A method for calculating lateral earth pressure of limited range fill

Abstract

This invention discloses a method for analyzing and calculating lateral earth pressure on a finite-range fill, comprising: S1, determining the basic parameters for calculating lateral earth pressure on a finite-range fill; S2, determining the expression for the total weight of the soil in the slip prism; S3, determining the expression for the actual shear force at the boundary of the slip prism; S4, constructing the vertical and horizontal force balance equations for the slip prism; S5, determining the expression for the lateral earth pressure on the outer surface of the newly constructed retaining structure; S6, based on the expression for the lateral earth pressure on the outer surface of the newly constructed retaining structure, considering the range of the slip surface rupture angle, assigning values ​​sequentially to obtain the lateral earth pressure value on the outer surface of the newly constructed retaining structure corresponding to each slip surface rupture angle, thereby obtaining the maximum value of the lateral earth pressure on the outer surface of the newly constructed retaining structure and its corresponding slip surface rupture angle. The method of this invention is applicable to the calculation of lateral earth pressure on newly constructed retaining structures in complex scenarios, and has high calculation efficiency, accuracy, and reliability.

Description

Technical Field

[0001] This invention relates to the field of roadbed engineering design, and in particular to a method for analyzing and calculating lateral earth pressure on a limited range of fill. Background Technology

[0002] Based on typical application scenarios of retaining wall-type retaining structures in railways, highways, urban rail transit, and municipal roads, some retaining structures are located in special areas such as road underpasses, tunnel entrance / exit transition sections, and foundation pit support, where construction sites are narrow, there are many adjacent structures, and environmental impacts are complex. For these scenarios, the backfill soil between the newly constructed retaining structure and existing structures is a finite-range fill. The lateral earth pressure analysis and calculation methods for this area differ significantly from those for conventional retaining structures, requiring a comprehensive consideration of the finite-range fill and the influence of external loads.

[0003] Accurate calculation of lateral earth pressure in finite-range fill is the foundation for the bearing capacity analysis and structural design of retaining structures. In conventional design, the classical Rankine earth pressure theory or Coulomb earth pressure theory is generally used. However, both of these earth pressure theories are based on the assumption of semi-infinite width fill. Directly applying them to the calculation of lateral earth pressure in finite-range fill will result in large calculation errors and is not suitable for the design of retaining structures in finite-range fill.

[0004] Currently, there are many research results on finite-range earth pressure analysis methods, and there are four main typical analysis methods:

[0005] First, based on the theory of the upper limit of soil plasticity and in accordance with the law of related flow, the active and passive earth pressure intensity of finite soil can be derived and used as the amplitude of lateral earth pressure of finite fill.

[0006] Second, based on the assumptions of rigidity of retaining structures and small deformation of soil, a simplified calculation method for earth pressure in finite soil is derived through the force equilibrium relationship of differential bodies.

[0007] Third, based on the limit equilibrium theory and the plane slip surface assumption, and considering the application of soil cohesion, a mathematical expression for calculating active earth pressure in finite soil is established.

[0008] Fourth, based on the premise of the non-limit state of the soil, and considering the empirical relationship between earth pressure and the lateral displacement of the support structure, a nonlinear displacement active earth pressure calculation formula is established.

[0009] The above methods partially solve the problem of calculating lateral earth pressure in finite fill, but they still have shortcomings in terms of the reasonable determination of external loads, inclined walls, and slip surfaces.

[0010] Therefore, how to effectively consider the slip surface form of the finite-range fill and the combined effect of external loads, conduct stress state analysis of the slip prism of the finite-range fill under ultimate bearing conditions, and accurately obtain the magnitude and distribution of lateral earth pressure of the finite-range fill under active failure mode is a key technical problem that should be focused on and solved at this stage. Summary of the Invention

[0011] To address the problems existing in the prior art, this invention provides an accurate and efficient method for calculating lateral earth pressure in finite-range fill.

