Non-limit active soil pressure numerical calculation method in mode of rotating around wall top

Abstract

The invention relates to the technical field of data analysis, in particular to a non-limit active soil pressure numerical calculation method in a mode of rotating around a wall top, and derives a function relationship between soil body strength parameters and wall body displacement in the mode of rotating around the wall top. It is assumed that a soil body behind a wall forms an arc-shaped soil arch and a slip crack surface is a logarithmic spiral curved surface, the soil body behind the wall is horizontally layered according to a small step length, a numerical iteration format of the non-limit active soil pressure in a mode of rotating around the wall top is constructed, and a numerical calculation method of the non-limit active soil pressure in the mode is given. A numerical solution is compared with a model test result, and it is found that a calculation result of the solution basically conforms to the model test result. The method provides a more accurate solution to the non-limit active soil pressure when the rigid retaining wall rotates around the top, and has a practical guidance value for the design of the retaining wall.

Description

Technical Field

[0001] The present invention relates to the technical field of data analysis, and in particular to a numerical calculation method for non-limit active earth pressure in a rotation mode around a wall top. Background Art

[0002] Retaining walls are widely used in practical engineering, and the calculation of soil pressure behind the wall is a key link in the design of retaining walls. The soil behind the retaining wall changes from static to ultimate displacement state in a gradual process, and the soil is generally in an intermediate active state between the initial state and the ultimate active state, so the study of non-limit earth pressure is an important content.

[0003] There are two main methods for calculating non-limit earth pressure: one is to obtain the relationship between earth pressure and retaining wall displacement by using the function fitting method based on the earth pressure distribution curve obtained from the model test; the other is to first establish the functional relationship between the soil strength parameters and the wall displacement, and then establish the relationship between earth pressure and wall displacement. Among them, the latter has a clear physical and mechanical model and has become the mainstream calculation method in the study of non-limit earth pressure. In addition to the wall displacement, factors such as soil arching effect, interlayer shear stress, and sliding surface shape will also have a certain impact on the soil pressure behind the wall: the soil arching effect will cause the principal stress deflection in the soil; the interlayer shear stress will affect the overall distribution of earth pressure; the sliding surface shape will affect the size and distribution of earth pressure. Many scholars have established the earth pressure theory under the retaining wall translation mode (T mode) based on the thin layer unit method, which can be well consistent with the model test. Compared with the T mode, the existing active earth pressure calculation model of the rotation mode around the top of the wall (RT mode) only increases the interlayer shear stress. The active earth pressure distribution curve obtained by this method is similar to the model test results, but the degree of fit with the model test is not high. The reasons are:

[0004] (1) The non-limit state of soil in RT mode is different from that in T mode. The non-limit state of soil in T mode is independent of soil depth, but the horizontal displacement of soil in RT mode increases with depth, resulting in different non-limit states of soil at different depths. Increasing interlayer shear stress based on the mechanical model of T mode cannot reflect the basic characteristics of RT mode.

[0005] (2) Interlayer shear stress has been proven to be an internal force that only affects the distribution of earth pressure but not the magnitude of earth pressure. The active earth pressure resultant obtained by this method is equal to the active earth pressure resultant of the T mode, while the model test shows that the active earth pressure in the RT mode is greater than that in the T mode. It can be seen that the existing active earth pressure calculation theory of the RT mode still needs to be further improved.

[0006] To this end, the present invention proposes a numerical calculation method for non-limit active earth pressure in a rotation mode around the wall top. Summary of the invention

[0007] In order to obtain a more accurate solution to the non-limit active earth pressure of a rigid retaining wall in the RT mode, the present invention assumes that the wall back is upright, the fill surface is horizontal, and the fill behind the wall is cohesive-free soil. The non-limit soil parameters are used to consider the different characteristics of the non-limit state of soil at different depths, and the numerical iterative calculation method of the strength, resultant force, and action point position of the non-limit active earth pressure is derived; thus, the numerical solution of the non-limit active earth pressure that conforms to the characteristics of the RT mode is obtained. The rationality of the numerical solution in this paper is verified by comparing it with the model test results. The details are as follows:

[0008] A numerical calculation method for non-limit active earth pressure in a rotation mode around a wall top comprises the following steps:

