Reinforced soil slope stability analysis method considering uniformly distributed frictional resistance between soil and reinforcement

Abstract

Disclosed in the present invention is a reinforced soil slope stability analysis method considering uniformly distributed frictional resistance between soil and reinforcement. The method comprises: establishing a cross-sectional model for a target reinforced soil slope to be analyzed; establishing a force equilibrium equation and a moment equilibrium equation for the reinforced soil slope; on the basis of the moment equilibrium equation, establishing a moment equation for any arbitrary point within the cross section of the reinforced soil slope; establishing the relationship between the force equilibrium equation, the moment equation for any arbitrary point within the cross section of the reinforced soil slope, and a yield function; then, calculating an anti-sliding moment and a sliding moment of the reinforced soil slope under the condition of rectangular distribution of frictional force between soil and reinforcement; then, establishing a stability coefficient calculation model for the reinforced soil slope; and finally, selecting a plurality of arbitrary points within the cross section of the reinforced soil slope, separately calculating a stability coefficient for each point on the basis of the stability coefficient calculation model, and selecting the smallest stability coefficient as a final stability coefficient of the reinforced soil slope for evaluating the stability of the reinforced soil slope.

Description

A method for stability analysis of reinforced soil slopes considering uniformly distributed skin friction between soil and reinforcement Technical Field

[0001] This invention belongs to the field of simulation analysis technology for the stability of reinforced soil slopes, and in particular relates to a method for stability analysis of reinforced soil slopes that considers the uniformly distributed frictional resistance between soil and reinforcement. Background Technology

[0002] Reinforcing slopes can effectively reduce cross-sectional dimensions and improve stability, resulting in significant economic benefits. However, current theoretical research on reinforcement is relatively underdeveloped, and methods for slope stability analysis considering reinforced subgrades are not yet perfect. Current slope stability analysis calculations do not fully reflect the effects of reinforcement, tend to be conservative, and differ significantly from actual engineering conditions, leading to waste. Summary of the Invention

[0003] To overcome the shortcomings of existing technologies that calculate the stability coefficient of reinforced soil slopes too small and do not consider the influence of the strength of the reinforcing material, this invention provides a method for analyzing the stability of reinforced soil slopes that considers the uniformly distributed frictional resistance between the soil and the reinforcing material.

[0004] This invention is achieved through the following technical solution:

[0005] A method for stability analysis of reinforced soil slopes considering uniformly distributed skin friction between soil and reinforcement includes the following steps:

[0006] Step 1: Establish a cross-sectional model of the reinforced soil slope to be analyzed, and establish the following calculation relationships for the reinforced soil slope: vertical load on the slope surface, horizontal load on the slope surface, unit width unit weight of soil, horizontal force of the slope, vertical shear force of the slope, and soil moment.

[0007] Vertical loads on the surface of the earth slope: ;

[0008] Horizontal load on the surface of the slope: ;

[0009] Unit weight of soil per unit width: ;

[0010] Horizontal forces on the slope: ;

[0011] Vertical shear force of the slope: ;

[0012] Soil moment: ;

[0013] in, For the vertical load on the surface of the slope, For horizontal loads on the soil slope surface, For sliding surfaces, The slope of the sliding surface. For the surface of the earthen slope, For the normal stress of the sliding surface, This refers to the tangential shear stress on the sliding surface. Unit weight per unit width of soil. For the density of soil, The horizontal force on the slope This represents the vertical shear force of the slope. The stress in the x-direction of the slope is... This represents the vertical shear stress of the slope. Let x be the soil moment, and let xz represent the cross-section of the reinforced soil slope, where x represents the transverse direction of the cross-section of the reinforced soil slope and z represents the vertical direction of the cross-section of the reinforced soil slope.

[0014] Step 2: Establish the force balance equations and moment balance equations for the reinforced soil slope;

[0015] The force balance equations are:

[0016] (1)

[0017] (2)

[0018] The torque balance equation is:

[0019] (3)

[0020] In the formula, For the shear stress of the reinforcing material, For the axial stress of the reinforcing material, where, , , For the tension of the reinforced pad layer;

[0021] Step 3: Based on the moment balance equation in Step 2, establish the moment equation at any point within the cross-section of the reinforced soil slope;

[0022] Any point within the cross-section of the reinforced soil slope The torque equation is:

[0023] (4)

[0024] Step 4: Establish the soil yield function considering the stability function;

[0025] The soil yield function considering the stability function is as follows:

[0026] (5)

