CN114818070A - Active soil pressure determination method for balance weight type retaining wall - Google Patents

Active soil pressure determination method for balance weight type retaining wall Download PDF

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CN114818070A
CN114818070A CN202210472016.7A CN202210472016A CN114818070A CN 114818070 A CN114818070 A CN 114818070A CN 202210472016 A CN202210472016 A CN 202210472016A CN 114818070 A CN114818070 A CN 114818070A
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罗强
熊诗杰
黄豫
张良
郭增瑞
蒋良潍
刘宏扬
王腾飞
吕鹏举
裴臻豪
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Southwest Jiaotong University
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Abstract

The invention discloses an active soil pressure determination method of a balance weight type retaining wall, which comprises the steps of S1, determining a structure of the balance weight type retaining wall and a wall back filling parameter; s2, calculating a first fracture surface shear angle of the fracture prism of the wall on the balance weight type retaining wall; s3, calculating to obtain a first fracture surface inclination angle and a second fracture surface inclination angle of the fracture prism of the wall on the weighing type retaining wall; s4, calculating to obtain a first fracture surface soil pressure and a second fracture surface soil pressure; s5, calculating the back soil pressure of the upper wall of the balance weight type retaining wall and the soil pressure of the balance weight platform according to the self weight of the soil on the balance weight platform between the second fracture surface and the upper wall back; and S6, calculating the tilt angle of the lower wall fracture surface of the balance weight retaining wall and the back soil pressure of the lower wall according to the self weight of the lower wall fracture prism. The method has the advantages that the damage mode of the wall back soil body of the balance weight type retaining wall is more in line with the actual engineering, the calculation precision of the soil pressure is higher, the influence of the height of the embankment above the wall top can be considered, and the structural design method and the stability evaluation technology of the balance weight type retaining wall are improved.

Description

Method for determining active soil pressure of balance weight type retaining wall
Technical Field
The invention belongs to the technical field of supporting structure design and stability evaluation in geotechnical engineering, and particularly relates to an active soil pressure determination method for a balance weight type retaining wall.
Background
A balance weight type retaining wall is a gravity type retaining wall structure form which is suitable for the innovation of mountainous terrain in China. Compared with the common gravity type retaining wall, the retaining wall has good slope collecting effect under the condition of steep ground cross slope and small masonry amount, the soil mass on the weighing platform enhances the anti-overturning stability of the wall body, the foundation stress distribution is more uniform, the foundation excavation and backfilling volume is greatly reduced, and in addition, the wall body can be prevented from invading the roadbed by adopting the weighing type retaining wall in the road shoulder section. Therefore, the balance weight retaining wall becomes a structural form of the retaining wall which is widely applied in railway and highway engineering in mountain areas in China.
Due to the existence of the weight table, the stress characteristic of the weight retaining wall is greatly changed compared with that of a plane wall back of a common gravity retaining wall, and the soil pressure borne by the wall back is more complex. At present, a balance weight type retaining wall can be generally divided into an upper wall section and a lower wall section in engineering, and the soil pressure born by a corresponding wall back is determined based on the coulomb soil pressure theory. The upper wall back soil pressure is determined by an imaginary wall back of a connecting line of the wall top and the outer edge of the weighing platform, and when a second fracture surface appears in the soil body, the upper wall back soil pressure is determined according to a second fracture surface method; the lower wall back soil pressure is determined by adopting an extension wall back method or a force polygon method. However, in practical engineering application, cases of excessive deformation and even instability of the balance weight retaining wall sometimes occur, and particularly, phenomena such as tensile fracture and damage easily occur at the junction of the upper wall and the balance weight table, which indicates that certain safety risks exist in the structural stability of the balance weight retaining wall determined by the traditional method.