[0009] S1. Calculate the relationship between soil strength parameters and wall displacement:

[0010] Based on the stress Mohr circle, the major principal stress is σ1 and the minor principal stress at rest is σ 30 , the minor principal stress in the intermediate state is σ 3m , the minor principal stress in the limit active state is σ 3f , the internal friction angle under the non-limit active state The internal friction angle under the limit active state It is expressed as formula (1):

[0011]

[0012] Assume that the radial stress and radial strain have a hyperbolic relationship as shown in formula (2):

[0013]

[0014] Where: ε m is the radial strain under non-limit state; a and b are parameters related to soil properties;

[0015] When ε m When it tends to infinity, we can get (σ 30 -σ 3m ) asymptotic value (σ 30 -σ 3m ) ult , as shown in formula (3):

[0016]

[0017] Introducing the destruction ratio R f , which is defined as the ultimate active state of soil (σ 30 -σ 3m ) and its asymptotic value (σ 30 -σ 3m ) ult The ratio is as shown in formula (4):

[0018]

[0019] Among them, R f The value of is generally 0.75-1, and the middle value 0.85 is taken for calculation;

[0020] When the soil is in the ultimate active state, equation (2) can be transformed into equation (5):

[0021]

[0022] Combining equation (4) and equation (5), we get ε f With R f The relationship is:

[0023]

[0024] Minor principal stress σ at rest 30 The major principal stress σ1 should satisfy equation (7):

[0025] σ 30 =K0σ1 (7)

[0026] The ratio of the wall top displacement in the intermediate active state to the wall top displacement in the ultimate active state is defined as η. The displacement required to reach the active limit state for cohesionless soil is 0.3%H-0.5%H. The soil displacement at any depth corresponds to the radial strain, and η×y / H=ε my / ε fy , we get ε my The expression is:

[0027]

[0028] Where: H is the height of the retaining wall; y is the depth of the soil;

[0029] Combining equations (1) to (8) to obtain the non-limiting internal friction angle at any depth in the RT mode: The calculation formula is:

[0030]

[0031] Pick K0 = 0.5, based on formula (9), the internal friction angle curves under different wall displacement ratios are plotted;

[0032] Assuming that the wall-soil friction angle changes with the wall displacement to a similar extent as the internal friction angle, the non-limiting wall-soil friction angle δ at any depth in the RT mode is obtained: my The calculation formula is:

[0033]

[0034] Where: δ is the wall-soil friction angle under the limit state, ξ is the measured wall-soil friction angle δ and the internal friction angle The proportional coefficient between is 2 / 3;

[0035] S2. Method for determining the curved sliding surface:

[0036] Assuming that the change in polar angle is linearly related to the change in depth, the inclination angle β of the non-limiting slip surface at any depth is my It can be determined by formula (14);

[0037]

[0038] Where: θ0 can be The polar angle θ between the pole and the bottom of the slip surface h Desirable

[0039] S3. Numerical solution of non-limit active earth pressure

[0040] S3.1. Soil arching effect and soil stress analysis

[0041] Assuming that the minor principal stress arch trace is an arc line with the center at point O and the soil arch radius as R, the polar coordinate equation can be expressed as ρ(θ)=R, where θ is an arbitrary value; for the assumed arch trace, its starting point is at the wall-soil contact surface and its end point is at the extension line of the line connecting the center O and the slip surface; the initial value of the principal stress deflection angle θ 1m With the termination value θ 2m Determined by formula (15):

[0042]

[0043] The non-limiting horizontal stress σ at any point on the horizontal plane of the micro-slip body ωm , non-limit vertical stress σ νm It can be obtained from formula (16):

[0044]

[0045] Where: θ m is the angle between the wall and the non-limiting minor principal stress at that location, which is equal to θ 1m ψ m is the angle between the tangent line of any point of the soil arch behind the wall and the vertical direction, that is, the angle between the non-limiting major principal stress of any point of the soil arch and the horizontal direction, and its value range is (θ 1m ,θ 2m );K am is the non-limit active earth pressure coefficient, which is determined by formula (17):

[0046]