[0012] Therefore, the present invention adopts the following technical solution:

[0013] A method for calculating lateral earth pressure on finite-area fill includes the following steps:

[0014] S1, determine the basic parameters for calculating the lateral earth pressure of the finite-range fill, including geometric parameters, load parameters, shear strength parameters of the fill, and parameters for the range of lateral earth pressure action; the finite-range fill is the fill between the newly constructed retaining structure and the existing structure; the finite-range fill includes an upper slip prism and a lower stable bearing soil; the contact surface between the newly constructed retaining structure and the finite-range fill is the outer surface of the newly constructed retaining structure, the contact surface between the existing structure and the finite-range fill is the outer surface of the existing structure, the contact surface between the slip prism and the stable bearing soil is the slip surface, and the upper surface of the slip prism bears the external load; wherein, the parameters for the range of lateral earth pressure action include the length of earth pressure action on the outer surface of the newly constructed retaining structure. Length of earth pressure acting on the outer surface of existing structures ;

[0015] S2, determine the expression for the total weight G of the slip-slip prism soil mass;

[0016] S3, determine the expressions for each actual shear force at the boundary of the slip prism, wherein each actual shear force includes the tangential force on the outer surface of the newly constructed retaining structure. Tangential forces on the outer surface of existing structures and the tangential force of the slip surface The , , Satisfies the Mohr-Coulomb strength criterion;

[0017] S4, considering the external load borne by the slip prism, the total weight G of the soil in the slip prism, and the aforementioned... , , Construct the vertical force balance equations and horizontal force balance equations for the slip prism;

[0018] S5, derived from S3 , , The expression, along with the vertical and horizontal force balance equations obtained from S4, determines the lateral earth pressure on the outer surface of the newly constructed retaining structure caused by the finite amount of fill. The expression for lateral earth pressure. Regarding the fracture angle of the slip surface Relationship;

[0019] S6, based on the lateral earth pressure on the outer surface of the newly constructed retaining structure. The expression considers the fracture angle of the slip surface. Within the range, the fracture angle of the slip surface is sequentially determined. By assigning values, the lateral earth pressure value on the outer surface of the newly built retaining structure corresponding to the rupture angle of each slip surface is obtained, and then the maximum value of the lateral earth pressure E on the outer surface of the newly built retaining structure and its corresponding slip surface rupture angle are obtained.

[0020] In step S1 above:

[0021] The geometric parameters include the height of the newly constructed retaining structure. Outer surface inclination angle Limited fill width and the fracture angle of the slip surface and the width of the upper surface of the slip prism , where the fracture angle of the slip surface The width of the upper surface of the slip prism is an undetermined variable. The calculation formula is:

[0022] ,

[0023] When the slip surface intersects with the upper surface. The distance between the intersection point and the top of the newly constructed retaining structure; when the slip surface does not intersect with the upper surface. For the limited range of fill width The load parameters include the load applied to the upper surface. and the unit weight of fill within a limited range The applied load External load;

[0024] The shear strength parameters of the fill include a limited range of fill cohesion. Friction angle within a limited range of fill soil The internal friction angle between the limited fill and the outer surface of the newly constructed retaining structure. and cohesion The internal friction angle between the fill and the outer surface of the existing structure within a limited range and cohesion .

[0025] In step S1 above, the length of earth pressure acting on the outer surface of the newly built retaining structure is obtained. Length of earth pressure acting on the outer surface of existing structures The method is as follows:

[0026] According to the basic theory of active earth pressure, a tensile stress distribution zone exists in soil with cohesion. The length of the crack in the upper part of a finite-range fill is... Within the range, the lateral earth pressure is 0, and the crack length is... It is applicable to both the outer surfaces of newly constructed retaining structures and the outer surfaces of existing structures, with a crack length of... The calculation formula is as follows:

[0027] ,

[0028] Calculate the length of earth pressure acting on the outer surface of the newly constructed retaining structure. The formula is as follows:

[0029] ,

[0030] Length of earth pressure acting on the outer surface of existing structures The expression is as follows:

[0031] ,

[0032] when At that time, take =0.

[0033] The total weight of the slip-ruptured prism soil mass mentioned in step S2 above The expression is:

[0034] .