The characteristics of the cracking surface of the back soil body of the balance weight type retaining wall and the soil pressure test show that when the retaining wall is in a limit balance state, only the second cracking surface of the upper wall passing through the balance weight table edge and the lower wall cracking surface passing through the heel of the wall are formed in the back soil body of the wall, but the first cracking surface of the upper wall assumed by the traditional method is not formed, and the difference causes the distribution of the soil pressure on the upper wall and the lower wall back to be changed, so that the obvious increase of the back soil pressure of the upper wall and the reduction of the back soil pressure of the lower wall are caused, and the characteristics and the soil pressure test result in the important reason that the tensile cracking damage is easy to occur at the junction of the upper wall and the balance weight table of the balance weight type retaining wall.
Disclosure of Invention
The present invention is directed to overcome the above-mentioned shortcomings in the prior art and to provide an active soil pressure determination method for a balance weight retaining wall, which solves the problems that the conventional method fails to consider that the first fracture surface of the upper wall fracture prism is not formed, and the difference causes the distribution of the soil pressure on the upper and lower wall backs to change, which causes the soil pressure on the upper wall back to increase significantly and the soil pressure on the lower wall back to decrease.
In order to achieve the purpose, the invention adopts the technical scheme that:
an active soil pressure determination method for a balanced retaining wall, comprising the steps of:
s1, determining the structure of the constant weight retaining wall and the filling parameters of the wall back;
s2, calculating a first fracture surface shear angle of a fracture prism of the wall on the balance weight type retaining wall according to the structure of the balance weight type retaining wall;
s3, constructing a force polygon closed static balance equation according to the structure of the balance weight type retaining wall, the wall back filling parameters and the first fracture surface shear angle, and calculating to obtain a first fracture surface inclination angle and a second fracture surface inclination angle of the fracture prism of the wall on the balance weight type retaining wall;
s4, calculating to obtain a first fracture surface soil pressure and a second fracture surface soil pressure based on the calculated first fracture surface inclination angle and second fracture surface inclination angle of the fracture prism of the balance weight type retaining wall;
s5, calculating the upper wall back soil pressure and the balance weight table soil pressure of the balance weight type retaining wall according to the self weight of the balance weight table soil body between the second fracture surface and the upper wall back;
and S6, calculating the tilt angle of the lower wall fracture surface of the balance weight retaining wall and the back soil pressure of the lower wall according to the self weight of the lower wall fracture prism.
Further, the determining of the weight-balanced retaining wall structure and the back filling parameters in step S1 includes:
upper wall height H of measured and determined balance weight type retaining wall 1 Height of lower wall H 2 Width L of the weighing platform and back inclination angle alpha of the upper wall 1 And the back inclination angle alpha of the lower wall 2 The height h of the side slope of the embankment above the wall top and the inclination angle lambda of the side slope;
and the volume weight gamma and the comprehensive internal friction angle of the wall back soil body obtained by adopting the geotechnical test
Figure BDA0003623064670000031
Wall soil friction angle delta.
Further, the step S2 of calculating the first fracture surface shear angle of the fracture prism of the balance weight retaining wall includes:
according to the height h of the embankment side slope above the wall top, calculating a first fracture surface shear angle exertion coefficient eta of the upper wall fracture prism body:
η＝0.841-0.478e -0.505h
according to the angle of comprehensive internal friction
Figure BDA0003623064670000032
First fracture surface shear angle ζ of upper wall fracture prism:
Figure BDA0003623064670000033
and h is less than or equal to 8 m.
Further, the step S3 of constructing a static equilibrium equation of force polygon closure and calculating a first fracture surface inclination angle and a second fracture surface inclination angle of the fractured prism of the counterweight retaining wall includes:
constructing a static equilibrium equation of force polygon closure:
Figure BDA0003623064670000034
wherein W' is based on the dead weight of the broken prism, R 1 Is the first fracture surface soil pressure, E' is the second fracture surface soil pressure, and zeta is the first fracture surface soil pressure R 1 And the included angle between the normal line and the normal line,
Figure BDA0003623064670000035
the second fracture surface soil pressure E' and the included angle with the normal line are adopted, and beta and alpha are respectively a first fracture surface inclined angle and a second fracture surface inclined angle of the fracture prism body of the wall on the balance weight type retaining wall;
and (4) derivation is carried out on the beta and the alpha by the static equilibrium equation to obtain a limit equation, and the limit equation is solved to obtain the beta and the alpha.