[0047] S3.2 Calculation of active lateral earth pressure coefficient

[0048] For the non-average vertical stress σ under non-limit state νm Integrate and then divide by the width L of the micro-slip body my , the non-limiting average vertical stress on the horizontal plane of the micro-slip body is obtained The integral in the rectangular coordinate system is converted into the integral in the polar coordinate system. At this time, the length of the micro-arc is ρ(ψ)dψ, and the corresponding micro-slip body has an infinitesimal width dx=Rdψsinψ. The solution process is shown in formula (18):

[0049]

[0050] Define σ ωm and The ratio of is the non-limit active lateral earth pressure coefficient, which is determined by formula (19):

[0051]

[0052] S3.3 Calculation of interlayer shear stress friction coefficient

[0053] Calculate the interlaminar shear stress coefficient:

[0054]

[0055] S3.4. Layered Iterative Solution of Active Earth Pressure

[0056] The non-limiting internal friction angle of the i-th layer of soil is defined as The non-limiting wall-soil friction angle is δ mi , the inclination angle of the non-limiting slip surface is β mi , the vertical average stress of the i-th layer of soil under non-limit state is Normal force σ on the wall ωmi , tangential force τ on the wall ωmi , the tangential force τ on the sliding surface smi and the shear stress between soil layers τ ωνmi Determined by formula (21):

[0057]

[0058] Where: K 1mi is the non-limit active lateral earth pressure coefficient of the i-th soil layer, calculated according to formula (19); K 2mi is the interlayer shear stress coefficient of the i-th soil layer, calculated according to formula (20);

[0059] Perform static equilibrium analysis on the i-th horizontal strip body ABCD. As the resultant force in the horizontal direction is 0, we can obtain equation (2):

[0060]

[0061] From the vertical force being zero, we can get equation (23):

[0062]

[0063] Where: ΔG i is the deadweight of the i-th layer of micro-slip body, determined by formula (24); L i is the upper interface width of the i-th layer of micro-slip body, which is determined by formula (25):

[0064]

[0065] L i =(H-iΔy)cotβ mi (25)

[0066] Combining equations (21) to (25) can establish the vertical stress σ νmi The iteration format is:

[0067]

[0068] Where: 1mi , 2mi is the combination coefficient in the iterative process, determined by formula (27):

[0069]

[0070] The non-limit active earth pressure strength is calculated according to formula (28):

[0071] σ ωmi =K 1mi σ νmi (28)

[0072] The non-limit active earth pressure resultant is calculated according to formula (29):

[0073]

[0074] The overturning moment generated by the non-limit active earth pressure on the wall heel can be calculated by formula (30):

[0075]

[0076] The vertical distance from the point of action of the non-limit active earth pressure resultant to the wall heel is calculated by formula (31):

[0077]

[0078] Furthermore, in formula (9), we take =30°, K0=0.5, and draw the curve of the internal friction angle under different wall displacement ratios. It can be concluded that only when the wall displacement ratio is 0, the internal friction angle does not change with depth; when the wall is displaced, the internal friction angle value will change with depth.

[0079] Furthermore, in step S2, the sliding surface of the soil behind the wall in the RT mode is not a plane, but a logarithmic spiral sliding surface, and the geometric equation is:

[0080]

[0081] Where: θ is the polar angle between the pole and any point on the slip surface in the polar coordinate system; θ0 is the polar angle between the pole and the top of the slip surface; is the internal friction angle of the soil;

[0082] Transform the slip surface equation in the polar coordinate system to obtain the slip surface equation in the rectangular coordinate system:

[0083]

[0084] Functional expression of the inclination angle of the non-limiting slip surface at any point:

[0085]

[0086] The beneficial effects of the present invention are:

[0087] (1) The numerical calculation method of the non-limit active earth pressure in the wall top rotation mode of the present invention can introduce any slip surface for solution, which makes it easier to use the logarithmic spiral slip surface that is more consistent with the actual situation to solve the earth pressure.

[0088] (2) From the sliding surface curve obtained by the present invention, it can be seen that the sliding surface of the soil in the RT mode is a logarithmic spiral sliding surface. The sliding surface width in a small range at the lower part of the wall is larger than the sliding surface assumed by the classical earth pressure theory, and in a larger range at the upper part of the wall, it is smaller than the sliding surface assumed by the classical earth pressure theory.

