CN114741763A - Method for calculating active soil pressure of limited soil body of cantilever type supporting structure of foundation pit - Google Patents

Method for calculating active soil pressure of limited soil body of cantilever type supporting structure of foundation pit Download PDF

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CN114741763A
CN114741763A CN202210408041.9A CN202210408041A CN114741763A CN 114741763 A CN114741763 A CN 114741763A CN 202210408041 A CN202210408041 A CN 202210408041A CN 114741763 A CN114741763 A CN 114741763A
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supporting structure
foundation pit
soil body
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CN114741763B (en
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尤涵锐
陈斌
谢亮
李春磊
于沉香
吴琪
杨光煜
刘绍卿
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Wuhan Surveying Geotechnical Research Institute Co Ltd of MCC
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Abstract

The invention relates to a method for calculating active soil pressure of limited soil body of a cantilever type supporting structure of a foundation pit, which mainly aims at the defects of the classic soil pressure theory and provides an active soil pressure calculation method considering the width of the soil body behind a wall, and the method comprises the following steps: determining design parameters of a foundation pit supporting structure and physical and mechanical parameters of a soil body; determining a displacement curve analytic expression of the supporting structure; determining a relational expression of the friction angle and the displacement; assuming that the shape of a soil body slip crack surface in a limit state is a spinning wheel line; dividing the trapezoidal soil wedge body behind the wall into two parts, establishing an equation according to the balance of forces by adopting a horizontal layer analysis method, and finally obtaining an expression of the shape of the slip fracture surface and the size of the active soil pressure. The soil pressure distribution obtained by the method is more accurate and reasonable, the calculation formula is simple and practical, and the method can be applied to the condition that the position of a foundation pit supporting structure to be excavated in actual engineering is closer to the position of an adjacent underground structure, is favorable for reasonable design and construction of foundation pit engineering, and has certain popularization and application values.

Description

Method for calculating active soil pressure of limited soil body of cantilever type supporting structure of foundation pit
Technical Field
The invention relates to the technical field of geotechnical engineering, in particular to a method for calculating active soil pressure of a limited soil body of a cantilever type supporting structure of a foundation pit.
Background
The problem of solving the soil pressure is one of hot problems in the field of geotechnical engineering, at present, most of the traditional soil pressure calculation adopts the classical Rankine, Coulomb soil pressure theory or an expression modified by the classical soil pressure theory, but the theories are all established on the basic assumption that the soil body behind the wall is a semi-infinite space body.
With the rapid development of infrastructure, a plurality of working conditions that the soil body behind the retaining wall is limited in width emerge in city construction, highway engineering and railway engineering, and relate to foundation pit engineering, roadbed engineering, side slope engineering and the like. Because the position between the foundation pit to be excavated and the adjacent underground structure is close, the width of the soil body behind the wall is limited, and the linear slip fracture surface considered by the classic Rankine and Coulomb calculation method cannot extend to the soil filling surface due to the limitation of the adjacent underground structure, so that the assumption of a semi-infinite space body is not met. Obviously, the classical rankine, coulomb pressure theory for this operating regime is clearly not suitable. In practical engineering, displacement of a foundation pit supporting structure is very strictly controlled, particularly, displacement of a foundation pit close to a surrounding building is far smaller than displacement of a soil body behind a wall to reach an active limit state, the soil pressure is between static soil pressure and active soil pressure, and the soil body behind the wall is in a non-limit state.
Based on the above, it is necessary to discuss a finite soil pressure calculation method which does not satisfy the semi-infinite space conditions in a non-extreme state, and a certain promotion effect is exerted on the design theory and the construction level of the foundation pit supporting structure.
Disclosure of Invention
The invention aims to provide a method for calculating the active soil pressure of the limited soil body of the cantilever type supporting structure of the foundation pit.
