A method for calculating the position of the slip line field stress discontinuity of active earth pressure

Abstract

The application relates to the technical field of civil engineering, and provides a calculation method of a stress discontinuity line position of a sliding line field of active earth pressure, which comprises the following steps: determining basic parameters of a retaining wall and soil bodies behind the wall; dividing a potential sliding area behind the wall into a Rankine area and a transition area; dividing the whole potential sliding area and the Rankine area into a plurality of triangular strips respectively; respectively selecting a triangular strip to perform stress analysis, and establishing a strip force recursive formula; taking different earth pressure values, and iteratively executing the following steps: calculating side pressure coefficients and strip force inclination angles on lines of the triangular strips in the Rankine area; starting from a wall surface, sequentially calculating corresponding strip line side pressure coefficients and strip force inclination angles of the triangular strips in the potential sliding area, and stopping when the strip force inclination angle is equal to an internal friction angle, and the area that has completed the calculation is referred to as the transition area; according to the condition that the side pressure coefficients and the strip force inclination angles calculated on an intersection line of the transition area and the Rankine area are equal, the intersection line is determined as the stress discontinuity line.

Description

Technical Field

[0001] This application relates to the field of civil engineering technology, and in particular to a method for calculating the location of stress discontinuities in an active earth pressure slip field. Background Technology

[0002] Slip line field is a key issue to consider in earth pressure calculation.

[0003] Currently, the main methods for calculating earth pressure include: the limit equilibrium method, the limit analysis method, the slip line method, and numerical analysis methods. Among these, the limit equilibrium method calculates the magnitude of earth pressure by assuming the shape of the slip surface; the limit analysis method obtains the upper and lower limits of earth pressure by constructing a kinematically permissible displacement field and a statically permissible stress field; the slip line method can accurately obtain the analytical solution of the slip line field without considering gravity, and when considering conditions such as soil self-weight and wall friction, it can calculate an approximate numerical solution, making it an effective method for calculating the complete slip line field.

[0004] In solving slip line fields, a stress discontinuity phenomenon can occur, where the slip line direction deflects at the stress discontinuity, thus affecting the calculated earth pressure. Most current research ignores the influence of stress discontinuity. Although some studies have proposed limit conditions for the occurrence of stress discontinuity in slip line fields, they have not provided detailed discussions on how to determine the specific location of the stress discontinuity line.

[0005] Therefore, there is a need to provide an improved technical solution that addresses the shortcomings of the existing technology. Summary of the Invention

[0006] The purpose of this application is to provide a method for calculating the location of stress discontinuities in an active earth pressure slip field. This method calculates the location of stress discontinuities in the active earth pressure slip field, thereby obtaining the slip field under stress discontinuity conditions, improving the earth pressure calculation theory, and solving or alleviating the problems existing in the prior art.

[0007] To achieve the above objectives, this application provides the following technical solution:

[0008] This application provides a method for calculating the location of stress discontinuities in an active earth pressure slip line field, including:

[0009] Step 1: Determine the basic parameters of the retaining wall and the soil behind it;

[0010] Step 2: Divide the potential sliding zone of the soil behind the wall into the Rankine zone and the transition zone;

[0011] Step 3: Divide the Rankine zone into m triangular blocks and calculate the lateral pressure coefficient K for each block in the Rankine zone. Ri and its inter-strip thrust angle δ Ri; where the strip lines are the two sides outside the sliding surface of the triangular strip;

[0012] Step 4: Divide the entire potential slip zone into n triangular blocks, and randomly select one triangular block for force analysis to establish the force and moment balance equation and derive the recursive formula for inter-strip forces.

[0013] Step 5: Assume the magnitude of the active earth pressure at the retaining wall surface is P. a Based on the recursive formula for interstrip forces, starting from the wall surface, the interstrip thrust P corresponding to each strip line in the potential slip zone is calculated sequentially. k Its inter-strip thrust angle δ k and the lateral pressure coefficient K k When the thrust angle δ on the kth block line of the potential slip zone k Equal to the internal friction angle of the soil behind the wall When the calculation stops, the calculated area is called the transition zone.

