A method and system for equivalent calculation of earth pressure of gabion retaining wall under earthquake conditions

Abstract

The present invention discloses a method and system for equivalent calculation of earth pressure of a gabion retaining wall under earthquake conditions. The modified slope angle β' of the upper slope of the retaining wall under earthquake conditions and the reduced fill height Δh of the top part of the slope are obtained according to the earthquake deflection angle ρ and the internal friction angle of the back fill of the retaining wall; multiple equivalent forces of the equivalent uniformly distributed load on the retaining wall are calculated according to the modified slope angle β' and the reduced fill height Δh of the top part of the slope; the equivalent uniformly distributed load is the uniformly distributed load acting on the top surface of the slope by equivalently reducing the deadweight of the fill. By using the method and system described in the present invention, a relatively reasonable force distribution of the gabion retaining wall under earthquake conditions can be obtained by using a quasi-static method with less time cost.

Description

Technical Field

[0001] The invention relates to a highway engineering design method, in particular to an equivalent calculation method and system for earth pressure of a gabion retaining wall under earthquake conditions. Background Art

[0002] Gabion retaining wall is a kind of building structure formed by combining gabion boxes. This structure can adapt to various soil properties and combine well with them. It can adapt well to foundation deformation. It has sufficient strength. As a gravity retaining wall, it is widely used in projects in high-intensity earthquake zones. E The calculation is mainly based on Coulomb's earth pressure theory. The most commonly used method for earthquake conditions is the pseudo-static method. According to the Monobe-Okabe theory, the Coulomb earth pressure is corrected to calculate the active earth pressure acting on the retaining wall under earthquake conditions. β Greater than the internal friction angle of the retaining wall backfill With earthquake declination r According to Coulomb's earth pressure theory, the active earth pressure on the back of the wall will be E There is no real number solution, which means that the fill slope does not meet the equilibrium condition. Therefore, in order to avoid this situation in existing conventional designs, the height of the retaining wall is usually increased or the support form is changed, or three-dimensional finite element software is used for modeling and calculation analysis during design. However, the former design method will greatly increase the cost of engineering construction, and the latter design method will increase the difficulty of design. Summary of the invention

[0003] In order to solve the problem of how to quickly, simply and reasonably calculate the force exerted by the soil on the retaining wall when the slope angle of the upper fill slope of the retaining wall is greater than the difference between the internal friction angle of the backfill material of the retaining wall and the seismic deflection angle under earthquake conditions, the present invention provides an equivalent calculation method and system for the earth pressure of a gabion retaining wall under earthquake conditions.

[0004] A method for calculating the equivalent earth pressure of a gabion retaining wall under earthquake conditions to achieve one of the purposes of the present invention comprises the following steps:

[0005] S1. According to the earthquake deflection r Internal friction angle of retaining wall backfill Get the corrected slope angle of the upper slope of the retaining wall under earthquake conditions β’ and the reduced fill height Δ at the top of the slope h ;

[0006] S2, according to the correction slope angle β ' and the reduced fill height Δ at the top of the slope hMultiple equivalent forces of the equivalent uniformly distributed load on the retaining wall are calculated; the equivalent uniformly distributed load is: the self-weight of the fill that is reduced due to the reduction of the fill height is equivalent to the uniformly distributed load acting on the top surface of the slope.

[0007] The multiple equivalent forces and the earth pressure of the remaining part of the slope on the retaining wall together constitute the earth pressure on the gabion retaining wall. The earth pressure of the remaining part of the slope on the retaining wall can be calculated using existing theoretical formulas.

[0008] Furthermore, in step S2, the multiple equivalent forces of the equivalent uniformly distributed load on the retaining wall include an equivalent force F1, which acts on the retaining wall below the boundary point of the equivalent uniformly distributed load.

[0009] Furthermore, in step S2, the multiple equivalent forces of the equivalent uniformly distributed load on the retaining wall include an equivalent force F2, which acts on the retaining wall above the boundary point of the equivalent uniformly distributed load.