Further, the step S5 of calculating the back soil pressure of the wall and the balance weight table soil pressure of the balance weight type retaining wall includes:
according to the self weight W of the soil body on the weighing platform between the second fracture surface and the upper wall back, the soil pressure E' of the second fracture surface and the included angle with the normal line
Figure BDA0003623064670000041
Soil pressure P of weighing platform and soil pressure E of upper wall 1 And constructing a static balance equation system of force polygon closure:
Figure BDA0003623064670000042
solving the force polygon closed static equilibrium equation set to obtain the upper wall back earth pressure E 1 And a counter-weight earth pressure P.
Further, in step S6, calculation is performedBalance weight type retaining wall lower wall cracking surface inclination angle theta and lower wall back earth pressure E 2 The method comprises the following steps:
according to the self weight W' of the lower wall fracture prism body and the first fracture surface soil pressure R 1 And angle zeta with the normal, lower wall cracking surface soil pressure R 2 And angle theta from normal, lower wall back earth pressure E 2 And angle delta from normal 2 And constructing a static balance equation system of force polygon closure:
Figure BDA0003623064670000043
derivation is carried out on theta of the force polygon closed static equilibrium equation set to obtain a limit equation, the limit equation is solved to obtain a lower wall fracture surface inclination angle theta, and the lower wall fracture surface inclination angle theta is substituted into the static equilibrium equation set to obtain a lower wall back earth pressure E 2 。
The method for determining the active soil pressure of the balance weight type retaining wall has the following beneficial effects:
the invention provides a method for considering that the shear angle zeta of a first fracture surface of a fracture prism on an upper wall is not more than the comprehensive internal friction angle of a soil body on the back of the wall
Figure BDA0003623064670000044
The method for determining the active soil pressure of the balance weight type retaining wall has important significance for perfecting the structural design and stability evaluation of the balance weight type retaining wall.
In the invention, the condition that the first fracture surface of the upper wall fracture prism is not formed is considered, the traditional method is modified, and a foundation is laid for perfecting the structural design and stability evaluation of the weight-balanced retaining wall.
The method has the advantages that the damage mode of the wall back soil body of the balance weight type retaining wall is more in line with the actual engineering, the calculation precision of the soil pressure is higher, the influence of the height of the embankment above the wall top can be considered, and the structural design method and the stability evaluation technology of the balance weight type retaining wall are improved.
Drawings
Fig. 1 is a mechanical model diagram of an active soil pressure determination method for a counterweight retaining wall.
Fig. 2 is a force polygon of an active soil pressure determination method for a balanced retaining wall.
Detailed Description
The following description of the embodiments of the present invention is provided to facilitate the understanding of the present invention by those skilled in the art, but it should be understood that the present invention is not limited to the scope of the embodiments, and it will be apparent to those skilled in the art that various changes may be made without departing from the spirit and scope of the invention as defined and defined in the appended claims, and all matters produced by the invention using the inventive concept are protected.
According to embodiment 1 of the present application, referring to fig. 1 and 2, the method for determining active soil pressure of a counterweight retaining wall of the present application includes the following steps:
step S1, determining the weight-balancing retaining wall structure and the wall back filling parameters, which comprises the following steps:
determining the height H of the retaining wall by measuring 1 (m) lower wall height H 2 (m), width L (m) of the weighing platform, and back inclination angle alpha of the upper wall 1 (°) and lower wall back inclination angle α 2 (DEG), the height h (m) of the embankment side slope above the top of the wall and the slope dip angle lambda (DEG);
and obtaining the unit weight gamma (kN/m) of the wall back soil body by geotechnical test 3 ) Comprehensive internal friction angle
Figure BDA0003623064670000051
Wall soil friction angle δ (°).