In order to achieve the technical purpose, the invention provides a method for calculating the active soil pressure of a limited soil body of a cantilever type supporting structure of a foundation pit, which specifically comprises the following steps:
the method comprises the following steps: determining design parameters of a foundation pit supporting structure and physical and mechanical parameters of a soil body, comprising the following steps of: excavation depth h of foundation pit0(ii) a Heavy gamma, cohesive force c, internal friction angle of soil
Figure BDA0003602865480000021
Uniformly distributing loads q on the surface of the soil body by using a friction angle delta between the foundation pit supporting structure and the soil body;
step two: determining the relation between the friction angle and the displacement, and obtaining the play value of the internal friction angle of any displacement of the soil body in a quasi-active state by means of a stress Mohr circle
Figure BDA0003602865480000022
External friction angle exertion value deltamThe calculation formula (c) is as follows:
Figure BDA0003602865480000023
in the formula: rfTaking 0.75-1.0 as a destruction ratio;
eta is the effective displacement area ratio of the supporting structure;
step three: assuming that the slip crack surface of the soil body on the support side in the limit state accords with the distribution of the spinning wheel line, the included angle between any tangent point on the slip crack surface and the horizontal direction can be obtained:
Figure BDA0003602865480000024
in the formula:
Figure BDA0003602865480000025
h is the distance from the intersection point of the soil slip crack surface and the existing building to the ground:
Figure BDA0003602865480000026
h is the length of the foundation pit supporting structure;
θcthe rotation angle of the cycloid passing through the wall toe;
step four: the trapezoidal soil wedge body formed after the cantilever supporting structure in the limit state is taken for analysis, a horizontal layer analysis method is adopted, two types of horizontal micro-elements are divided according to the relative motion trend of the trapezoidal soil wedge body, horizontal and vertical differential equations are respectively established according to the force balance, and simultaneous simplification is achieved:
when y is more than or equal to 0 and less than or equal to h:
Figure BDA0003602865480000031
when H is more than y and is less than or equal to H:
Figure BDA0003602865480000032
boundary conditions: when y is 0, σy=q;
Since the expressions (c) and (c) continue at the depth y-h, the expression (c) is substituted for the expression (c) to obtain σyNamely the corresponding boundary condition of the formula (iv);
in the formula: l is1The distance between the supporting structure and the existing building;
L2the upper surface of the second type of micro-element is longDegree, according to the trochoid line slip crack surface analytic formula:
Figure BDA0003602865480000033
σythe vertical pressure of the top surface of the micro element body;
Figure BDA0003602865480000034
Figure BDA0003602865480000035
xi is 0.8-1.0;
K1the lateral soil pressure coefficient of the soil arch effect is considered for the rectangular area:
Figure BDA0003602865480000036
theta is the main stress deflection angle of two sides of the limited soil body:
Figure BDA0003602865480000037
K2the lateral soil pressure coefficient of the soil arching effect is considered for the triangular area:
Figure BDA0003602865480000038
θ1、θ2main stress deflection angles on two sides of a slip surface:
Figure BDA0003602865480000041
Kais Rankine active soil pressure coefficient;
step five: according to the formula I, the value is exerted by an internal friction angle and an external friction angle
Figure BDA0003602865480000042
And deltamSoil pressure in alternative formula (III) and formula (IV)Force parameter
Figure BDA0003602865480000043
And delta to obtain a calculation formula of the soil pressure under different displacements, and when H is more than y and less than or equal to H, corresponding to a y point sigmayThe differential equation of values can be solved by numerical methods.
The invention further adopts the technical scheme that: the soil body is non-cohesive soil, and the surface of the soil body is horizontal.
The invention further adopts the technical scheme that: the calculation formula of the effective displacement area ratio eta of the supporting structure in the second step is as follows:
Figure BDA0003602865480000044
Sataking 3.75-6H per mill for the displacement of the supporting side soil body when the supporting side soil body reaches the limit state;
h is the length of the foundation pit supporting structure;
S(z)the relation between the horizontal displacement and the depth of the supporting structure can be obtained by polynomial linear regression according to the site foundation pit monitoring data;
z is equation S(z)=SaThe solution of (1).