[0014] Step Six: Based on the calculation results of Steps Five and Three, plot the lateral pressure coefficient (K). k K Ri ) and the angle of thrust between bars (δ) k δ Ri The curve showing how the inclination angle θ of the strip line changes;

[0015] Step 7: Based on the lateral pressure coefficient (K) k K Ri ) and the angle of thrust between strips (δ) k δ Ri The curve showing the change in inclination angle θ of the block line is used to determine whether there exists an intersecting line between the Rankine zone and the transition zone, and whether the forces on this intersecting line satisfy K. k =K Ri δ k =δ Ri ;

[0016] Among them, when When the value is less than a preset threshold, it is determined that the intersecting line exists in the Rankine region and the transition region;

[0017] In the formula, Δδ is the inter-strip thrust angle δ of the transition zone corresponding to strips with the same inclination angle. k δ between the thrust angles of the Rankine zone Ri The difference, The thrust angle δ between strips in the transition zone corresponding to the same block line k δ between the thrust angles of the Rankine zone Ri The average value, ΔK is the lateral pressure coefficient K of the transition zone corresponding to the strips with the same inclination angle. k Rankine zone lateral pressure coefficient K Ri The difference, The lateral pressure coefficient K of the transition zone corresponding to the same block line k Rankine zone lateral pressure coefficient K Ri The average value;

[0018] Step 8: When there is no intersection line that satisfies Step 7, change the assumed magnitude of the active earth pressure Pa and repeat Steps 5 to 7 until an intersection line that satisfies Step 7 exists.

[0019] Step Nine: When the intersecting line exists, determine the position corresponding to the intersecting line. If the intersecting line is the boundary line of the Rankine region, and the interstrip thrust angle on the intersecting line satisfies... Then the intersecting line is determined to be a slip line, not a stress discontinuity line; if the inclination angle of the intersecting line is less than the inclination angle θ of the Rankine zone boundary line. R And simultaneously satisfy K k =K Ri , The intersecting line is then determined to be a stress discontinuity line, thus identifying the location of the stress discontinuity line.

[0020] In a further technical solution of the present invention, in step one, the basic parameters of the retaining wall and the soil behind the wall include:

[0021] The retaining wall height H;

[0022] The wall back dip angle ε; where the angle value of the wall back dip angle that dips towards the soil behind the wall is a positive number;

[0023] The wall-back friction angle δ0; where the angle value of the wall-back friction angle away from the soil behind the wall is a positive number.

[0024] The unit weight of the soil behind the wall is γ.

[0025] Internal friction angle of soil behind wall

[0026] The inclination angle β of the backfill behind the wall; where the angle of inclination of the backfill behind the wall that is higher than the horizontal plane is a positive number;

[0027] Active earth pressure P a , where its initial value is taken as the magnitude of the Coulomb active earth pressure.

[0028] In a further technical solution of the present invention, in step two, when there is no stress discontinuity, the position of the transition zone is determined by the inclination angle ε of the retaining wall and the inclination angle θ of the Rankine zone boundary line. R Determine; when stress discontinuity exists, the location of the transition zone is determined by calculation in step five.

[0029] A further technical solution of the present invention is that, after the basic parameters of the retaining wall and the soil behind the wall are determined, the inclination angle θ of the boundary line of the Rankine zone is determined. RAnd the ranken zone slip angle α R The calculation formula is as follows:

[0030]

[0031]

[0032] In the formula, β is the internal friction angle of the soil behind the wall; β is the inclination angle of the backfill behind the wall.

[0033] In a further technical solution of the present invention, step three, dividing the Rankine region into m triangular blocks, specifically involves:

[0034] Based on the pre-set included angle d of the triangular blocks, determine the number m of triangular blocks that divide the Rankine area;

[0035] in, The inclination angle of the i-th block line in the Rankine district is θ. Ri , when i=1, θ R1 =θ R When i = m + 1, θ Rm+1 =-β. Wherein, the inclination angle of the strip line along the horizontal direction is 0°, and the inclination angle of the strip line is positive when rotated clockwise along the horizontal direction and negative when rotated counterclockwise.