[0035] In step S3 above:

[0036] Tangential force on the outer surface of the newly constructed retaining structure The expression is as follows:

[0037] ,

[0038] Where E represents the lateral earth pressure on the outer surface of the newly constructed retaining structure, which is an unknown quantity that needs to be confirmed in subsequent steps.

[0039] In step S3 above:

[0040] Tangential force on the outer surface of the existing structure The expression is as follows:

[0041] ,

[0042] In the formula, The horizontal reaction force of the existing structure's outer surface to the slipped prism.

[0043] In step S3 above:

[0044] The tangential force on the slip surface The expression is as follows:

[0045] ,

[0046] In the formula, This represents the normal reaction force of the stable bearing soil below the slip surface on the slip prism.

[0047] In step S4 above:

[0048] The vertical force balance equation is:

[0049] .

[0050] In step S4 above:

[0051] The horizontal force balance equation is:

[0052] .

[0053] Lateral earth pressure on the outer surface of the newly constructed retaining structure mentioned in step S5 above The expression is:

[0054] ,

[0055] In the formula, To determine the proportional values ​​of earth pressure at the same height on the outer surface of the newly constructed retaining structure and the outer surface of the existing structure, based on the principle that horizontal earth pressure is equal at the same height, the following formula is used. Value:

[0056] .

[0057] Compared with the prior art, the present invention has the following beneficial effects:

[0058] 1. The lateral earth pressure analysis and calculation method for finite-range fill in this invention considers the Mohr-Coulomb strength criterion and active failure limit state analysis. By determining the range of the slip prism of the finite-range fill and establishing the force equilibrium conditions of the slip prism, the accurate solution of the lateral earth pressure on the outer surface of the newly constructed retaining structure is achieved. The method fully considers the influence of the spatial dimensions of the finite-range fill, the magnitude of the external load, and the inclination angle of the outer surface, and realizes the calculation of active earth pressure of finite-range fill under complex load distribution and spatial dimension parameter control.

[0059] 2. The expression for the lateral earth pressure on the outer surface of the finite-range fill obtained by the method of this invention is only a relationship with the slip surface rupture angle. According to the principle of extreme value of horizontal active earth pressure, the lateral earth pressure E of the finite-range fill and its corresponding slip surface rupture angle θ under the ultimate active failure state can be obtained quickly and conveniently by assigning the slip surface rupture angle. The solution process is efficient and intuitive, applicable to relatively complex analysis and calculation scenarios, and has high calculation accuracy.

[0060] 3. The method for calculating lateral earth pressure in finite-range fill in this invention basically follows the most widely used Coulomb earth pressure theory. The relevant calculation parameters are all commonly used geotechnical parameters, and the range of empirical parameters is relatively clear and easy to obtain.

[0061] 4. The lateral earth pressure on the outer surface of the newly constructed retaining structure obtained by the lateral earth pressure analysis and calculation method of the limited-range backfill of the present invention can more scientifically and rationally determine the size design of the retaining structure under the limited-range backfill conditions, avoid material waste, improve the rationality of the retaining structure design, and provide important technical support for the scientific and rational design of retaining wall and anti-slide pile retaining structures. Attached Figure Description

[0062] Figure 1 This is a flowchart of a method for analyzing and calculating lateral earth pressure in a limited-range fill body according to the present invention;

[0063] Figure 2 It is a schematic diagram showing the geometric dimensions of the fill and the relative positional relationships between the retaining structures within a limited range;

[0064] Figure 3 This is a schematic diagram of the forces acting on a finite-range slip prism;

[0065] Figure 4 This is a graph showing the trend of lateral earth pressure on the finite-range fill as a function of the slip surface rupture angle under different finite-range fill widths in this embodiment of the invention.

[0066] Figure 5 This is a graph showing the trend of the maximum lateral earth pressure of the finite-range fill as a function of the finite-range fill width in an embodiment of the present invention.

[0067] Figure 6 This is a graph showing the trend of lateral earth pressure on fill within a limited range as a function of the rupture angle under different newly constructed retaining structures in this embodiment of the invention.

