be less than its shear strength S i , its stability safety factor K is S i With τ i The ratio of is, that is, formula (1):

[0053]

[0054] In the formula, c′ i , ——effective cohesion and effective internal friction angle of soil, °;

[0055] σ i——normal stress at the arc sliding surface of the ith soil strip, kPa;

[0056] u i ——Pore water pressure at the circular sliding surface of the ith soil strip, kPa.

[0057] When the soil strip is in equilibrium, τ i Should be equal to the tangential force T at the sliding surface of the soil strip i Divide by the length l of the arc of the sliding surface of the soil strip i , that is, T i / l i , normal stress σ i Should be equal to the normal pressure N i Divide by l i , that is, N i / l i . The above T i and N i Substituting the value of into formula (1), we get formula (2):

[0058]

[0059] From the balance of vertical forces in the soil strip, we can obtain formula (3):

[0060] W i cosθ i +Y i -Y i+1 -T i sinα i -N i cosα i =0

[0061] or

[0062] N i cosα i =W i cosθ i +Y i -Y i+1 -T i sinα i (3)

[0063] Substituting formula (1) into formula (2), we get formula (4) and formula (5):

[0064]

[0065] In the formula

[0066] When the sliding soil is in overall equilibrium, the algebraic sum of the moments of the forces on each soil strip about the center of the sliding surface should be equal to 0. At this time, the inter-strip force X i , Y i , Xi+1 and Y i+1 As an internal force, its moment will appear positive and negative once and then cancel each other out, so we get formula (6):

[0067] ∑W i cosθ i Rsinα i -∑T i R+∑(Q i +W i sinθ i ) i =0

[0068] Therefore In the formula, Q i ——lateral force on the soil strip, kN;

[0069] θ i ——The angle between the gravity direction of the soil strip and the vertical direction, °;

[0070] e i ——The moment arm of the lateral force about the center O, m.

[0071] Substituting formula (2) into the above formula, we can get formula (7):

[0072]

[0073] Therefore

[0074]

[0075] The N in formula (4) i Substitute into the above formula and let b i ≈l i cosα i , after sorting, we can get formula (8):

[0076]

[0077] Formula (8) is the basic formula for calculating the stability safety factor K by the Bishop method. i -Y i+1 is unknown, and the value of K cannot be obtained. Considering The term is generally very small, and ignoring it will have little impact (but it is safer). Formula (8) can be simplified to formula (9):

[0078]

[0079] This formula is called the simplified Bishop formula that takes into account the earth's curvature. It is derived based on the effective stress method. The derivation steps are the same as above, except that W i cosθ i -u i b i Convert to W i cosθ i , Convert to c i 'Convert to c i The converted formula (10) and formula (11) are:

[0080]

[0081] and

[0082] It should be noted that the coefficient m expressed by equations (5) and (11) i There is also a factor K in it, so an iterative calculation method is used to calculate K. Usually, we can first assume that K = 1 and calculate m i Then use formula (10) to find the K value. If K≠1 at this time, use the new K value to find the next m i and K value, and repeat the iteration until the assumed K is very close to the calculated K. According to experience, 3 to 4 iterations are usually enough to meet the accuracy requirements, and the iterations usually converge.

[0083] It should also be noted that when the soil block is divided into 2i blocks, the i-th block separates the left and right sides, and from the first block onwards, W i The angles with the vertical downward are θ 1 ,θ 2 ,…,θ 2i-1 ,θ 2i It can be seen that the horizontal force produced by the earth's curvature on the slider is as follows:

[0084]

[0085] The above description is only one embodiment of the present invention and does not limit the present invention in any form. Any simple modification, equivalent changes and modifications made to the above embodiment based on the technical essence of the present invention are within the scope of the technical solution of the present invention.