[0089] (3) The present invention deduces the functional relationship between soil strength parameters and wall displacement under RT mode, provides a curve sliding surface calculation method that is consistent with reality, further considers soil arching effect and interlayer shear stress, divides the soil behind the wall into layers according to small step lengths, and constructs a numerical calculation method for non-limit active earth pressure under RT mode. Compared with the model test results, it is found that the numerical solution of this paper is more accurate and can more accurately predict the distribution of active earth pressure. BRIEF DESCRIPTION OF THE DRAWINGS

[0090] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments are briefly introduced below. It should be understood that the following drawings only show certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without creative work.

[0091] Figure 1 is the stress Mohr circle;

[0092] Figure 2 is the variation of internal friction angle with wall displacement ratio;

[0093] Figure 3 It is a schematic diagram of the curved slip surface;

[0094] Figure 4 For soil arch and soil stress analysis;

[0095] Figure 5 Horizontal strip division and stress analysis of soil;

[0096] Figure 6 Comparison results of soil pressure distribution;

[0097] Figure 7 Comparison results for the sliding surface; DETAILED DESCRIPTION

[0098] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings here can be arranged and designed in various different configurations.

[0099] A numerical calculation method for non-limit active earth pressure in a rotation mode around a wall top comprises the following steps:

[0100] S1. Calculate the relationship between soil strength parameters and wall displacement:

[0101] In the prior art, it is assumed that the radial stress and radial strain are in a hyperbolic relationship. Based on the stress Mohr circle of the soil, the functional relationship between the internal friction angle of the soil and the wall displacement that conforms to the T-mode characteristics is derived. Since the non-limit state of the soil in the RT mode varies with the depth of the soil, it is not appropriate to directly apply it to the RT mode; on the other hand, the above derivation process introduces a key parameter, namely the static earth pressure coefficient K0 of the soil, and the method directly introduces the Jaky formula to solve it, which is questionable. Studies have shown that for soils with a large internal friction angle, the calculated value of the Jaky formula will significantly underestimate K0; particle size and density will also affect the K0 value. For sand with the same particle size, the K0 value gradually increases with the increase of the relative density of the sand, and for sand with the same density, the K0 value decreases with the increase of the sand particle size. In view of this, the K0 value of the soil should not be estimated by an empirical formula, but should be determined by a triaxial instrument to perform a K0 consolidation test on the original soil. Taking into account the characteristics of the soil strength under the RT mode, the present invention derives the calculation formula of the corresponding non-limit soil strength parameters, and the specific derivation process is as follows.

[0102] by Figure 1 Based on the stress Mohr circle shown in the figure, the major principal stress is σ1 and the minor principal stress at rest is σ 30 , the minor principal stress in the intermediate state is σ 3m , the minor principal stress in the limit active state is σ 3f .

[0103] according to Figure 1 The geometric relationship in the non-limit active state can be used to The internal friction angle under the limit active state It is expressed as formula (1).

[0104]

[0105] It is assumed that the radial stress and radial strain have a hyperbolic relationship as shown in equation (2).

[0106]

[0107] Where: ε m is the radial strain under non-limit state; a and b are parameters related to soil properties.

[0108] Analyzing formula (2), when ε m When it tends to infinity, we can get (σ 30 -σ 3m ) asymptotic value (σ 30 -σ 3m ) ult , as shown in formula (3).

[0109]

[0110] Introducing the destruction ratio R f , which is defined as the ultimate active state of soil (σ 30 -σ 3m ) and its asymptotic value (σ 30 -σ 3m ) ult The ratio is as shown in formula (4).

[0111]

[0112] Among them, R f The value is generally 0.75-1. If there is no test data, the middle value of 0.85 can be used for estimation.

[0113] When the soil is in the ultimate active state, equation (2) can be transformed into equation (5).

[0114]

[0115] Combining equation (4) and equation (5), we can get ε f With R f The relationship is:

[0116]

[0117] Minor principal stress σ at rest 30 The major principal stress σ1 should satisfy equation (7).