[0036] A further technical solution of the present invention is that the lateral pressure coefficient K of the i-th block line in the Rankine zone Ri The calculation process is as follows:

[0037] With the tilt angle as θ Ri OA of the block line i Slip surface line A i The area BOA formed by B and the slope line OB i To calculate the computational domain, we analyze its force state and establish force equilibrium equations along the x and y directions respectively:

[0038]

[0039]

[0040] Among them, W Ri For BOA i The gravity of the region, R Ri For smooth surface A i The force acting on B forms an angle with the normal direction of the sliding surface.

[0041] Combination Combining the above equations and transforming them, we can obtain the lateral pressure coefficient K of the i-th strip in the Rankine zone. Ri The calculation formula is as follows:

[0042]

[0043] The interstrip thrust angle δ of the i-th strip in the Rankine district is obtained by transforming the following formula. Ri :

[0044]

[0045] In the formula, α R The angle of inclination of the Rankine zone slip surface.

[0046] In a further technical solution of the present invention, step four, dividing the entire potential slip zone into n triangular blocks, specifically involves:

[0047] Based on the pre-defined included angle d of the triangular blocks, the entire potential slip zone is divided into n triangular blocks;

[0048] in, The inclination angle of the k-th strip line in the entire potential slip zone is θ. k The horizontal strip line has an inclination angle of 0°, and clockwise rotation of the strip line along the horizontal direction is positive, while counterclockwise rotation is negative.

[0049] In a further technical solution of the present invention, in step four, a triangular block is randomly selected from the triangular blocks in the potential slip zone for force analysis, a force and moment balance condition is established, the recursive formula for the inter-strip force is derived, and based on K... k =2P k / (γL k 2 The relationship between P and P k Converted to lateral pressure coefficient K k The recursive formula for the inter-strip force is as follows:

[0050]

[0051]

[0052]

[0053] In the formula, W k Let be the weight of the k-th triangular block in the entire potential slip zone. L k-1 L k α represents the lengths of the lower and upper stripes of the k-th triangular block, respectively; k P is the inclination angle of the sliding surface of the k-th triangular block; k-1 P k These are the forces acting on the lower and upper lines of the k-th triangular block, respectively; δ k-1 δ kZ represents the angle between the forces acting on the lower and upper lines of the k-th triangular block and their normal directions, also known as the inter-strip force inclination angle; k-1 Z k θ represents the distance from the origin of the point of application of the thrust on the lower and upper lines of the k-th triangular block, respectively; k-1 θ k θ represents the inclination angles of the lower and upper lines of the k-th triangular block, respectively. k ' is the angle of inclination of the angle bisector of the k-th triangular block; h k Let x0 be the length of the angle bisector of the k-th triangular block; x0, x wk These are the x-coordinates of the origin and the centroid of the k-th triangular block, respectively.

[0054] A further technical solution of the present invention is based on the inclination angle α of the sliding surface of the k-th triangular block. k With the thrust angle δ between the bars k The relationship between the two strips was used to calculate the thrust angle δ between the strips. k ;

[0055] Wherein, the inclination angle α of the sliding surface of the k-th triangular block k With the thrust angle δ between the bars k The relationship between them is:

[0056]

[0057]

[0058] In the formula, δ k ' is the angle between the direction of the thrust and the direction of its normal on the k-th block angle bisector.

[0059] In a further technical solution of the present invention, the soil behind the wall is non-cohesive soil, the surface of the retaining wall is rough, and the backfill behind the wall is sloping but has no overburden load.

[0060] The beneficial effects of this invention are as follows: The method for calculating the location of stress discontinuities in the slip line field of active earth pressure provided by this invention can accurately calculate the location of stress discontinuities in the slip line field, thereby obtaining the slip line field containing stress discontinuities, making the calculated earth pressure more accurate and reasonable. The method for calculating the location of stress discontinuities in the slip line field of active earth pressure provided by this invention has a simple calculation process, is easy to implement in a program, has high calculation efficiency, and reliable calculation results. It can be used to calculate earth pressure on cohesionless soil slopes with rough wall surfaces and sloping backfill. Attached Figure Description

[0061] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. Wherein:

[0062] Figure 1 These are schematic flowcharts provided according to some embodiments of this application;