[0027] In the formula, Let be the soil yield function. For stability coefficient, ,in, For sliding torque, For anti-slip torque; Pore ​​water pressure, The internal friction angle of the soil. It is the soil cohesion;

[0028] Step 5: Establish the force equilibrium equation, the moment equation at any point within the cross-section of the reinforced soil slope, and the relationship between the yield function;

[0029] Combining equations (1), (2), and (5), we obtain:

[0030] (6)

[0031] In the formula, —Considering the internal friction angle parameter of the stability coefficient, ;

[0032] Combine equations (4) and (6) Adding them together, we get:

[0033] (7)

[0034] Step Six: Determine the anti-sliding moment of the reinforced soil slope;

[0035] When the sliding surface is an arc Equation (7) can be rearranged as follows:

[0036] (8)

[0037] Taking the same assumptions as when no reinforcement is added, let Integrating equation (7), we obtain:

[0038] ;

[0039] Sorted as:

[0040] (9)

[0041] In the formula, —The x-coordinate of the intersection of the sliding surface and the crest of the slope. —The x-coordinate of the intersection point of the sliding surface and the ground;

[0042] The expression for the anti-sliding moment of reinforced soil slope is obtained by rearranging equation (9) as follows:

[0043] (10)

[0044] Step 7: Determine the sliding moment of the reinforced soil slope;

[0045] For reinforced cushion layers arranged horizontally and When the constant is , from equations (9) and (10) we get:

[0046] ;

[0047] Summarized as follows:

[0048] (11)

[0049] think , The design tensile strength per unit width of the reinforcing bar. The x-coordinate of the right slope toe is... Let x be the x-coordinate of the intersection point of the sliding surface and the bottom surface of the slope, then we get:

[0050] ;

[0051] Finally, the expression for the sliding moment of the reinforced soil slope is obtained:

[0052] (12)

[0053] In the formula, — Tangent of the internal friction angle of the soil ;

[0054] Step 8: Based on the anti-sliding moment obtained in Step 6 and the sliding moment obtained in Step 7, establish a stability coefficient calculation model for the reinforced soil slope:

[0055] (13)

[0056] Step 9: Select multiple arbitrary points within the cross-section of the reinforced soil slope. Then, input the following information into the stability coefficient calculation model of the reinforced soil slope obtained in step eight: vertical load on the slope surface, horizontal load on the slope surface, soil unit weight, soil internal friction angle, soil cohesion, design tensile strength per unit width of the reinforcement, abscissa of the right slope toe, abscissa of the intersection of the sliding surface and the bottom of the slope, abscissa of the intersection of the sliding surface and the top of the slope, and abscissa of the intersection of the sliding surface and the ground surface; then, according to the stability coefficient calculation model of the reinforced soil slope, calculate the values ​​for each point. The stability coefficients are calculated, and the smallest stability coefficient is selected as the final stability coefficient of the reinforced soil slope to evaluate its stability.

[0057] The advantages and beneficial effects of this invention are as follows:

[0058] The method of this invention takes into account the influence of reinforced cushion layer on slope stability, greatly reduces the assumptions, and the calculated stability coefficient is more accurate. Detailed Implementation

[0059] To enable those skilled in the art to better understand the present invention, the technical solution of the present invention will be further described below with reference to specific embodiments.

[0060] A method for stability analysis of reinforced soil slopes considering uniformly distributed skin friction between soil and reinforcement includes the following steps:

[0061] Step 1: Establish a cross-sectional model of the reinforced soil slope to be analyzed, and establish the following calculation relationships for the reinforced soil slope: vertical load on the slope surface, horizontal load on the slope surface, unit width unit weight of soil, horizontal force of the slope, vertical shear force of the slope, and soil moment.

[0062] Vertical loads on the surface of the earth slope: ;

[0063] Horizontal load on the surface of the slope: ;

[0064] Unit weight of soil per unit width: ;

[0065] Horizontal forces on the slope: ;

[0066] Vertical shear force of the slope: ;

[0067] Soil moment: ;

[0068] in, For the vertical load on the surface of the slope, For horizontal loads on the soil slope surface, For sliding surfaces, The slope of the sliding surface. For the surface of the earthen slope, For the normal stress of the sliding surface, This refers to the tangential shear stress on the sliding surface. Unit weight per unit width of soil. For the density of soil, The horizontal force on the slope This represents the vertical shear force of the slope. The stress in the x-direction of the slope is... This represents the vertical shear stress of the slope. Let x be the soil moment, and let xz represent the cross-section of the reinforced soil slope, where x represents the transverse direction of the cross-section of the reinforced soil slope and z represents the vertical direction of the cross-section of the reinforced soil slope.