[0118] σ 30 =K0σ1 (7)

[0119] Considering the depth characteristics of the internal friction angle in the RT mode, the ratio of the wall top displacement in the intermediate active state to the wall top displacement in the ultimate active state is defined as η. In actual engineering design, the allowable displacement value can be divided by the ultimate displacement of the wall to determine it. The displacement required for non-cohesive soil to reach the active limit state is generally 0.3%H-0.5%H. The soil displacement at any depth corresponds to the radial strain, and η×y / H=ε my / ε fy , we can get ε my The expression is:

[0120]

[0121] Where: H is the height of the retaining wall; y is the depth of the soil.

[0122] Combining equations (1) to (8) can obtain the non-limiting internal friction angle at any depth in the RT mode: The calculation formula is:

[0123]

[0124] Pick K0 = 0.5, based on formula (9), the internal friction angle curves under different wall displacement ratios are plotted, as shown in the attached figure. Figure 2 It can be seen that the internal friction angle does not change with depth only when the wall displacement ratio is 0; when the wall is displaced, the internal friction angle value will change with depth, which fully demonstrates the characteristic that the soil displacement increases with depth in the RT mode.

[0125] Assuming that the wall-soil friction angle changes with the wall displacement to a similar extent as the internal friction angle, the non-limiting wall-soil friction angle δ at any depth in the RT mode can be obtained: my The calculation formula is:

[0126]

[0127] Where: δ is the wall-soil friction angle under the limit state, ξ is the measured wall-soil friction angle δ and the internal friction angle The proportional coefficient between them can be taken as 2 / 3.

[0128] S2. Method for determining the curved sliding surface:

[0129] The model test shows that the sliding surface of the soil behind the wall in the RT mode is not a plane, but a logarithmic spiral sliding surface, and the geometric equation is:

[0130]

[0131] Where: θ is the polar angle between the pole and any point on the slip surface in the polar coordinate system; θ0 is the polar angle between the pole and the top of the slip surface; is the internal friction angle of the soil.

[0132] By transforming the slip surface equation in the polar coordinate system, we can get the slip surface equation in the rectangular coordinate system:

[0133]

[0134] By the attached Figure 3 The geometric relationship shown can be used to obtain the functional expression of the inclination angle of the non-limiting slip surface at any point on the logarithmic spiral:

[0135]

[0136] To simplify the calculation, it is assumed that the change in polar angle is linearly related to the change in depth. The inclination angle β of the non-limiting slip surface at any depth is my It can be determined by formula (14).

[0137]

[0138] Where: θ0 can be The polar angle θ between the pole and the bottom of the slip surface h Desirable

[0139] S3. Numerical solution of non-limit active earth pressure

[0140] S3.1. Soil arching effect and soil stress analysis

[0141] The soil arching effect will cause stress redistribution in the soil, which is the main reason for the nonlinear distribution of soil pressure. In order to quantify the influence of soil arching effect on active earth pressure, it is usually assumed that a certain shape of arch trace can approximate the actual distribution of soil stress. Studies have shown that the shape of the arch trace has little effect on the final calculation results. In this paper, in order to simplify the calculation, it is assumed that the minor principal stress arch trace is a circular arc. Figure 4 As shown, the center of the circle is at point O, the radius of the soil arch is R, and the polar coordinate equation can be expressed as ρ(θ) = R, where θ is an arbitrary value. For the assumed arch trace, its starting point is at the wall-soil contact surface, and its end point is at the extension line of the line connecting the center of the circle O and the slip surface. The initial value of the principal stress deflection angle θ 1m With the termination value θ 2m It can be determined by formula (15).

[0142]

[0143] The non-limiting horizontal stress σ at any point on the horizontal plane of the micro-slip body ωm , non-limit vertical stress σ νm It can be obtained by formula (16).

[0144]

[0145] Where: θ m is the angle between the wall and the non-limiting minor principal stress at that location, which is equal to θ 1m ψ m is the angle between the tangent line of any point of the soil arch behind the wall and the vertical direction, that is, the angle between the non-limiting major principal stress of any point of the soil arch and the horizontal direction, and its value range is (θ 1m ,θ 2m );K am is the non-limit active earth pressure coefficient, determined by formula (17).