The further technical scheme of the invention is as follows: the rotation angle of the cycloid passing through the wall and toe in the third step refers to the following formula, wherein the related parameters are the same as those in claim 1:
Figure BDA0003602865480000045
the further technical scheme of the invention is as follows: the calculation formula of the soil pressure under different displacements obtained in the fifth step is as follows, and related parameters in the following formula are the same as those in claim 1:
Figure BDA0003602865480000051
according to the distance L between a supporting structure and an existing building, the method is divided into two conditions:
Figure BDA0003602865480000052
if it is considered to satisfy the semi-infinite space body assumption, in the fifth step, h is 0;
Figure BDA0003602865480000053
when it is determined that it meets the limited soil conditions, it is calculated according to the equation
Figure BDA0003602865480000054
Calculating h and substituting the equation to calculate the active soil pressure of the limited soil body.
In the formula: sigmax1And σx2The soil pressure strength of the supporting structures at different depths is respectively.
The invention has the following excellent technical scheme: and in the fifth step, programming solution is carried out by adopting Matlab software based on a Runge Kutta method.
The parameters in the different formulas in the invention are consistent.
The invention has the beneficial effects that: by adopting the method for calculating the active soil pressure of the limited soil body of the cantilever type supporting structure of the foundation pit, which is provided by the invention, the influence of displacement on the soil pressure can be considered, the assumption that the spinning wheel line slip crack surface is more in line with the reality is adopted, the condition that the soil body behind the wall is the limited soil body is considered in calculation and analysis, the obtained soil pressure distribution is more accurate and reasonable, the calculation formula is simple and practical, the method can be suitable for calculating the active soil pressure of the limited soil body of the cantilever type supporting structure, is favorable for reasonable design and construction of foundation pit engineering, and has certain popularization and application values.
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FIG. 1 is a schematic flow chart of a soil pressure calculation method according to the present invention;
FIG. 2 is a model for calculation and analysis of active soil pressure of a cantilever supporting structure of a foundation pit;
FIG. 3 is a force analysis diagram of a horizontal infinitesimal body;
fig. 4 is a graph of active earth pressure distribution in an example.
In the figure: 1-ground, 2-supporting structure, 3-cantilever type displacement, 4-base, 5-slip surface and 6-existing building.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and embodiments, wherein fig. 1 to 4 are drawings of the embodiments of the present invention, and are simplified for the purpose of concisely and clearly illustrating the embodiments of the present invention. It should be understood, however, that the scope of the embodiments of the present invention is not limited to the embodiments, and the embodiments may be implemented in various forms. These embodiments are provided so that this disclosure will be thorough and complete.
The invention provides a method for calculating active soil pressure of a limited soil body of a cantilever type supporting structure of a foundation pit, which is characterized in that aiming at the limitation of the assumption of a semi-infinite space body of the traditional soil pressure theory, the invention designs an accurate calculation method for calculating the active soil pressure of the limited soil body considering the supporting side, and referring to figure 1, the soil body in the embodiment is non-cohesive soil, and the surface of the soil body is horizontal; the parameters in different formulas in the embodiment are consistent, and the method comprises the following steps:
the method comprises the following steps: determining design parameters of a foundation pit supporting structure and physical and mechanical parameters of a soil body, comprising the following steps of: excavation depth h of foundation pit0(ii) a Heavy gamma, cohesive force c, internal friction angle of soil
Figure BDA0003602865480000061
Uniformly distributing loads q on the surface of the soil body by using a friction angle delta between the foundation pit supporting structure and the soil body; the mechanical parameters appearing in the following formulas are all consistent with those in step one.
Step two: determining the relation between friction angle and displacement, and setting the internal friction angle in non-limit state
Figure BDA0003602865480000062
The external friction angle delta is not fully exerted, and the exerted value is
Figure BDA0003602865480000063
δmTriaxial test analog master using unloading stress pathThe improved stress Mohr circle is used in the lateral displacement process of the soil body after the wall is in a dynamic state, and the existing parameters are utilized to obtain the inner friction angle exertion value of any displacement of the soil body in a quasi-active state
Figure BDA0003602865480000064
External friction angle exertion value deltamThe calculation formula (c) is as follows:
Figure BDA0003602865480000071
in the formula: rfTaking 0.75-1.0 as a destruction ratio;
eta is the ratio of the horizontal displacement value of a certain point in the height range of the supporting structure to the limit displacement value required for reaching the active limit state;
for a foundation pit supporting structure with a complex displacement form, the friction angle parameter of the filling soil
Figure BDA0003602865480000072
δmThe method is not only influenced by displacement, but also related to the height of the wall, and the intermediate state of the displacement of the supporting structure is reflected by replacing the displacement ratio with the effective displacement area ratio;
coefficient of intermediate state
Figure BDA0003602865480000073
SaTaking 3.75-6H per mill for the displacement of the supporting side soil body when the supporting side soil body reaches the limit state;
h is the length of the foundation pit supporting structure;
S(z)the relation between the horizontal displacement and the depth of the supporting structure can be obtained by polynomial linear regression according to the site foundation pit monitoring data;
z is equation S(z)=SaThe solution of (1).