[0069] Step 2: Establish the force balance equations and moment balance equations for the reinforced soil slope;

[0070] The force balance equations are:

[0071] (1)

[0072] (2)

[0073] The torque balance equation is:

[0074] (3)

[0075] In the formula, For the shear stress of the reinforcing material, For the axial stress of the reinforcing material, The vertical axis represents the reinforcement material, where, , , For the tension of the reinforced pad layer;

[0076] Step 3: Based on the moment balance equation in Step 2, establish the moment equation at any point within the cross-section of the reinforced soil slope;

[0077] Any point within the cross-section of the reinforced soil slope The torque equation is:

[0078] (4)

[0079] Step 4: Establish the soil yield function considering the stability function;

[0080] The soil yield function considering the stability function is as follows:

[0081] (5)

[0082] In the formula, Let be the soil yield function. For stability coefficient, ,in, For sliding torque, For anti-slip torque; Pore ​​water pressure, The internal friction angle of the soil. It is the soil cohesion;

[0083] Step 5: Establish the force equilibrium equation, the moment equation at any point within the cross-section of the reinforced soil slope, and the relationship between the yield function;

[0084] Combining equations (1), (2), and (5), we obtain:

[0085] (6)

[0086] In the formula, —Considering the internal friction angle parameter of the stability coefficient, ;

[0087] Combine equations (4) and (6) Adding them together, we get:

[0088] (7)

[0089] Step Six: Determine the anti-sliding moment of the reinforced soil slope;

[0090] When the sliding surface is an arc Equation (7) can be rearranged as follows:

[0091] (8)

[0092] Taking the same assumptions as when no reinforcement is added, let Integrating equation (7), we obtain:

[0093] ;

[0094] This can be further summarized as follows:

[0095] (9)

[0096] In the formula, —The x-coordinate of the intersection of the sliding surface and the crest of the slope. —The x-coordinate of the intersection point of the sliding surface and the ground;

[0097] The expression for the anti-sliding moment of reinforced soil slope is obtained by rearranging equation (9) as follows:

[0098] (10)

[0099] Step 7: Determine the sliding moment of the reinforced soil slope;

[0100] For reinforced cushion layers arranged horizontally and When the frictional force between the soil and the reinforcement is constant (i.e., the frictional force between the soil and the reinforcement is distributed in a rectangular pattern), we can obtain from equations (9) and (10):

[0101] ;

[0102] Further analysis reveals:

[0103] (11)

[0104] think , The design tensile strength per unit width of the reinforcing bar. The x-coordinate of the right slope toe is... Let be the x-coordinate of the intersection point of the sliding surface and the bottom surface of the slope, therefore:

[0105] ;

[0106] Further simplification yields the expression for the sliding moment of the reinforced soil slope:

[0107] (12)

[0108] In the formula, — Tangent of the internal friction angle of the soil ;

[0109] Step 8: Based on the anti-sliding moment obtained in Step 6 and the sliding moment obtained in Step 7, establish a stability coefficient calculation model for the reinforced soil slope:

[0110] That is, the stability coefficient of the reinforced soil slope is obtained from equations (10) and (12). Computational model:

[0111] (13)

[0112] It should be noted that when the reinforced pad layer is arranged horizontally... For soil strips that do not have a reinforced cushion layer, .

[0113] Step 9: Select multiple arbitrary points within the cross-section of the reinforced soil slope. Then, input the following information into the stability coefficient calculation model of the reinforced soil slope obtained in step eight: vertical load on the slope surface, horizontal load on the slope surface, soil unit weight, soil internal friction angle, soil cohesion, design tensile strength per unit width of the reinforcement, abscissa of the right slope toe, abscissa of the intersection of the sliding surface and the bottom of the slope, abscissa of the intersection of the sliding surface and the top of the slope, and abscissa of the intersection of the sliding surface and the ground surface; then, calculate the stability coefficient calculation model of the reinforced soil slope (i.e., Equation 13) for each point. The stability coefficients are calculated, and the smallest stability coefficient is selected as the final stability coefficient of the reinforced soil slope to evaluate its stability.

[0114] The present invention has been described above by way of example. It should be noted that any simple modifications, alterations or other equivalent substitutions that can be made by those skilled in the art without creative effort without departing from the core of the present invention fall within the protection scope of the present invention.