[0063] Figure 2 This is a schematic diagram illustrating the division of the Rankine zone and transition zone under stress discontinuity conditions according to some embodiments of this application;

[0064] Figure 3 This is a schematic diagram of the division of Rankine zone blocks and stress analysis provided according to some embodiments of this application;

[0065] Figure 4 This is a schematic diagram of the potential slip zone block division according to some embodiments of this application;

[0066] Figure 5 These are typical stress diagrams of transition zones provided according to some embodiments of this application;

[0067] Figure 6 This is a graph showing the relationship between the lateral pressure coefficient and the interstrip force inclination angle as a function of the inclination angle of the strip line, provided according to some embodiments of this application.

[0068] Figure 7 This is a diagram showing the positional relationship between the Rankine zone boundary line, the transition zone boundary line, and the stress discontinuity line, provided according to some embodiments of this application. Detailed Implementation

[0069] The present application will now be described in detail with reference to the accompanying drawings and embodiments. Various examples are provided by way of interpretation and not by way of limitation. In fact, those skilled in the art will recognize that modifications and variations can be made to the present application without departing from the scope or spirit thereof. For example, a feature shown or described as part of one embodiment may be used in another embodiment to produce yet another embodiment. Therefore, it is desirable that the present application encompass such modifications and variations that fall within the scope of the appended claims and their equivalents.

[0070] In the following description, the terms "first / second / third" are used merely to distinguish similar objects and do not represent a specific order of objects. It is understood that "first / second / third" may be interchanged in a specific order or sequence where permitted, so that the embodiments of this application described herein can be implemented in an order other than that illustrated or described herein.

[0071] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this disclosure belongs. The terminology used herein is for the purpose of describing embodiments of this disclosure only and is not intended to limit this disclosure.

[0072] See Figure 1This invention provides a method for calculating the location of stress discontinuities in an active earth pressure slip line field, comprising the following steps:

[0073] Step 1: Determine the basic parameters of the retaining wall and the soil behind it.

[0074] The basic parameters of the retaining wall and the soil behind it include: the height H of the retaining wall; the inclination angle ε of the wall back; where the inclination angle of the wall back towards the soil behind the wall is a positive number; the friction angle δ0 of the wall back; where the friction angle of the wall back away from the soil behind the wall is a positive number; the unit weight of the soil behind the wall γ; and the internal friction angle of the soil behind the wall. The inclination angle β of the backfill behind the wall; where the angle of inclination of the backfill behind the wall above the horizontal plane is a positive number; the active earth pressure P a Among them, the active earth pressure P a The initial value is taken as the magnitude of the Coulomb active earth pressure, and the active earth pressure P a The point of application is located at the lower 1 / 3 of the height of the retaining wall (distance from the toe of the wall).

[0075] Step 2: Divide the potential slip zone of the soil behind the wall into the Rankine zone and the transition zone.

[0076] It should be noted that, in the embodiments of this application, when the retaining wall moves an appropriate distance away from the backfill so that the stress state in the soil behind the wall reaches an active limit equilibrium state, the earth pressure on the back of the wall is called the active earth pressure. The potential slip zone of the soil behind the wall mentioned in this invention refers to the area surrounded by the slip surface in the soil, the back of the retaining wall, and the surface of the backfill when the soil reaches an active limit equilibrium state.

[0077] Assume that during plastic deformation, the displacement is independent of the z-axis of the rectangular coordinate system, and the displacement of each point occurs in the xOy plane, where O is the origin of the coordinate system.

[0078] According to some embodiments of this application, the potential sliding zone of the soil behind the wall is divided into a Rankine zone and a transition zone, i.e., according to the dip angle θ of the Rankine zone boundary line. R The angle α of the Rankine zone slip surface R The values ​​are used to divide the Rankine zone region. When stress discontinuity exists, the transition zone region intersects with the Rankine zone region. The specific boundary line of the transition zone needs to be calculated according to step five. The schematic diagram of the division result can be referred to... Figure 2 .

[0079] Once the basic parameters of the retaining wall and the soil behind it are determined, the inclination angle θ of the boundary line of the Rankine zone is described. R And the ranken zone slip angle α R The calculation formula is as follows:

[0080]

[0081]

[0082] In the formula, β is the internal friction angle of the soil behind the wall; β is the inclination angle of the backfill behind the wall.