Step S2, calculating a first fracture surface shear angle of the fractured prism of the counterweight retaining wall according to the counterweight retaining wall structure, which specifically includes:
according to the height h of the embankment side slope above the wall top, calculating a first fracture surface shear angle exertion coefficient eta of the upper wall fracture prism body:
η＝0.841-0.478e -0.505h
according to the angle of comprehensive internal friction
Figure BDA0003623064670000061
Computing wallFirst fracture surface shear angle ζ of fracture prism:
Figure BDA0003623064670000062
the applicable condition of the shear angle zeta of the first fracture surface of the upper wall is determined to be that the height h of the slope above the top of the wall is less than or equal to 8 m.
Step S3, according to the structure of the balance weight type retaining wall, the filling parameters of the wall back and the shear angle of the first fracture surface, a static equilibrium equation of force polygon closing is constructed, and the first fracture surface inclination angle and the second fracture surface inclination angle of the fracture prism of the wall on the balance weight type retaining wall are obtained through calculation, and the method specifically comprises the following steps:
determining the weight-balanced retaining wall structure and the back filling parameters according to the step S1, and the first fracture surface shear angle zeta of the upper wall fracture prism obtained in the step S2 based on the self weight W' of the fracture prism and the first fracture surface soil pressure R 1 And angle zeta to the normal, second fracture surface earth pressure E 'and angle E' to the normal
Figure BDA0003623064670000063
Establishing a static equilibrium equation of force polygon closure:
Figure BDA0003623064670000064
and (4) obtaining a limit equation by deriving the equation set from the first fracture surface inclination angle beta and the second fracture surface inclination angle alpha, and solving the limit equation to obtain the first fracture surface inclination angle beta and the second fracture surface inclination angle alpha of the upper wall.
First fracture surface inclination angle β:
Figure BDA0003623064670000065
Figure BDA0003623064670000066
Figure BDA0003623064670000067
Figure BDA0003623064670000068
H′＝H 1 +h h″＝H 1 secα′cos(α′-λ)
wherein h' is the vertical distance (m) from the edge of the weighing platform to the side slope surface or the roadbed surface; α' is an imaginary wall back tilt angle (°); h' is the upper wall height H 1 The sum (m) of the slope height h; q, S 1 、S 2 、S 3 Intermediate quantities in the calculation process defined by simplified formulas have no practical significance; λ is the slope inclination (°).
Second fracture surface inclination angle α:
Figure BDA0003623064670000071
step S4, based on the calculated first fracture surface inclination angle and second fracture surface inclination angle of the fracture prism of the balance weight type retaining wall, substituting the first fracture surface inclination angle and the second fracture surface inclination angle into the equation set established in the step S3, and calculating to obtain a first fracture surface soil pressure and a second fracture surface soil pressure;
second fracture surface earth pressure E':
Figure BDA0003623064670000072
step S5, calculating the back soil pressure of the upper wall of the balance weight type retaining wall and the soil pressure of the balance weight platform according to the self weight of the soil body on the balance weight platform between the second fracture surface and the upper wall back, which specifically comprises the following steps:
according to the self weight W of the soil body on the weighing platform between the second fracture surface and the upper wall back, the soil pressure E' of the second fracture surface and the included angle with the normal line
Figure BDA0003623064670000073
Pressure of the weighing platformP, upper wall back earth pressure E 1 Wherein the balance weight platform and the upper wall back assume no friction, the included angle with the normal is 0, a force polygon closed static balance equation set is established, and the equation set is solved to obtain the upper wall back earth pressure E 1 And a counter-weight earth pressure P.