[0010] Furthermore, the method for determining the demarcation point of the equivalent uniformly distributed load is as follows: starting from the top set point of the slope, horizontally facing the retaining wall as the starting position, rotating counterclockwise to the internal friction angle of the back filler of the retaining wall , draw a ray, and the intersection with the retaining wall is the demarcation point of equivalent load action 。

[0011] Furthermore, in step S2, when the equivalent load action boundary point is located in the middle of a certain layer of gabions, the equivalent force corresponding to the gabion is F1.

[0012] Furthermore, in step S1, the slope angle is corrected β’ The value of is:

[0013] β ' ≤ ϕ - r .

[0014] Furthermore, in step S2, the calculation method of the equivalent force F1 is:

[0015] F 1= k h . c .Δ h . s x . s y

[0016] Where:

[0017] k h : represents the horizontal seismic coefficient;

[0018] c : Packing weight, unit is KN / m 3 ;

[0019] Δ h :According to the modified slope angle β’ the resulting reduced fill height;

[0020] s x : The set horizontal unit action width;

[0021] s y : Set the vertical unit action width.

[0022] Furthermore, in step S2, the calculation method of the equivalent force F1 is:

[0023] F 1= k h . ( c . Δ h + q 0) . s x .s y

[0024] Where:

[0025] k h : represents the horizontal seismic coefficient;

[0026] c : Packing weight, unit is KN / m 3 ;

[0027] Δ h :According to the modified slope angle β’ the resulting reduced fill height;

[0028] q 0 : Specified uniformly distributed load;

[0029] s x : The set horizontal unit action width;

[0030] s y : Set the vertical unit action width.

[0031] Above q 0 The load may be a road vehicle load, but the present invention is not limited thereto.

[0032] Furthermore, in step S2, the calculation method of the equivalent force F2 is:

[0033] F 2= k h . c .Δ h . s x . s y

[0034] Where:

[0035] k h : represents the horizontal seismic coefficient;

[0036] c : Packing weight, unit is KN / m 3 ;

[0037] Δ h :According to the modified slope angle β’ the resulting reduced fill height;

[0038] s x : The set horizontal unit action width;

[0039] s y : Set the vertical unit action width.

[0040] Furthermore, the reduced fill height Δ h According to the upper slope height H of the retaining wall and the upper slope angle of the retaining wall β and the modified slope angle of the upper slope of the retaining wall β’ Calculated;

[0041] Furthermore, the reduced fill height Δ h The calculation methods include:

[0042]

[0043] Where:

[0044] H: height of the upper slope of the retaining wall;

[0045] β : The slope angle of the upper side slope of the retaining wall before correction;

[0046] β’ : Corrected slope angle of the upper slope of the retaining wall after correction.

[0047] A soil pressure equivalent calculation system for a gabion retaining wall under earthquake conditions to achieve the second purpose of the present invention includes a slope angle correction acquisition module, a fill height change value acquisition module and an equivalent action force acquisition module;

[0048] The modified slope angle acquisition module is used to obtain the slope angle according to the earthquake deflection angle. r Internal friction angle of retaining wall backfill Get the corrected slope angle of the upper slope of the retaining wall under earthquake conditions β’ ;

[0049] The fill height change value acquisition module is used to obtain the corrected slope angle of the slope according to the slope β’ and the original slope β Calculate the reduced fill height Δ h ;

[0050] The equivalent force acquisition module is used to correct the slope angle β’ and the reduced fill height Δ at the top of the slope h Multiple equivalent forces of the equivalent uniformly distributed load on the retaining wall are calculated; the equivalent uniformly distributed load is: the reduced self-weight of the fill is equivalent to the uniformly distributed load acting on the top surface of the slope.

[0051] Furthermore, it also includes a first equivalent force calculation module and a second equivalent force calculation module; the first equivalent force acts on the retaining wall below the equivalent uniformly distributed load action dividing point, and the second equivalent force acts on the retaining wall above the equivalent uniformly distributed load action dividing point.