[0083] Step 3: Divide the Rankine region into m triangular blocks and calculate the lateral pressure coefficient K of the i-th block line in the Rankine region. Ri and its inter-strip thrust angle δ Ri ; where the strip lines are the two sides outside the sliding surface of the triangular strip.

[0084] See Figure 3 Using triangular blocks BOA i For example, A i B is the sliding surface of the triangular block, which intersects the surface of the soil behind the wall at point B. The triangular block BOA... i It contains two strip lines, namely OB and OA. i Among them, the strip line OA i Lateral pressure coefficient K Ri and its inter-strip thrust angle δ Ri .

[0085] In some implementations, the Rankine region is divided into m triangular blocks. Specifically, the number m of triangular blocks into which the Rankine region is divided is determined based on a pre-defined included angle d between the triangular blocks; where, The inclination angle of the i-th strip in the Rankine district is θ. Ri The inclination angle of the strips along the horizontal direction is 0°. The inclination angle of the strips is positive when rotated clockwise along the horizontal direction and negative when rotated counterclockwise.

[0086] The pre-set angle d of the triangular blocks can be 1° or less than 1°.

[0087] In some implementations, the lateral pressure coefficient K of the i-th strip line in the Rankine zone Ri The calculation formula is as follows:

[0088]

[0089] The interstrip thrust angle δ of the i-th strip in the Rankine district is obtained by transforming the following formula. Ri :

[0090]

[0091] In the formula, α R The angle of inclination of the Rankine zone slip surface.

[0092] Step 4: Divide the entire potential slip zone into n triangular blocks, and randomly select one triangular block for force analysis to establish the force and moment balance equations and derive the recursive formula for inter-strip forces.

[0093] In some embodiments, dividing the entire potential slip zone into n triangular blocks specifically involves dividing the entire potential slip zone into n triangular blocks according to a pre-defined included angle d between the triangular blocks; wherein, The inclination angle of the k-th strip line in the entire potential slip zone is θ. k The horizontal strip line has an inclination angle of 0°, and clockwise rotation of the strip line along the horizontal direction is positive, while counterclockwise rotation is negative.

[0094] See Figure 5 From the triangular blocks in the potential slip zone, randomly select one triangular block for force analysis and establish a force analysis along R. k Direction and perpendicularity R k The force balance equations for the direction and the moment balance equations about point O are combined, and the three equations can be simplified.

[0095] The recursive formula for inter-strip forces is obtained, and based on K... k =2P k / (γL k 2 The relationship between P and P k Converted to lateral pressure coefficient K k The recursive formula for the inter-strip force is as follows:

[0096]

[0097]

[0098]

[0099] In the formula, W k Let be the weight of the k-th triangular block in the entire potential slip zone. L k-1 L k α represents the lengths of the lower and upper stripes of the k-th triangular block, respectively; k P is the inclination angle of the sliding surface of the k-th triangular block; k-1 P k These are the forces acting on the lower and upper lines of the k-th triangular block, respectively; δ k-1 δ k Z represents the angle between the forces acting on the lower and upper lines of the k-th triangular block and their normal directions, also known as the inter-strip force inclination angle; k-1 Z k θ represents the distance from the origin O to the point of application of the thrust on the lower and upper lines of the k-th triangular block, respectively;k-1 θ k θ represents the inclination angles of the lower and upper lines of the k-th triangular block, respectively. k ' is the angle of inclination of the angle bisector of the k-th triangular block; h k Let x0 be the length of the angle bisector of the k-th triangular block; x0, x wk These are the x-coordinates of the origin O and the centroid of the k-th triangular block, respectively.

[0100] Step 5: Assume the magnitude of the active earth pressure at the retaining wall surface is P. a Based on the recursive formula for interstrip forces, starting from the retaining wall surface, the interstrip thrust P corresponding to each strip line in the potential slip zone is calculated sequentially. k Its inter-strip thrust angle δ k and the lateral pressure coefficient K k When the thrust angle δ on the kth block line of the potential slip zone k Equal to the internal friction angle of the soil behind the wall When the calculation stops, the calculated area is called the transition zone, and the corresponding strip line inclination angle is...