[0068] Figure 7 This is a graph showing the trend of the maximum lateral earth pressure of the fill within a limited range as a function of the height of the newly built retaining structure in an embodiment of the present invention.

[0069] In the figure: 1. New retaining structure; 2. Existing structure; 3. Slip prism; 31. Outer surface of the new retaining structure; 32. Outer surface of the existing structure; 33. Slip surface; 34. Upper surface; 4. Stable bearing soil; 5. External load. Detailed Implementation

[0070] The technical solution of the invention will be clearly and completely described below with reference to the accompanying drawings and embodiments. Obviously, the following embodiments are only some embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0071] See Figure 1 The present invention provides a method for calculating lateral earth pressure in a limited-range fill, comprising the following steps:

[0072] S1, Determine the basic parameters for calculating lateral earth pressure on a limited area of ​​fill:

[0073] like Figure 2 As shown, the fill between the newly constructed retaining structure 1 and the existing structure 2 is a limited-range fill, which includes the upper slip prism 3 and the lower stable bearing soil 4. The contact surface between the newly constructed retaining structure 1 and the limited-range fill is the outer surface 31 of the newly constructed retaining structure, the contact surface between the existing structure 2 and the limited-range fill is the outer surface 32 of the existing structure, the contact surface between the slip prism 3 and the stable bearing soil 4 is the slip surface 33, which is also the lower boundary of the slip prism 3, and the upper surface 34 of the slip prism 3 bears the external load 5.

[0074] According to such Figure 2 The geometric dimensions of the finite-range fill and the relative positional relationship between the finite-range fill and the retaining structure are shown. The geometrical parameters, load parameters, shear strength parameters of the fill, and the range of lateral earth pressure involved in the calculation of the finite-range fill are determined, where:

[0075] (1) The geometric dimensions include the height of the newly built retaining structure. Outer surface inclination angle Limited fill width and the fracture angle of the slip surface and the width of the upper surface of the slip prism ,in:

[0076] The height of the newly built retaining structure The height of the outer surface 31 of the newly constructed retaining structure is determined based on the type of the newly constructed retaining structure 1 (gravity retaining wall, lightweight retaining wall, trench side wall, pile-slab wall, etc.) and the earth pressure distribution range from the top to the bottom of the wall of the newly constructed retaining structure 1.

[0077] The outer surface tilt angle The angle between the outer surface 31 of the newly built retaining structure and the vertical direction;

[0078] The limited range of fill width The width of the upper surface 34 is determined based on the distance between the top of the existing structure 2 and the top of the newly built retaining structure 1; the upper surface 34 is generally assumed to be horizontal.

[0079] The fracture angle of the slip surface It is an undetermined variable, which is the angle between the slip surface 33 and the horizontal direction. The minimum value of the range of variation is the internal friction angle of the fill body within a limited range, and the maximum value of the range of variation is the angle between the outer surface 31 of the newly built retaining structure and the horizontal direction.

[0080] Width of the upper surface of the slip prism The calculation formula is:

[0081] ,

[0082] When the slip surface 33 intersects with the upper surface 34 The distance between the intersection point and the top of the newly built retaining structure 1; when the slip surface 33 and the upper surface 34 do not intersect. For the limited range of fill width .

[0083] (2) The load parameters include the load applied to the upper surface 34. and the unit weight of fill within a limited range The applied load The external load is 5.

[0084] (3) The shear strength parameters of the fill include the cohesion of the fill within a limited range. Friction angle within a limited range of fill soil The internal friction angle between the backfill and the outer surface 31 of the newly constructed retaining structure. and cohesion The internal friction angle of the fill material with the outer surface of the existing structure is 32°. and cohesion ;

[0085] (4) The parameters of the lateral earth pressure range include the length of the earth pressure acting on the outer surface of the newly built retaining structure. Length of earth pressure acting on the outer surface of existing structures The method to obtain it is as follows:

[0086] According to the basic theory of active earth pressure, a tensile stress distribution zone exists in soil with cohesion. The crack length in the upper part of a finite-range fill is... Within this range, the lateral earth pressure is generally taken as 0, and the crack length is... It is applicable to both the outer surface 31 of newly constructed retaining structures and the outer surface 32 of existing structures, with a crack length of... The calculation formula is as follows:

[0087] ,

[0088] Length of earth pressure acting on the outer surface of the newly constructed retaining structure The calculation formula is as follows:

[0089] ,

[0090] Length of earth pressure acting on the outer surface of existing structures The expression is as follows:

[0091] ,

[0092] when At that time, take =0.