[0052] Beneficial effects:

[0053] The present invention calculates the theoretical limit slope angle of the upper side slope of the embankment gabion retaining wall according to the Monobe Okabe method, and selects the modified slope angle that meets the balance condition according to the theoretical limit slope angle. β ', the fill height Δ will be reduced due to the change in slope angle h Equivalent conversion to uniformly distributed load on the top of the slope. Determine the range of action of the equivalent uniformly distributed load on the retaining wall according to the diffusion theory, and calculate the uniformly distributed load as multiple equivalent forces acting on the retaining wall for the structure and stability verification of the gabion retaining wall. The present invention adopts a simple and easy-to-operate conversion method, which takes less time and cost, and can obtain a more reasonable force distribution of the gabion retaining wall under the quasi-static method under earthquake conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 : Schematic diagram of equivalent conversion of upper slope load of retaining wall;

[0055] Figure 2 : Schematic diagram of the implementation calculation case. DETAILED DESCRIPTION

[0056] The following specific implementations are used to explain the technical solutions of the claims of the present invention so that those skilled in the art can understand the claims. The protection scope of the present invention is not limited to the following specific implementation structures. The technical solutions of the claims of the present invention made by those skilled in the art but different from the following specific implementations are also within the protection scope of the present invention.

[0057] The present invention is further described in detail below in conjunction with the accompanying drawings and a specific engineering embodiment.

[0058] like Figure 2 The figure shows a stepped embankment gabion retaining wall of a highway with a wall height of 5m under earthquake conditions. The height of each gabion layer is 1m. The height of the upper slope of the retaining wall is 6m, the slope ratio is 1:1.5, and the weight of the filler behind the wall is c 19.5KN / m 3 , internal friction angle of retaining wall backfill =34°. Driving load q0=15kPa.

[0059] S1. According to the earthquake deflection r Internal friction angle of retaining wall backfill Get the corrected slope angle of the upper slope of the retaining wall under earthquake conditions β ' and the reduced fill height Δ at the top of the slope h ;

[0060] According to the investigation, the horizontal seismic coefficient k of the project site h =0.2, vertical seismic coefficient k v =0.1, according to the type of project site, refer to the "China Earthquake Motion Parameter Zoning Map" GB18306-2015 and the "Highway Engineering Seismic Code" JTG B02-2013 to determine the horizontal seismic coefficient k h and the vertical seismic coefficient k v , the earthquake deflection angle is calculated according to the following formula r :

[0061]

[0062] According to the slope ratio of 1:1.5, the slope angle of the upper side slope of the retaining wall is obtained. β for:

[0063]

[0064] Calculate the angle limits specified by the Monobe-Okabe method:

[0065]

[0066] In earthquake conditions, , which obviously exceeds the angle limit specified in the Monobe-Okabe method theory.

[0067] To make the slope angle β Less than or equal to the theoretical limit slope angle of Monobe Okabe method , so the slope is adjusted so that the slope angle β Less than or equal to In this embodiment, the slope ratio is adjusted to 1:2.6, and the corrected slope angle is β '=21.037°.

[0068] The corresponding reduction in fill height is

[0069] Since the height of the fill is reduced, the reduced fill height is converted into an equivalent uniformly distributed load on the top of the slope according to the fill weight. q ,Right now q=c. Δ h ;

[0070] Where:

[0071] c : Filler weight;

[0072] Δ h : Equivalently reduced fill height;

[0073] S2, according to the correction slope angle β ' and the reduced fill height Δ at the top of the slope h Calculate the equivalent uniformly distributed load q Multiple equivalent forces acting on a retaining wall.

[0074] Equivalent uniform load q The multiple equivalent forces on the retaining wall include the equivalent force F1, which acts on the retaining wall below the delimiting point of the equivalent uniformly distributed load; the equivalent uniformly distributed load q The multiple equivalent forces on the retaining wall include an equivalent force F2, which acts on the retaining wall above the delimiting point of the equivalent uniformly distributed load;

[0075] The calculation of the above F1 and F2 is as follows. In this embodiment, s x With s y The value of is 1;

[0076] F 1= k h .( c .Δ h+q 0 ) . s x . s y=0.2 (19.5 × 2.54+15) ×1×1=12.91KN

[0077] or F 1= k h . c .Δ h . s x . s y =0.2× 19.5 × 2.54 ×1×1=9.906KN

[0078] F 2= k h . c .Δ h . s x . s y =0.5×0.2×19.5×2.54×1×1=4.95KN

[0079] Next, determine the range of action of the equivalent forces F1 and F2:

[0080] like Figure 1 As shown in the figure, point O is set at the edge of the slope as the starting point of the equivalent load, the horizontal direction towards the retaining wall is the starting position, and the internal friction angle of the back filler of the retaining wall is rotated counterclockwise. Draw a ray, and the intersection with the retaining wall is the dividing point of equivalent load action. For the retaining wall below the dividing point S, add the equivalent force F1 at the midpoint of the gabion; for the retaining wall above the dividing point, add the equivalent force F2 at the midpoint of the gabion.