[0146]

[0147] S3.2 Calculation of active lateral earth pressure coefficient

[0148] The soil arching effect will deflect the principal stress in the soil, resulting in unequal vertical stresses at various points on the horizontal plane of the micro-slip body. νm Integrate and then divide by the width L of the micro-slip body my, we can get the non-limiting average vertical stress on the horizontal plane of the micro-slip body To simplify the calculation, the integral in the rectangular coordinate system is converted into the integral in the polar coordinate system. At this time, the length of the micro-arc is ρ(ψ)dψ, which is given by Figure 4 The geometric relationship in can be used to obtain the infinitesimal width of the corresponding micro-slip body dx = Rdψsinψ, and the solution process is shown in formula (18).

[0149]

[0150] Define σ ωm and The ratio of is the non-limit active lateral earth pressure coefficient, which is determined by formula (19).

[0151]

[0152] S3.3 Calculation of interlayer shear stress friction coefficient

[0153] Since the non-limit state of the soil in the RT mode changes with depth, the corresponding micro-slip body has a dislocation potential, and there is a large shear stress between horizontal soil layers. However, if the sliding friction coefficient is directly used Calculating the shear stress between soil layers indicates that the soil has undergone horizontal shear failure, which is obviously inconsistent with the actual situation. Therefore, this paper uses the coefficient reduction method, that is, formula (20) to calculate the interlayer shear stress coefficient.

[0154]

[0155] S3.4. Layered Iterative Solution of Active Earth Pressure

[0156] Due to the different non-limit states of soil at different depths in the RT mode, the corresponding soil parameters and sliding surface inclination will change with depth. At this time, it will be very difficult to solve the problem by using the analytical method of differentiation followed by integration. Therefore, this paper adopts a numerical calculation method, that is, the soil is layered according to a small step size, as shown in the attached figure. Figure 5 As shown in the figure, it is assumed that the non-limit state of the soil in the small step range is consistent. The active earth pressure problem is solved by constructing a numerical iteration format for the active earth pressure in the depth range. The non-limit internal friction angle of the i-th layer of soil is defined as The non-limiting wall-soil friction angle is δ mi , the inclination angle of the non-limiting slip surface is β mi , the vertical average stress of the i-th layer of soil under non-limit state is Normal force σ on the wall ωmi , tangential force τ on the wall ωmi , tangential force τ on the sliding surface smi and the shear stress between soil layers τ ωνmi Determined by formula (21).

[0157]

[0158] Where: K 1mi is the non-limit active lateral earth pressure coefficient of the i-th soil layer, calculated according to formula (19); K 2mi is the interlayer shear stress coefficient of the i-th soil layer, calculated according to formula (20).

[0159] right Figure 4 The i-th layer horizontal strip body ABCD shown in the figure is subjected to static equilibrium analysis, and the resultant force in the horizontal direction is 0, so equation (22) can be obtained.

[0160]

[0161] Equation (23) can be obtained from the fact that the vertical resultant force is zero.

[0162]

[0163] Where: ΔG i is the deadweight of the i-th layer of micro-slip body, determined by formula (24); L i is the upper interface width of the i-th layer of micro-slip body, determined by formula (25).

[0164]

[0165] L i =(H-iΔy)cotβ mi (25)

[0166] Combining equations (21) to (25) can establish the vertical stress σ νmi The iteration format is:

[0167]

[0168] Where: 1mi , 2mi is the combination coefficient in the iterative process, determined by formula (27).

[0169]

[0170] The non-limit active earth pressure strength is calculated according to formula (28).

[0171] σ ωmi =K 1mi σ νmi (28)

[0172] The non-limit active earth pressure resultant is calculated according to formula (29).

[0173]

[0174] The overturning moment caused by the non-limit active earth pressure on the wall heel can be calculated by formula (30).

[0175]

[0176] The vertical distance from the point of action of the non-limit active earth pressure resultant to the wall heel is calculated by formula (31).

[0177]

[0178] S4. Model test verification

[0179] The dimensions of the model box are 2.4m (length) × 1.8m (width) × 1.2m (height); the bulk density of the fill soil is γ = 15.51 kN / m 3 ; Soil height H = 1m; Limit fill internal friction angle Limit wall-soil friction angle δ = 17.5°; failure ratio R f =0.85; fill surface load q = 0kN / m; based on Figure 6 The static earth pressure test data inversion results in K0 = 0.61. Figure 6 It can be seen that the active earth pressure distribution curve given by the numerical solution in this paper is basically consistent with the model test results, showing a nonlinear distribution, and the nonlinearity gradually increases with the increase of displacement.