Step three: assuming that the slip crack surface of the soil body on the support side in the limit state accords with the distribution of the spinning wheel line, the included angle between any tangent point on the slip crack surface and the horizontal direction can be obtained:
Figure BDA0003602865480000074
in the formula:
Figure BDA0003602865480000075
h is the distance from the intersection point of the soil slip crack surface and the existing building to the ground:
Figure BDA0003602865480000081
θcfor the rotation angle when the cycloid passes through the wall toe, the value can refer to the following formula:
Figure BDA0003602865480000082
step four: analyzing a trapezoidal soil wedge body formed after the cantilever supporting structure in an extreme state, wherein an analysis model is shown as figure 2, the trapezoidal soil wedge body can be divided into a rectangular part and a triangular part, and a horizontal layer analysis method is adopted to divide the trapezoidal soil wedge body into two types of horizontal infinitesimal bodies according to the relative motion trend of the trapezoidal soil wedge body as shown in figure 3;
respectively establishing horizontal and vertical differential equations of two types of infinitesimal bodies according to the balance of forces, and simultaneously simplifying the equations to obtain:
when y is more than or equal to 0 and less than or equal to h:
Figure BDA0003602865480000083
when H is more than y and less than or equal to H:
Figure BDA0003602865480000084
boundary conditions: when y is equal to 0, σy=q;
Since the expressions (c) and (c) continue at the depth y-h, the expression (c) is substituted for the expression (c) to obtain σyI.e. the corresponding boundary condition of the formula (iv)。
In the formula: l is1The distance between the supporting structure and the existing building;
L2the length of the upper surface of the second type of micro-element is expressed according to the analytic formula of the sliding surface of the spinning wheel line:
Figure BDA0003602865480000091
σythe vertical pressure of the top surface of the micro element body;
Figure BDA0003602865480000092
Figure BDA0003602865480000093
xi is 0.8-1.0;
K1the lateral soil pressure coefficient of the soil arch effect is considered for the rectangular area:
Figure BDA0003602865480000094
theta is the main stress deflection angle of two sides of the limited soil body:
Figure BDA0003602865480000095
K2the lateral soil pressure coefficient of the soil arch effect is considered for the triangular area:
Figure BDA0003602865480000096
θ1、θ2main stress deflection angles on two sides of a slip surface:
Figure BDA0003602865480000097
Kais Rankine active soil pressure coefficient;
step five: according to formula 1, the value is expressed by the internal and external friction angles
Figure BDA0003602865480000098
And deltamSoil pressure parameter in replacement type (c) and replacement type (c)
Figure BDA0003602865480000099
And delta, obtaining a soil pressure calculation formula under different displacements:
Figure BDA0003602865480000101
in the formula: sigmax1And σx2The soil pressure strength of the supporting structures at different depths is respectively.
Further, when H is more than y and less than or equal to H, corresponding to y point sigmayThe differential equation of the value is solved by a numerical method, Matlab software is adopted to program based on the Runge Kutta method, and a reasonable rotation angle theta is assumedcAnd trial calculation, wherein the maximum value of the corresponding resultant force in the obtained active soil pressure distribution is the calculated value of the active soil pressure.
Further, according to the distance L between the supporting structure and the existing building, the method can be divided into two conditions:
Figure BDA0003602865480000102
when the space is considered to satisfy the semi-infinite space body assumption, in the fifth step, h is 0;
Figure BDA0003602865480000103
when it is determined that it meets the limited soil conditions, it is calculated according to the equation
Figure BDA0003602865480000104
And (5) calculating h and substituting the h into the formula (fifthly), and calculating the active soil pressure of the finite soil body.