[0093] S2, the expression for determining the total weight of the slip-faced prism soil mass:

[0094] See Figure 3 Based on the fracture angle of the slip surface The extent of the slip prism 3 is defined as the area enclosed by the outer surface 31 of the newly constructed retaining structure, the outer surface 32 of the existing structure, the slip surface 33, and the upper surface 34. The total weight of the soil within the slip prism is also defined. The expression is:

[0095] .

[0096] S3, determine the expressions for each actual shear force at the boundary of the slip prism, including:

[0097] 1) Determine the tangential force on the outer surface of the newly constructed retaining structure. :

[0098] The Mohr-Coulomb strength criterion is satisfied, and its expression is as follows:

[0099] ,

[0100] Where E represents the lateral earth pressure on the outer surface of the newly constructed retaining structure, which is an unknown quantity that needs to be confirmed in subsequent steps.

[0101] 2) Determine the tangential force on the outer surface of the existing structure. :

[0102] The Mohr-Coulomb strength criterion is satisfied, and its expression is as follows:

[0103] ,

[0104] In the formula, The horizontal reaction forces of the existing structure's outer surface 32 pairs of slip prisms 3;

[0105] 3) Determine the tangential force on the slip surface 33. :

[0106] It satisfies the Mohr-Coulomb strength criterion, expressed as follows:

[0107] ,

[0108] In the formula, The normal reaction force of the stable bearing soil 4 below the slip surface on the slip prism 3;

[0109] S4. Establish the vertical and horizontal force balance equations for the slip prism:

[0110] according to Figure 3 The diagram showing the stress distribution of the slip prism considers the external load q borne by slip prism 3, the total weight G of the soil mass within the slip prism, and... , , The force equilibrium conditions for forming the slipped prism 3 include the force equilibrium equations in the vertical direction and the force equilibrium equations in the horizontal direction, wherein:

[0111] The equations for force equilibrium in the vertical direction are:

[0112] ,

[0113] The equations for force equilibrium in the horizontal direction are:

[0114] .

[0115] S5, Determine the lateral earth pressure on the outer surface of the newly constructed retaining structure caused by the limited fill. The expression:

[0116] According to S3 , , The expression and the force balance equations in the vertical and horizontal directions obtained from S4 are combined to obtain the lateral earth pressure on the outer surface of the newly built retaining structure. The expression is:

[0117] ,

[0118] In the formula, To ensure that the earth pressure at the same height position on the outer surface 31 of the newly constructed retaining structure and the outer surface 32 of the existing structure is proportional, the following formula is used to determine the earth pressure at the same height position, based on the principle that the horizontal earth pressure is equal at the same height position. Value:

[0119] .

[0120] At this point, the above expression is only the relationship between the lateral earth pressure E on the outer surface of the newly built retaining structure and the rupture angle of the slip surface.

[0121] S6, Determine the lateral earth pressure of a finite-range fill mass approaching its ultimate active failure state. :

[0122] Based on the lateral earth pressure on the outer surface of the newly constructed retaining structure Regarding the fracture angle of the slip surface The relationship considers the fracture angle of the slip surface. The numerical variation range is then used to sequentially determine the fracture angle of the slip surface. By assigning values, the lateral earth pressure value on the outer surface of the newly built retaining structure corresponding to the rupture angle of each slip surface is obtained, and then the maximum value of the lateral earth pressure E on the outer surface of the newly built retaining structure and its corresponding slip surface rupture angle are obtained.