[0101] Step Six: Based on the calculation results of Steps Five and Three, plot the lateral pressure coefficient (K). k K Ri ) and the angle of thrust between strips (δ) k δ Ri The curve showing how the inclination angle θ of the strip line changes.

[0102] In a specific example, a retaining wall has a height H = 5m, a wall back inclination angle ε = 20°, a wall back friction angle δ0 = 0°, and a soil unit weight γ = 20kN / m³. 3 internal friction angle of soil behind the wall The backfill angle β = 0°, and the lateral pressure coefficient (K) is calculated according to steps five and three. k K Ri ) and the angle of thrust between strips (δ) k δ Ri The curve drawn according to step six is ​​as follows: Figure 6 As shown.

[0103] Step 7: Based on the lateral pressure coefficient (K) k K Ri ) and the angle of thrust between strips (δ) k δ Ri The curve showing the change in inclination angle θ of the block line is used to determine whether there exists an intersecting line between the Rankine zone and the transition zone, and whether the forces on this intersecting line satisfy K. k =K Ri δ k =δ Ri ;

[0104] Among them, when Less than a preset threshold (e.g., 10) -3 When ), it is determined that the intersecting line exists in the Rankine region and the transition region;

[0105] In the formula, Δδ is the inter-strip thrust angle δ of the transition zone corresponding to strips with the same inclination angle. k δ between the thrust angles of the Rankine zone Ri The difference, The thrust angle δ between strips in the transition zone corresponding to the same block line k δ between the thrust angles of the Rankine zone Ri The average value, ΔK is the lateral pressure coefficient K of the transition zone corresponding to the strips with the same inclination angle. k Rankine zone lateral pressure coefficient K Ri The difference, The lateral pressure coefficient K of the transition zone corresponding to the same block line k Rankine zone lateral pressure coefficient K Ri The average value.

[0106] Step 8: When there is no intersection line that satisfies Step 7, change the assumed magnitude of the active earth pressure Pa and repeat Steps 5 to 7 until an intersection line that satisfies Step 7 exists.

[0107] Step Nine: When the intersection line exists, determine the position corresponding to the intersection line. If the intersection line is the boundary line OA of the Rankine zone, and the interstrip thrust angle on the intersection line satisfies... Then the intersecting line is determined to be a slip line, not a stress discontinuity line; if the inclination angle of the intersecting line is less than the inclination angle θ of the Rankine zone boundary line OA. R And simultaneously satisfy K k =K Ri , The intersecting line is then determined to be a stress discontinuity line, thus identifying the location of the stress discontinuity line.

[0108] Preferably, the soil behind the retaining wall is non-cohesive soil, the wall surface is rough, and the backfill behind the wall is sloping and has no overburden load.

[0109] by Figure 6 The example shown illustrates that the retaining wall has a height H = 5m, a wall back inclination angle ε = 20°, a wall back friction angle δ0 = 0°, and a soil unit weight γ = 20kN / m³. 3 internal friction angle of soil behind the wall The backfill angle β = 0°. Substituting the above parameters into the calculation steps above, we can obtain... Figure 6 , Figure 7 The calculation results show that the active earth pressure coefficient Ka = 0.517, which is greater than the Coulomb active earth pressure coefficient of 0.498.

[0110] Figure 6 In the figure, the curves showing the variation of the lateral pressure coefficient and intersegment force dip angle between the Rankine zone and the transition zone with the dip angle of the strip line are shown. At the intersection of the Rankine zone and the transition zone, Δ = 5.9969e. -4 <10 -3 The intersecting lines correspond to the stress discontinuity lines, which have an inclination angle of 55.2°.

[0111] like Figure 7 The diagram shows the positional relationship between the Rankine zone boundary line, the transition zone boundary line, and the stress discontinuity line. The stress discontinuity line is located in the area where the Rankine zone and the transition zone intersect.