[0180] The existing analytical solutions all assume that the slip surface is a Rankine slip surface or a Coulomb slip surface before solving. However, the Rankine slip surface is not valid when δ is not equal to zero, and the solution process of the Coulomb rupture surface is also controversial. The advantage of the numerical solution in this paper is that any slip surface can be introduced for solution, which makes it easier to use the logarithmic spiral slip surface that is more consistent with the actual situation to solve the earth pressure. Figure 7 This is the slip surface curve solved in this paper. It can be seen that the slip surface of the soil in the RT mode is a logarithmic spiral slip surface. In a small range at the bottom of the wall, the slip surface width is greater than the slip surface assumed by the classical earth pressure theory, and in a larger range at the top of the wall, it is smaller than the slip surface assumed by the classical earth pressure theory.

[0181] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention shall be included in the protection scope of the present invention.

Claims

1. A numerical calculation method for non-limit active earth pressure in a rotation mode around the top of a wall, characterized in that: The following steps are involved: S1. Calculate the relationship between soil strength parameters and wall displacement: Based on the stress Mohr circle, the major principal stress is σ1 and the minor principal stress at rest is σ 30 , the minor principal stress in the intermediate state is σ 3m , the minor principal stress in the limit active state is σ 3f , the internal friction angle under the non-limit active state The internal friction angle under the limit active state It is expressed as formula (1): Assume that the radial stress and radial strain have a hyperbolic relationship as shown in formula (2): Where: ε m is the radial strain under non-limit state; a and b are parameters related to soil properties; When ε m When it tends to infinity, we can get (σ 30 -σ 3m ) asymptotic value (σ 30 -σ 3m ) ult , as shown in formula (3): Introducing the destruction ratio R f , which is defined as the ultimate active state of soil (σ 30 -σ 3m ) and its asymptotic value (σ 30 -σ 3m ) ult The ratio is as shown in formula (4): Among them, R f The value of is generally 0.75-1, and the middle value 0.85 is taken for calculation; When the soil is in the ultimate active state, equation (2) can be transformed into equation (5): Combining equation (4) and equation (5), we get ε f With R f The relationship is: Minor principal stress σ at rest 30 The major principal stress σ1 should satisfy equation (7): s 30 =K0σ1 (7) The ratio of the wall top displacement in the intermediate active state to the wall top displacement in the ultimate active state is defined as η. The displacement required to reach the active limit state for cohesionless soil is 0.3%H-0.5%H. The soil displacement at any depth corresponds to the radial strain, and η×y / H=ε my / ε fy , we get ε my The expression is: Where: H is the height of the retaining wall; y is the depth of the soil; Combining equations (1) to (8) to obtain the non-limiting internal friction angle at any depth in the RT mode: The calculation formula is: Pick K0 = 0.5, based on formula (9), the internal friction angle curves under different wall displacement ratios are plotted; Assuming that the wall-soil friction angle changes with the wall displacement to a similar extent as the internal friction angle, the non-limiting wall-soil friction angle δ at any depth in the RT mode is obtained: my The calculation formula is: Where: δ is the wall-soil friction angle under the limit state, ξ is the measured wall-soil friction angle δ and the internal friction angle The proportional coefficient between is 2 / 3; S2. Method for determining the curved sliding surface: Assuming that the change in polar angle is linearly related to the change in depth, the inclination angle β of the non-limiting slip surface at any depth is my It can be determined by formula (14); Where: θ0 can be The polar angle θ between the pole and the bottom of the slip surface h Desirable S3. Numerical solution of non-limit active earth pressure S3.