[0081] According to the unfavorable principle, when the dividing point of equivalent load is located in the middle of a layer of gabions, the equivalent concentrated force of the gabions in this layer shall be taken as F1.

[0082] In this embodiment, Figure 2 As shown in the figure, the equivalent load on the retaining wall at the demarcation point S is set from the top edge of the slope to the point O according to the internal friction angle of the back filler of the retaining wall. It is the intersection of 34° counterclockwise diffusion and the retaining wall; it can be seen from the figure that the equivalent load demarcation point S is located between the 2nd and 3rd layers of gabions, so the equivalent force of the 1st and 2nd layers of gabions is taken as F2, and the equivalent force of the remaining 3 layers is taken as F1.

[0083] Since the slope height is reduced during the calculation process, and the earth pressure of the retaining wall due to the reduced slope height has been equivalent to equivalent forces F1 and F2, the slope angle after the slope height is reduced has satisfied the Coulomb earth pressure theory. Therefore, the active earth pressure behind the retaining wall can be calculated according to the Coulomb active earth pressure formula. E , which is calculated as E=

[0084] Where:

[0085] c : It is the heavy weight of the filler behind the wall;

[0086] H : is the height of the retaining wall;

[0087] in k ae The calculation of is as follows:

[0088]

[0089] In the formula

[0090] : internal friction angle of fill behind the wall;

[0091] α : The angle between the back of the retaining wall and the vertical direction;

[0092] r : earthquake deflection;

[0093] β ': The modified slope angle of the upper slope of the retaining wall after equivalent conversion;

[0094] d : The friction angle between the back of the wall and the fill behind the wall.

[0095] Then, the earth pressure acting on the retaining wall under earthquake conditions consists of the above two parts: one is the equivalent force F1 and F2 calculated by converting the earth pressure of the reduced fill part on the retaining wall after reducing the slope angle, and the other is the active earth pressure behind the retaining wall calculated according to Coulomb's active earth pressure formula after reducing the slope height. E .

[0096] It should be understood that the size of the serial numbers of the steps in the above embodiments does not mean the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present application.

[0097] The embodiment of the present application also provides an equivalent calculation system for earth pressure of a gabion retaining wall under earthquake conditions, including a modified slope angle acquisition module, a fill height change acquisition module and an equivalent force acquisition module;

[0098] The slope angle correction module is used to obtain the slope angle according to the earthquake deflection angle. r Internal friction angle of retaining wall backfill Get the corrected slope angle of the upper slope of the retaining wall under earthquake conditions β ';

[0099] The fill height change value acquisition module is used to obtain the corrected slope angle of the slope according to the slope β ' and the original slope angle β Calculate the reduced fill height Δ h ;

[0100] The equivalent force acquisition module is used to correct the slope angle β ' and the reduced fill height Δ at the top of the slope h Multiple equivalent forces of the equivalent uniformly distributed load on the retaining wall are calculated; the equivalent uniformly distributed load is: the reduced self-weight of the fill is equivalent to the uniformly distributed load acting on the top surface of the slope.

[0101] In another embodiment, it also includes a first equivalent force calculation module and a second equivalent force calculation module; the first equivalent force acts on the retaining wall below the equivalent uniformly distributed load action dividing point, and the second equivalent force acts on the retaining wall above the equivalent uniformly distributed load action dividing point.