[0112] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A method for calculating the position of the slip line field stress discontinuity of an active earth pressure, characterized by, include: Step 1: Determine the basic parameters of the retaining wall and the soil behind it; Step 2: Divide the potential sliding zone of the soil behind the wall into the Rankine zone and the transition zone; Step 3: Divide the Rankine zone into m triangular blocks and calculate the lateral pressure coefficient K for each block in the Rankine zone. Ri and its inter-strip thrust angle δ Ri Among them, the strip lines are the two sides outside the sliding surface of the triangular strip; Step 4: Divide the entire potential slip zone into n triangular blocks, and randomly select one triangular block for force analysis to establish the force and moment balance equation and derive the recursive formula for inter-strip forces. Step 5: Assume the magnitude of the active earth pressure at the retaining wall surface is P. a Based on the recursive formula for interstrip forces, starting from the retaining wall surface, the interstrip thrust P corresponding to each strip line in the potential slip zone is calculated sequentially. k Its inter-strip thrust angle δ k and the lateral pressure coefficient K k When the thrust angle δ on the kth block line of the potential slip zone k When the internal friction angle φ of the soil behind the wall is equal to the angle of friction of the soil behind the wall, the calculation stops. At this time, the calculated area is called the transition zone. Step six: plot the curves of side pressure coefficient (K k , K Ri ) and inter-rib thrust angle (δ k , δ Ri ) versus rib line angle θ based on the results of step five and step three; Step 7: Based on the lateral pressure coefficient (K) k K Ri ) and the angle of thrust between strips (δ) k δ Ri The curve showing the change in inclination angle θ of the strip line is used to determine whether there exists an intersecting line between the Rankine zone and the transition zone, and whether the forces on this intersecting line satisfy K. k =K Ri δ k =δ Ri ; wherein, when if the difference is less than a preset threshold, it is determined that the intersection line exists in the Rankine zone and the transition zone. In the formula, Δδ is the inter-strip thrust angle δ of the transition zone corresponding to strips with the same inclination angle. k δ between the thrust angles of the Rankine zone Ri The difference, The thrust angle δ between strips in the transition zone corresponding to the same block line k δ between the thrust angles of the Rankine zone Ri The average value, ΔK is the lateral pressure coefficient K of the transition zone corresponding to the strips with the same inclination angle. k Rankine zone lateral pressure coefficient K Ri The difference, The lateral pressure coefficient K of the transition zone corresponding to the same block line k Rankine zone lateral pressure coefficient K Ri The average value; Step 8: When there is no intersection line that satisfies Step 7, change the assumed magnitude of the active earth pressure Pa and repeat Steps 5 to 7 until an intersection line that satisfies Step 7 exists. Step Nine: When the intersection line exists, determine the position corresponding to the intersection line. If the intersection line is the boundary line of the Rankine region, and the interstrip thrust angle on the intersection line satisfies δ... k =δ Ri If the angle of inclination is φ, then the intersecting line is determined to be a slip line, not a stress discontinuity line; if the angle of inclination of the intersecting line is less than the angle of inclination θ of the Rankine zone boundary line... R And simultaneously satisfy K k =K Ri δ k =δ Ri If the intersection line is not equal to φ, then the intersection line is determined to be a stress discontinuity line, thus determining the location of the stress discontinuity line.

2. The method of calculating the position of the active earth pressure slip line field stress discontinuity line according to claim 1, wherein, In step one, the basic parameters of the retaining wall and the soil behind it include: The retaining wall height H; The wall back dip angle ε; where the angle value of the wall back dip angle that dips towards the soil behind the wall is a positive number; The wall-back friction angle δ0; where the angle value of the wall-back friction angle away from the soil behind the wall is a positive number. The unit weight of the soil behind the wall is γ. The internal friction angle φ of the soil behind the wall; The inclination angle β of the backfill behind the wall; where the angle of inclination of the backfill behind the wall that is higher than the horizontal plane is a positive number; Active earth pressure P a where its initial value is taken as the Coulomb active earth pressure magnitude.

3. The method of calculating the position of the active earth pressure slip line field stress discontinuity line according to claim 2, wherein, In step two, the location of the transition zone is determined by the wall heel angle ε of the retaining wall and the angle θ of the Rankine zone boundary line when there is no stress discontinuity R is determined; when there is a stress discontinuity, the location of the transition zone is determined by step five.