The following is a description of an embodimentAnd (3) comparison shows that: the indoor model test of cantilever pile in some sandy soil foundation pit is used as target, pile length H is 1.5m, and filling weight gamma is 18.2kN/m3Angle of internal friction
Figure BDA0003602865480000105
And the external friction angle delta is 16.2 degrees, the distance between the pile body and the model groove boundary is 0.8m, and the soil body behind the pile is known to be the type of the limited soil body according to the judgment condition of the limited soil body. And (5) excavating the foundation pit in layers, and respectively recording displacement and soil pressure values at different depths under different working conditions.
The method calculates the active soil pressure in the height range of the cantilever pile, firstly linearly regresses the displacement data of the pile body by a polynomial, calculates the analytical formula of the displacement S to the depth Z, substitutes the analytical formula into the formula I, and calculates
Figure BDA0003602865480000106
δm=13.4°。
Further, substituting formula II and formula V solves the differential equation by numerical method, assuming thetacThe comparison graph of the calculated value of the active earth pressure distribution when the pit is excavated to the bottom, the theoretical calculated value of the rankine earth pressure and the actual test value is shown in fig. 4.
As can be seen from fig. 4, compared with the rankine soil pressure theory in the specification, the change rule of the calculated value of the invention is closer to the change rule of the measured value, the calculated value of the soil pressure is distributed in a trend of approximately linearly increasing from the surface of the filled soil to the depth h of the intersection point of the slip crack surface and the existing building, the calculated value of the soil pressure is still linearly increased along with the depth from h to the base, but is reduced after increasing to the maximum value at a certain depth, and as a whole, the calculated curve of the soil pressure is nonlinearly distributed along the depth. Compared with an actual measured value, the Rankine theoretical calculation value is obviously larger, so that the limited soil pressure is analyzed, and if the calculation is designed according to a semi-infinite space body, the waste is larger, and the control cost is not facilitated.
Finally, the above-described embodiments are intended to be illustrative only and not to be limiting, and although the present invention has been described in detail by way of the foregoing examples, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit of the invention and without departing from the scope of the invention as defined by the appended claims.

Claims (6)

1. A method for calculating active soil pressure of a limited soil body of a cantilever type supporting structure of a foundation pit is characterized by comprising the following steps:
the method comprises the following steps: determining design parameters of a foundation pit supporting structure and physical and mechanical parameters of a soil body, comprising the following steps of: excavation depth h of foundation pit0(ii) a Heavy gamma, cohesive force c, internal friction angle of soil
Figure FDA0003602865470000011
Uniformly distributing loads q on the surface of the soil body by using a friction angle delta between the foundation pit supporting structure and the soil body;
step two: determining the relation between the friction angle and the displacement, and obtaining the play value of the internal friction angle of any displacement of the soil body in a quasi-active state by means of a stress Mohr circle
Figure FDA0003602865470000012
External friction angle exertion value deltamThe calculation formula of (c):
Figure FDA0003602865470000013
in the formula: rfTaking 0.75-1.0 as a destruction ratio;
eta is the effective displacement area ratio of the supporting structure;
step three: assuming that the slip crack surface of the soil body on the support side in the limit state accords with the distribution of the spinning wheel line, the included angle between any tangent point on the slip crack surface and the horizontal direction can be obtained:
Figure FDA0003602865470000014
in the formula:
Figure FDA0003602865470000015
h is the distance from the intersection point of the soil slip crack surface and the existing building to the ground:
Figure FDA0003602865470000016
h is the length of the foundation pit supporting structure;
θcthe rotation angle of the cycloid passing through the wall toe;
step four: the trapezoidal soil wedge body formed after the cantilever supporting structure in the limit state is taken for analysis, a horizontal layer analysis method is adopted, two types of horizontal micro-elements are divided according to the relative motion trend of the trapezoidal soil wedge body, horizontal and vertical differential equations are respectively established according to the force balance, and simultaneous simplification is achieved:
when y is more than or equal to 0 and less than or equal to h:
Figure FDA0003602865470000021
when H is more than y and is less than or equal to H:
Figure FDA0003602865470000022
boundary conditions: when y is 0, σy=q;
Since the expressions (c) and (c) continue at the depth y-h, the expression (c) is substituted for the expression (c) to obtain σyNamely the corresponding boundary condition of the formula (iv);
in the formula: l is1The distance between the supporting structure and the existing building;
L2the length of the upper surface of the second type of micro-element is expressed according to the analytic formula of the sliding surface of the spinning wheel line:
Figure FDA0003602865470000023
σythe vertical pressure of the top surface of the micro element body;
Figure FDA0003602865470000024
Figure FDA0003602865470000025
xi is 0.8-1.0;
K1the lateral soil pressure coefficient of the soil arching effect is considered for the rectangular area:
Figure FDA0003602865470000026
theta is the main stress deflection angle of two sides of the limited soil body:
Figure FDA0003602865470000027
K2the lateral soil pressure coefficient of the soil arch effect is considered for the triangular area:
Figure FDA0003602865470000031
θ1、θ2main stress deflection angles on two sides of a slip surface:
Figure FDA0003602865470000032
Kais Rankine active soil pressure coefficient;
step five: according to the formula I, the value is exerted by an internal friction angle and an external friction angle
Figure FDA0003602865470000033
And deltamSoil pressure parameter in the replacement formula III and the replacement formula IV
Figure FDA0003602865470000034
Is different from deltaThe earth pressure calculation formula under displacement corresponds to a y point sigma when H is more than y and less than or equal to HyThe differential equation of values can be solved by numerical methods.
2. The active soil pressure calculation method for the limited soil body of the cantilever type supporting structure of the foundation pit as claimed in claim 1, wherein: the soil body is non-cohesive soil, and the surface of the soil body is horizontal.
3. The method for calculating the active soil pressure of the limited soil body of the cantilever type supporting structure of the foundation pit according to claim 1, wherein the calculation formula of the effective displacement area ratio η of the supporting structure in the second step is as follows:
Figure FDA0003602865470000035
Sataking 3.75-6H per mill for the displacement of the supporting side soil body when the supporting side soil body reaches the limit state;
h is the length of the foundation pit supporting structure;
S(z)the relation between the horizontal displacement and the depth of the supporting structure can be obtained by polynomial linear regression according to the site foundation pit monitoring data;
z is equation S(z)=SaThe solution of (1).
4. The method for calculating the active soil pressure of the limited soil body of the cantilever type supporting structure of the foundation pit according to claim 1, wherein the rotation angle of the cycloid curve passing through the wall toe in the step three is obtained by referring to the following formula, wherein the related parameters are the same as those in claim 1:
Figure FDA0003602865470000041
5. the active soil pressure calculation method for limited soil mass of the cantilever type supporting structure of foundation pit according to claim 1, wherein the soil pressure calculation formula under different displacements obtained in the fifth step is as follows, and the relevant parameters in the following formula are the same as those in claim 1:
Figure FDA0003602865470000042
according to the distance L between a supporting structure and an existing building, the method is divided into two conditions:
Figure FDA0003602865470000043
when the space is considered to satisfy the semi-infinite space body assumption, in the fifth step, h is 0;
Figure FDA0003602865470000044
when the soil is determined to meet the limited soil condition, the equation is followed
Figure FDA0003602865470000045
Calculating h and substituting the equation to calculate the active soil pressure of the limited soil body.
In the formula: sigmax1And σx2The soil pressure strength of the supporting structure at different depths is respectively.
6. The active soil pressure calculation method for the limited soil body of the cantilever type supporting structure of the foundation pit as claimed in claim 1, wherein: and in the fifth step, programming solution is carried out by adopting Matlab software based on a Runge Kutta method.
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CN117057101A (en) * 2023-07-18 2023-11-14 山东建筑大学 Method and system for evaluating upper layer-adding construction safety of existing underground structure
CN117057101B (en) * 2023-07-18 2024-04-19 山东建筑大学 Method and system for evaluating upper layer-adding construction safety of existing underground structure

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