[0123] Example

[0124] This embodiment analyzes and calculates the lateral earth pressure of the fill within a limited area at a high-speed railway closed cutting design site with an existing underground continuous wall structure, including the following steps:

[0125] S1, determine the basic parameters for calculating the lateral earth pressure on the finite-range fill, including:

[0126] 1) Geometric dimensional parameters: Height of the newly built retaining structure =10 m; Outer surface inclination angle =2°; Limited fill width =4 m; fracture angle of the slip surface The variable is between 20° and 88° and is yet to be determined.

[0127] When the fracture angle of the slip surface When ≤69.94°:

[0128] ,

[0129] Width parameters of the upper surface of the slip prism ;

[0130] When the fracture angle of the slip surface When the temperature is >69.94°:

[0131] ,

[0132] Width of upper surface of the slip prism .

[0133] 2) Load parameters: applied load =10 kPa; Unit weight of fill within a limited range =18 kN / m 3 .

[0134] 3) Shear strength parameters of the fill soil:

[0135] Limited range of fill cohesion =10 kPa; Friction angle within the finite-range fill soil =20°; the internal friction angle between the backfill and the outer surface of the newly constructed retaining structure. =10°; Cohesion between the backfill and the outer surface of the newly constructed retaining structure. =5 kPa; the internal friction angle between the fill and the outer surface of the existing structure. =10°; Cohesion between the fill and the outer surface of the existing structure. =5 kPa.

[0136] 4) Parameters of the range of action of lateral earth pressure:

[0137] Crack length ;

[0138] Length of earth pressure acting on the outer surface of the newly constructed retaining structure ;

[0139] Length of earth pressure acting on the outer surface of existing structures ;when At that time, take =0.

[0140] S2, confirm the expression for the total weight of the slip-faced prism soil mass:

[0141] When the fracture angle of the slip surface When ≤69.94°:

[0142] ,

[0143] When the fracture angle of the slip surface When the temperature is >69.94°:

[0144] .

[0145] S3, determine the expressions for each actual shear force at the boundary of the slip prism, including:

[0146] 1) Expression for the tangential force on the outer surface of the newly constructed retaining structure:

[0147] ,

[0148] 2) Expression for tangential force on the outer surface of existing structures:

[0149] ,

[0150] 3) Expression for the tangential force on the slip surface:

[0151] .

[0152] S4. Establish the vertical and horizontal force balance equations for the slip prism:

[0153] Based on the external load q of the finite fill soil sliding prism, the total weight G of the sliding prism soil, and... , , The expression further forms the vertical and horizontal force balance equations for the slip prism of the finite-range fill, where:

[0154] The equations for the force balance in the vertical direction are expressed as follows:

[0155] ,

[0156] The equations for the equilibrium of forces in the horizontal direction are expressed as follows:

[0157] .

[0158] S5, Determine the expression for the lateral earth pressure E on the outer surface of the newly constructed retaining structure caused by the finite amount of fill:

[0159] ,

[0160] The following formula is used to calculate and determine. Substitute the numerical values ​​into the above formula:

[0161] .

[0162] S6, Determine the lateral earth pressure of a finite-range fill mass approaching its ultimate active failure state. Value:

[0163] sequentially assess the fracture angle of the slip surface Within the range of 20° to 88°, values ​​are assigned in increments of 0.01° to obtain the lateral earth pressure value on the outer surface of the newly constructed retaining structure corresponding to each slip surface rupture angle, thereby obtaining the lateral earth pressure on the outer surface of the newly constructed retaining structure. The maximum value is 284.85 kN / m, and the corresponding fracture angle of the slip surface is 55.86°.

[0164] In comparison, the active earth pressure coefficient calculated using Coulomb's earth pressure theory is approximately 0.49, corresponding to a Coulomb earth pressure value of 441 kN / m.