Claims

1. A method for analyzing the stability of reinforced soil slopes considering uniformly distributed skin friction between soil and reinforcement, characterized in that, Includes the following steps: Step 1: Establish a cross-sectional model of the reinforced soil slope to be analyzed, and establish the following calculation relationships for the reinforced soil slope: vertical load on the slope surface, horizontal load on the slope surface, unit width unit weight of soil, horizontal force of the slope, vertical shear force of the slope, and soil moment. Vertical loads on the surface of the earth slope: ； Horizontal load on the surface of the slope: ； Unit weight of soil per unit width: ； Horizontal forces on the slope: ； Vertical shear force of the slope: ； Soil moment: ； in, For the vertical load on the surface of the slope, For horizontal loads on the soil slope surface, For sliding surfaces, The slope of the sliding surface. For the surface of the earthen slope, For the normal stress of the sliding surface, This refers to the tangential shear stress on the sliding surface. Unit weight per unit width of soil. For the density of soil, The horizontal force on the slope This represents the vertical shear force of the slope. The stress in the x-direction of the slope is... This represents the vertical shear stress of the slope. Let x be the soil moment, and let xz represent the cross-section of the reinforced soil slope, where x represents the transverse direction of the cross-section of the reinforced soil slope and z represents the vertical direction of the cross-section of the reinforced soil slope. Step 2: Establish the force balance equations and moment balance equations for the reinforced soil slope; The force balance equations are: （1） （2） The torque balance equation is: （3） In the formula, For the shear stress of the reinforcing material, For the axial stress of the reinforcing material, where, ， ， For the tension of the reinforced pad layer; Step 3: Based on the moment balance equation in Step 2, establish the moment equation at any point within the cross-section of the reinforced soil slope; Any point within the cross-section of the reinforced soil slope The torque equation is: （4） Step 4: Establish the soil yield function considering the stability function; The soil yield function considering the stability function is as follows: （5） In the formula, Let be the soil yield function. For stability coefficient, ,in, For sliding torque, For anti-slip torque; Pore ​​water pressure, The internal friction angle of the soil. It is the soil cohesion; Step 5: Establish the force equilibrium equation, the moment equation at any point within the cross-section of the reinforced soil slope, and the relationship between the yield function; Combining equations (1), (2), and (5), we obtain: （6） In the formula, —Considering the internal friction angle parameter of the stability coefficient, ； Combine equations (4) and (6) Adding them together, we get: （7） Step Six: Determine the anti-sliding moment of the reinforced soil slope; When the sliding surface is an arc Equation (7) can be rearranged as follows: （8） Taking the same assumptions as when no reinforcement is added, let Integrating equation (7), we obtain: ； Sorted as: （9） In the formula, —The x-coordinate of the intersection of the sliding surface and the crest of the slope. —The x-coordinate of the intersection point of the sliding surface and the ground; The expression for the anti-sliding moment of reinforced soil slope is obtained by rearranging equation (9) as follows: （10） Step 7: Determine the sliding moment of the reinforced soil slope; For reinforced cushion layers arranged horizontally and When the constant is , from equations (9) and (10) we get: ； Summarized as follows: （11） think ， The design tensile strength per unit width of the reinforcing bar. The x-coordinate of the right slope toe is... Let x be the x-coordinate of the intersection point of the sliding surface and the bottom surface of the slope, then we get: ； Finally, the expression for the sliding moment of the reinforced soil slope is obtained: （12） In the formula, — Tangent of the internal friction angle of the soil ； Step 8: Based on the anti-sliding moment obtained in Step 6 and the sliding moment obtained in Step 7, establish a stability coefficient calculation model for the reinforced soil slope: （13） Step 9: Select multiple arbitrary points within the cross-section of the reinforced soil slope. Then, input the following information into the stability coefficient calculation model of the reinforced soil slope obtained in step eight: vertical load on the slope surface, horizontal load on the slope surface, soil unit weight, soil internal friction angle, soil cohesion, design tensile strength per unit width of the reinforcement, abscissa of the right slope toe, abscissa of the intersection of the sliding surface and the bottom of the slope, abscissa of the intersection of the sliding surface and the top of the slope, and abscissa of the intersection of the sliding surface and the ground surface; then, according to the stability coefficient calculation model of the reinforced soil slope, calculate the values ​​for each point. The stability coefficients are calculated, and the smallest stability coefficient is selected as the final stability coefficient of the reinforced soil slope to evaluate its stability.

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