4. The method of calculating the position of the active earth pressure slip line field stress discontinuity line according to claim 3, wherein, When the retaining wall and the basic parameters of the soil body behind the wall are determined, the inclination θ of the Rankine zone boundary line R and the inclination α of the Rankine zone sliding surface R are calculated according to the following formulae: ； ； In the formula, φ is the internal friction angle of the soil behind the wall; β is the inclination angle of the backfill behind the wall.

5. The method of calculating the position of the active earth pressure slip line field stress discontinuity line according to claim 4, wherein, In step three, dividing the Rankine region into m triangular blocks specifically involves: Based on the pre-set included angle d of the triangular blocks, determine the number m of triangular blocks that divide the Rankine area; wherein, ; the inclination of the i-th block line of the Rankine zone is θ Ri wherein, the inclination of the block line along the horizontal direction is 0°, and the inclination of the block line is positive when rotating clockwise along the horizontal direction and negative when rotating counterclockwise.

6. The method of calculating the position of the active earth pressure slip line field stress discontinuity line according to claim 5, wherein, The side pressure coefficient K of the i-th block line in the Rankine region Ri The calculation formula is as follows: ； The inter-tract thrust inclination δ of the i-th tract line in the Rankine region is obtained by solving the following equation of transformation Ri : ； In the formula, α R is the Rankine zone slide surface inclination angle.

7. The method of claim 1, wherein: In step four, dividing the entire potential slip zone into n triangular blocks specifically involves: Based on the pre-defined included angle d of the triangular blocks, the entire potential slip zone is divided into n triangular blocks; wherein, wherein, the inclination of the kth block line of the whole potential slip zone is θ k wherein, the inclination of the horizontal block line is 0°, and the clockwise rotation of the block line along the horizontal direction is positive, and the counterclockwise rotation is negative.

8. The method of calculating the position of the active earth pressure slip line field stress discontinuity line according to claim 7, wherein, In step four, a triangular block is randomly selected from the triangular blocks in the potential slip zone for force analysis. Force and moment equilibrium conditions are established, and the recursive formula for the inter-strip forces is derived. Based on... The relationship between P k Converted to lateral pressure coefficient K k The recursive formula for the inter-strip force is as follows: ； ； ； In the formula, R k M is the force acting on the sliding surface of the k-th triangular block. k For P on the k-th triangular block k-1 P k W k R k The sum of the moments about point O; W k Let be the weight of the k-th triangular block in the entire potential slip zone. L k-1 L k α represents the lengths of the lower and upper stripes of the k-th triangular block, respectively; k P is the inclination angle of the sliding surface of the k-th triangular block; k-1 P k These are the forces acting on the lower and upper lines of the k-th triangular block, respectively; δ k-1 δ k Z represents the angle between the forces acting on the lower and upper lines of the k-th triangular block and their normal directions, also known as the inter-strip force inclination angle; k-1 Z k θ represents the distance from the origin of the point of application of the thrust on the lower and upper lines of the k-th triangular block, respectively; k-1 θ k θ represents the inclination angles of the lower and upper lines of the k-th triangular block, respectively. k ’ h is the angle of inclination of the angle bisector of the k-th triangular block. k Let x0 be the length of the angle bisector of the k-th triangular block; x0, x wk These are the x-coordinates of the origin and the centroid of the k-th triangular block, respectively.

9. The method of calculating the position of the active earth pressure slip line field stress discontinuity line according to claim 8, wherein, According to the relationship between the inclination angle a of the kth triangular strip sliding surface k and the inter- strip thrust inclination angle d k , the inter- strip thrust inclination angle d k is calculated. wherein the inclination angle a of the kth triangular strip sliding surface k and the interstrip thrust inclination angle d k is related by ； ； where δkis the angle between the thrust direction and the normal direction of the kth block corner bisector. k is the angle between the thrust direction and the normal direction of the kth block corner bisector.

10. The method of calculating the position of the active earth pressure slip line field stress discontinuity line according to claim 1, wherein, The soil behind the wall is cohesive-free soil, the retaining wall surface is rough, and the backfill behind the wall is sloping but has no overburden load.

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