[0165] To verify the accuracy of the method of the present invention, a lateral earth pressure monitoring system was installed at a design site of a closed roadbed for a high-speed railway in this embodiment, and the system was monitored along the height of the wall. Earth pressure monitoring points were set at 2m intervals to obtain the measured earth pressure results after the backfilling was completed. In addition, to cross-validate the measured results, the finite element method was used to conduct simulation analysis of the earth pressure distribution data based on field parameters, obtaining simulated earth pressure values ​​at the same locations as the measured earth pressure monitoring points. The measured and simulation results are shown in Table 1:

[0166] Table 1

[0167]

[0168] Therefore, according to Table 1, the measured value of the resultant earth pressure per unit length of the newly constructed retaining structure is as follows:

[0169] ,

[0170] The simulated resultant earth pressure per unit meter of the newly constructed retaining structure is as follows:

[0171] .

[0172] As can be seen, the earth pressure calculation result of 284.85 kN / m obtained by the method of the present invention is close to the field measured result of 293.8 kN / m, and also closely matches the simulation result of 283.8 kN / m, with a maximum error of no more than 5%, which is much smaller than the Coulomb earth pressure analysis result of 441 kN / m. This indicates that the method of the present invention can effectively reflect the influence of finite-range fill on lateral earth pressure, and the calculated earth pressure result is more accurate and closer to the actual engineering scenario.

[0173] In addition, by setting different limited ranges of fill width ,get Figure 4 Lateral earth pressure under different finite fill widths Fracture angle of slip surface The changing trend shows that the lateral earth pressure varies under different finite fill widths. All have a maximum value. Figure 4 Further obtain based on Figure 5 The lateral earth pressure corresponding to different finite fill widths shown is as follows. The maximum value, as can be seen, is when the fill width is within a limited range. Beyond a certain range, lateral earth pressure The maximum value approaches constant, and the magnitude approaches the lateral earth pressure caused by an infinitely wide fill.

[0174] By setting different heights for newly constructed retaining structures ,get Figure 6 Different heights of newly built retaining structures Lower lateral earth pressure Fracture angle of slip surface The changing trend shows that the lateral earth pressure varies with the height of the newly constructed retaining structure. All have a maximum value. Figure 6 Further obtain based on Figure 7 The lateral earth pressure corresponding to different heights of newly constructed retaining structures is shown. Maximum value, which shows the lateral earth pressure. The maximum value is the same as the height of the newly built retaining structure. Positive correlation.

Claims

1. A method for analyzing and calculating lateral earth pressure on a finite-range fill mass, characterized in that, Includes the following steps: S1, determine the basic parameters for calculating the lateral earth pressure of the finite-range fill, including geometric parameters, load parameters, shear strength parameters of the fill, and parameters for the range of lateral earth pressure action; the finite-range fill is the fill between the newly constructed retaining structure and the existing structure; the finite-range fill includes an upper slip prism and a lower stable bearing soil; the contact surface between the newly constructed retaining structure and the finite-range fill is the outer surface of the newly constructed retaining structure, the contact surface between the existing structure and the finite-range fill is the outer surface of the existing structure, the contact surface between the slip prism and the stable bearing soil is the slip surface, and the upper surface of the slip prism bears the external load; wherein, the parameters for the range of lateral earth pressure action include the length of earth pressure action on the outer surface of the newly constructed retaining structure. Length of earth pressure acting on the outer surface of existing structures S2, determine the expression for the total weight G of the slip-slip prism soil mass; S3, determine the expressions for each actual shear force at the boundary of the slip prism, wherein each actual shear force includes the tangential force on the outer surface of the newly constructed retaining structure. Tangential forces on the outer surface of existing structures and the tangential force of the slip surface The , , Satisfies the Mohr-Coulomb strength criterion; S4, considering the external load borne by the slip prism, the total weight G of the soil in the slip prism, and the aforementioned... , , Construct the vertical force balance equations and horizontal force balance equations for the slip prism; S5, derived from S3 , , The expression, along with the vertical and horizontal force balance equations obtained from S4, determines the lateral earth pressure on the outer surface of the newly constructed retaining structure caused by the finite amount of fill. The expression for lateral earth pressure. Regarding the fracture angle of the slip surface Relationship; S6, based on the lateral earth pressure on the outer surface of the newly constructed retaining structure. The expression considers the fracture angle of the slip surface. Within the range, the fracture angle of the slip surface is sequentially determined. By assigning values, the lateral earth pressure value on the outer surface of the newly built retaining structure corresponding to the rupture angle of each slip surface is obtained, and then the maximum value of the lateral earth pressure E on the outer surface of the newly built retaining structure and its corresponding slip surface rupture angle are obtained.