1. Soil arching effect and soil stress analysis Assuming that the minor principal stress arch trace is a circular arc with the center at point O and the soil arch radius R, the polar coordinate equation can be expressed as ρ(θ)=R, where θ is an arbitrary value; for the assumed arch trace, its starting point is at the wall-soil contact surface and its end point is at the extension line of the line connecting the center O and the slip surface; the initial value of the principal stress deflection angle θ 1m With the termination value θ 2m ; The non-limiting horizontal stress σ at any point on the horizontal plane of the micro-slip body ωm , non-limit vertical stress σ νm ; K am is the non-limit active earth pressure coefficient, which is determined by formula (17): S3.2 Calculation of active lateral earth pressure coefficient For the non-average vertical stress σ under non-limit state νm Integrate and then divide by the width L of the micro-slip body my , the non-limiting average vertical stress on the horizontal plane of the micro-slip body is obtained The integral in the rectangular coordinate system is converted into the integral in the polar coordinate system. At this time, the length of the micro-arc is ρ(ψ)dψ, and the corresponding micro-slip body has an infinitesimal width dx=Rdψsinψ. The solution process is shown in formula (18): Define σ ωm and The ratio of is the non-limit active lateral earth pressure coefficient, which is determined by formula (19): S3.3 Calculation of interlayer shear stress friction coefficient Calculate the interlaminar shear stress coefficient: S3.

4. Layered Iterative Solution of Active Earth Pressure The non-limiting internal friction angle of the i-th layer of soil is defined as The non-limiting wall-soil friction angle is δ mi , the inclination angle of the non-limiting slip surface is β mi , the vertical average stress of the i-th layer of soil under non-limit state is Normal force σ on the wall ωmi , tangential force τ on the wall ωmi , the tangential force τ on the sliding surface smi and the shear stress between soil layers τ ωνmi Determined by formula (21): Where: K 1mi is the non-limit active lateral earth pressure coefficient of the i-th soil layer, calculated according to formula (19); K 2mi is the interlayer shear stress coefficient of the i-th soil layer, calculated according to formula (20); Perform static equilibrium analysis on the i-th layer of horizontal strip ABCD. As the resultant force in the horizontal direction is 0, we can obtain equation (22): From the vertical force being zero, we can get equation (23): Where: ΔG i is the deadweight of the i-th layer of micro-slip body, determined by formula (24); L i is the upper interface width of the i-th layer of micro-slip body, which is determined by formula (25): L i =(H-iΔy)cotβ mi (25) Combining equations (21) to (25) can establish the vertical stress σ νmi The iteration format is: Where: 1mi , 2mi is the combination coefficient in the iterative process, determined by formula (27): The non-limit active earth pressure strength is calculated according to formula (28): s ωmi =K 1mi s νmi (28) The non-limit active earth pressure resultant is calculated according to formula (29): The overturning moment caused by the non-limit active earth pressure on the wall heel can be calculated by formula (30): The vertical distance from the point of action of the non-limit active earth pressure resultant to the wall heel is calculated by formula (31):

2. The method for numerically calculating the non-limiting active earth pressure in the wall top rotation mode according to claim 1 is characterized in that: In formula (9), we take =30°, K0=0.5, and draw the curve of the internal friction angle under different wall displacement ratios. It can be concluded that only when the wall displacement ratio is 0, the internal friction angle does not change with depth; when the wall is displaced, the internal friction angle value will change with depth.

3. The method for numerically calculating the non-limiting active earth pressure in the wall top rotation mode according to claim 1, characterized in that: In step S2, the sliding surface of the soil behind the wall in the RT mode is not a plane, but a logarithmic spiral sliding surface, and the geometric equation is: Where: θ is the polar angle between the pole and any point on the slip surface in the polar coordinate system; θ0 is the polar angle between the pole and the top of the slip surface; is the internal friction angle of the soil; Transform the slip surface equation in the polar coordinate system to obtain the slip surface equation in the rectangular coordinate system: Functional expression of the inclination angle of the non-limiting slip surface at any point:

4. The method for numerically calculating non-limiting active earth pressure in a rotation mode around the top of a wall according to claim 1, characterized in that: In step S3.1, the initial value of the principal stress deflection angle θ 1m With the termination value θ 2m Determined by formula (15): The non-limiting horizontal stress σ at any point on the horizontal plane of the micro-slip body ωm , non-limit vertical stress σ νm It can be obtained from formula (16): Where: θ m is the angle between the wall and the non-limiting minor principal stress at that location, which is equal to θ 1m ψ m is the angle between the tangent line of any point of the soil arch behind the wall and the vertical direction, that is, the angle between the non-limiting major principal stress of any point of the soil arch and the horizontal direction, and its value range is (θ 1m ,θ 2m ).

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