Claims

1. A method for equivalent calculation of earth pressure of gabion retaining wall under earthquake conditions, characterized in that: The steps include: S1. According to the earthquake deflection ρ The modified slope angle of the upper side slope of the retaining wall under earthquake conditions is obtained by combining the internal friction angle φ of the backfill of the retaining wall β '; According to the slope angle of the upper side of the retaining wall β and the modified slope angle of the upper slope of the retaining wall β 'Calculate the reduced fill height Δ of the slope top part h ; S2, according to the correction slope angle β ' and the reduced fill height Δ at the top of the slope h Calculate multiple equivalent forces of the equivalent uniformly distributed load on the retaining wall; the equivalent uniformly distributed load is: the reduced fill deadweight is equivalent to the uniformly distributed load acting on the top surface of the slope; The earthquake deflection ρ The calculation methods include: ； Where: k h is the horizontal seismic coefficient; k v is the vertical seismic coefficient; In the step S2, the multiple equivalent forces of the equivalent uniformly distributed load on the retaining wall include an equivalent force F1, which acts on the retaining wall below the delimiting point of the equivalent uniformly distributed load; The calculation method of the equivalent force F1 is: F 1= k h . γ .D h . s x . s y In the step S2, the multiple equivalent forces of the equivalent uniformly distributed load on the retaining wall include an equivalent force F2, which acts on the retaining wall located above the boundary point of the equivalent uniformly distributed load; The calculation method of the equivalent force F2 is: F 2= k h . γ .D h . s x . s y Where: k h : represents the horizontal seismic coefficient; γ : Packing weight, unit is KN / m 3 ; Δ h :According to the modified slope angle β 'The resulting reduced fill height; s x : The set horizontal unit action width; s y : Set the vertical unit action width.

2. The method for equivalent calculation of earth pressure of gabion retaining wall under earthquake conditions as claimed in claim 1 is characterized in that: The method for determining the demarcation point of the equivalent uniformly distributed load is as follows: starting from the set point at the top of the slope, horizontally toward the gabion retaining wall as the starting position, rotating counterclockwise the internal friction angle φ of the back filler of the retaining wall, and making a ray, and the intersection with the retaining wall is the demarcation point of the equivalent load.

3. The method for equivalent calculation of earth pressure of gabion retaining wall under earthquake conditions as claimed in claim 1, characterized in that: In step S1, the slope angle is corrected β 'The value method is: β ' ≤ ϕ - ρ.

4. The method for equivalent calculation of earth pressure of gabion retaining wall under earthquake conditions as claimed in claim 1, characterized in that: The calculation method of the equivalent force F1 is: F 1= k h . ( γ . D h + q 0).s x .s y Where: k h : represents the horizontal seismic coefficient; γ : Packing weight, unit is KN / m 3 ; Δ h :According to the modified slope angle β 'The resulting reduced fill height; q 0: Specified uniform load; s x : The set horizontal unit action width; s y : Set the vertical unit action width.

5. A system for calculating the earth pressure equivalent of a gabion retaining wall under earthquake conditions using the method for calculating the earth pressure equivalent of a gabion retaining wall under earthquake conditions as described in claim 1, characterized in that: It includes a slope angle correction acquisition module, a fill height change value acquisition module and an equivalent force acquisition module; The modified slope angle acquisition module is used to obtain the slope angle according to the earthquake deflection angle. ρ The modified slope angle of the upper side slope of the retaining wall under earthquake conditions is obtained by combining the internal friction angle φ of the backfill of the retaining wall β '; The fill height change value acquisition module is used to obtain the corrected slope angle of the slope according to the slope β ' and the original slope angle β Calculate the reduced fill height Δ h ; The equivalent force acquisition module is used to correct the slope angle β ' and the reduced fill height Δ at the top of the slope h Multiple equivalent forces of the equivalent uniformly distributed load on the retaining wall are calculated; the equivalent uniformly distributed load is: the reduced self-weight of the fill is equivalent to the uniformly distributed load acting on the top surface of the slope.

6. The earth pressure equivalent calculation system of the gabion retaining wall under earthquake conditions as claimed in claim 5, characterized in that: It also includes a first equivalent force calculation module and a second equivalent force calculation module; the first equivalent force acts on the retaining wall below the equivalent uniformly distributed load action dividing point, and the second equivalent force acts on the retaining wall above the equivalent uniformly distributed load action dividing point.

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