2. The method for analyzing and calculating lateral earth pressure on finite-range fill as described in claim 1, characterized in that, In S1: The geometric parameters include the height of the newly constructed retaining structure. Outer surface inclination angle Limited fill width and the fracture angle of the slip surface and the width of the upper surface of the slip prism Wherein, the fracture angle of the slip surface The width of the upper surface of the slip prism is an undetermined variable. The calculation formula is: ， When the slip surface intersects with the upper surface. The distance between the intersection point and the top of the newly constructed retaining structure; when the slip surface does not intersect with the upper surface. For the limited range of fill width ; The load parameters include the load applied to the upper surface. and the unit weight of fill within a limited range The applied load External load; The shear strength parameters of the fill include a limited range of fill cohesion. Friction angle within a limited range of fill soil The internal friction angle between the limited fill and the outer surface of the newly constructed retaining structure. and cohesion The internal friction angle between the fill and the outer surface of the existing structure within a limited range and cohesion .

3. The method for analyzing and calculating lateral earth pressure on finite-range fill as described in claim 2, characterized in that, The length of the soil pressure acting on the outer surface of the newly built retaining structure is obtained in S1. Length of earth pressure acting on the outer surface of existing structures The method is as follows: According to the basic theory of active earth pressure, a tensile stress distribution zone exists in soil with cohesion. The length of the crack in the upper part of a finite-range fill is... Within the range, the lateral earth pressure is 0, and the crack length is... It is applicable to both the outer surfaces of newly constructed retaining structures and the outer surfaces of existing structures, with a crack length of... The calculation formula is as follows: ， Calculate the length of earth pressure acting on the outer surface of the newly constructed retaining structure. The formula is as follows: ， Length of earth pressure acting on the outer surface of existing structures The expression is as follows: ， when At that time, take =0.

4. The method for analyzing and calculating lateral earth pressure on finite-range fill as described in claim 3, characterized in that, Total weight of the slip-rhomboid soil mass described in S2 The expression is: 。 5. The method for analyzing and calculating lateral earth pressure on finite-range fill as described in claim 4, characterized in that, In S3: Tangential force on the outer surface of the newly constructed retaining structure The expression is as follows: ， Where E represents the lateral earth pressure on the outer surface of the newly constructed retaining structure, which is an unknown quantity that needs to be confirmed in subsequent steps.

6. The method for analyzing and calculating lateral earth pressure on finite-range fill as described in claim 5, characterized in that, In S3: Tangential force on the outer surface of the existing structure The expression is as follows: ， In the formula, The horizontal reaction force of the existing structure's outer surface to the slipped prism.

7. The method for analyzing and calculating lateral earth pressure on finite-range fill as described in claim 6, characterized in that, In S3: The tangential force on the slip surface The expression is as follows: ， In the formula, This represents the normal reaction force of the stable bearing soil below the slip surface on the slip prism.

8. The method for analyzing and calculating lateral earth pressure on finite-range fill as described in claim 7, characterized in that, In S4: The vertical force balance equation is: 。 9. The method for analyzing and calculating lateral earth pressure on a limited-range fill mass according to claim 8, characterized in that, In S4: The horizontal force balance equation is: 。 10. The method for analyzing and calculating lateral earth pressure on a finite-range fill mass according to claim 9, characterized in that, Lateral earth pressure on the outer surface of the newly constructed retaining structure described in S5 The expression is: ， In the formula, To determine the proportional values ​​of earth pressure at the same height on the outer surface of the newly constructed retaining structure and the outer surface of the existing structure, based on the principle that horizontal earth pressure is equal at the same height, the following formula is used. Value: 。

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