Claims

1. A super giant landslide stability analysis method considering the influence of earth curvature factors, characterized by: The following steps are involved: S1. Determination of criteria for stability analysis of mega-landslides and data for characterizing analysis results: Based on the Franius stability safety factor criterion, the slope stability analysis is carried out and the interaction force between soil strips is considered. Finally, the safety factor K is needed to characterize the analysis results. S2. According to the Franius stability safety factor criterion described in step S1, when the soil strip is in equilibrium, the vertical force balance equation is analyzed for each soil strip to obtain the tangential force at the sliding surface of the soil strip; the normal stress of the soil strip is obtained from the vertical force balance of the soil strip; when the sliding soil body is in overall equilibrium, the algebraic sum of the moments of the forces on each soil strip about the center of the sliding surface is zero, and the overall equilibrium equation is calculated; according to the overall equilibrium of the landslide, the horizontal force effect of gravity on the sliding block under the influence of the earth's curvature is obtained, and the complete stability coefficient of the landslide is derived under this condition; S3. According to the result obtained in step S2, the safety factor K is obtained according to the effective stress method. At this time, the converted formula is: in In the formula, c i , Soil cohesion and internal friction angle, °; Q i ——lateral force on the soil strip, kN; e i ——The moment arm of the lateral force about the center O, m; θ i ——The angle between the gravity direction of the soil strip and the vertical direction, °; R——radius of the earth, km; α i ——the angle between the normal direction of the soil strip sliding surface and the vertical direction, °; W i ——gravity of the soil strip, kN; According to the converted formula, pre-set the coefficient K and substitute it to find m i Then inversely calculate the K value, and repeat this process until the true safety factor is calculated.

2. The method for analyzing the stability of a super-giant landslide taking into account the influence of the earth curvature factor according to claim 1 is characterized in that: When the soil strip is in a balanced state in step S2, the gravity W of the soil strip pointing to the center of the earth is considered. i There is an angle θ between the vertical force of the soil strip i , so the vertical force of the soil strip is W i cosθ i ; From this, the vertical force equilibrium equation of the soil strip is obtained, and the relationship between the tangential force and the normal stress is obtained: W i cosθ i -T i sinα i -N i cosα i =0 Where: T i is the tangential force at the sliding surface of the soil strip; N i is the normal pressure; thus, the normal stress of the soil strip is obtained from the vertical force balance of the soil strip.

3. The method for analyzing the stability of a super-giant landslide taking into account the influence of the earth curvature factor according to claim 1 is characterized in that: In step S2, the soil strip is directed toward the center of the earth by gravity W i , there is a lateral component of the soil strip gravity W i sinθ i , the algebraic sum of the moments of the forces on each soil strip about the center of the sliding surface is zero, thus the overall equilibrium equation of the soil is obtained: ∑W i cosθ i Rsinα i -∑T i R+∑(Q i +W i sinθ i )e i =0 In the formula, Q i It represents the lateral force on the soil strip, in kN; θ i It represents the angle between the soil strip along the gravity direction pointing to the center of the earth and the vertical direction, in degrees; e i It represents the force arm of the lateral force to the center of the circle O, in m; thus, the tangential force T is obtained. i Relationship with safety factor K; According to the tangential force T i The relationship between it and the safety factor K is used to derive the safety factor K.

4. The method for analyzing the stability of a super-giant landslide taking into account the influence of the earth curvature factor according to claim 1 is characterized in that: In step S2, the influence of gravity on the horizontal force of the slider as a whole under the influence of the earth's curvature is determined as follows: Suppose the soil block is divided into 2i blocks, with the i-th block separating the left and right sides. From the first block, W i The angles with the vertical downward are θ1, θ2, ..., θ 2i-1 ,θ 2i ; From this we can see that at this time, the horizontal force produced by gravity on the slider as a whole under the influence of the earth's curvature is:

5. The method for analyzing the stability of a super-giant landslide taking into account the influence of the earth curvature factor according to claim 1 is characterized in that: When iterative calculation is used to finally calculate K, first assume K = 1 and calculate m i Then substitute it to find the K value; if K≠1 at this time, use the new K value to find the next m i and K value, and iterates repeatedly until the K before the last iteration is very close to the K after the calculated iteration. At this time, the slope safety factor K obtained by the iteration is used as the final stability analysis result; the K before the iteration and the K after the calculated iteration are very close means that the difference between the two is less than the set threshold.

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