Figure BDA0003623064670000074
Upper wall back earth pressure E 1 ：
Figure BDA0003623064670000075
Weighing platform soil pressure P:
Figure BDA0003623064670000076
Figure BDA0003623064670000081
step S6, calculating the tilt angle of the lower wall fracture surface and the lower wall back soil pressure of the balance weight retaining wall according to the self weight of the lower wall fracture prism, and the method specifically comprises the following steps:
according to the self weight W' of the lower wall fracture prism body and the first fracture surface soil pressure R 1 And angle zeta with the normal, lower wall cracking surface soil pressure R 2 And angle theta from normal, lower wall back earth pressure E 2 And angle delta from normal 2 And establishing a static equilibrium equation system of force polygon closure.
Figure BDA0003623064670000082
The equation set is derived from theta to obtain a limit equation, the limit equation is solved to obtain a lower wall fracture surface inclination angle theta, and then the lower wall fracture surface inclination angle theta is substituted into a static equilibrium equation to obtain a lower wall back earth pressure E 2 。
Lower wall fracture surface inclination angle θ:
Figure BDA0003623064670000083
Figure BDA0003623064670000084
Figure BDA0003623064670000085
Figure BDA0003623064670000086
Figure BDA0003623064670000087
lower wall back earth pressure E 2 ：
Figure BDA0003623064670000088
Wherein psi, B 0 、A 0 The intermediate quantity in the process of calculation has no practical significance; h 2 The lower wall height (m).
According to example 2 of the present application, the regression formula of the first fracture surface shear angle exertion coefficient η of the upper wall fracture prism of the present example is established based on the multifactor orthogonal test and the regression analysis, and the procedure thereof is described below:
firstly, according to the characteristics of the weight-balanced retaining wall, six main factors influencing the active soil pressure of the wall back are selected from three aspects of the embankment side slope form, the filling property and the retaining wall structure form: the height of the side slope, the slope rate of the side slope, the internal friction angle of the filled soil, the width of the weighing platform, the height of the retaining wall and the height ratio of the upper wall are calculated according to the three levels of all the factors, and the three levels are shown in the table 1.
TABLE 1 orthogonal test factor horizon
Figure BDA0003623064670000091
Then, based on the orthogonal test design, an orthogonal test scheme L is determined 18 (3 6 ) And respectively obtaining the soil pressures borne by the second fracture surface, the upper wall back, the lower wall back and the weighing platform of each group of tests according to finite element calculation and the active soil pressure determination method, and determining the eta value under each group of test conditions on the basis of the principle that the deviation between the soil pressure value obtained by the active soil pressure determination method and the finite element value is minimum. Table 2 shows the protocol of the orthogonal test and the corresponding eta values.
TABLE 2 multifactor orthogonal test L 18 (3 6 ) And eta value
Figure BDA0003623064670000092
Figure BDA0003623064670000101
Finally, the factor (i) the height h (m) of the side slope has obvious influence on the first fracture surface shear angle exertion coefficient eta through range and variance analysis, and the influence of other factors is not obvious, and is shown in a table 3 and a table 4. Establishing a regression formula eta of 0.841-0.478e for the main influence factor of slope height h (m) and the first fracture surface shear angle exertion coefficient eta according to multiple regression analysis -0.505h Wherein e is a natural logarithm, and a coefficient of regression model R 2 The fitting effect is better when the value is equal to 0.883.
TABLE 3 range analysis
Figure BDA0003623064670000102
TABLE 4 analysis of variance
Figure BDA0003623064670000103
According to the invention, model tests and finite element calculation find that when the balance weight retaining wall is in an active limit balance state, only the upper wall second fracture surface and the lower wall fracture surface are formed in the wall back soil body, and the upper wall first fracture surface is not formed; through an orthogonal test method, the exertion degree of the shear angle of the first fracture surface is closely related to the height of the side slope of the embankment, and the influence of the slope gradient, the internal friction angle, the width of the weighing platform, the height of the retaining wall and the ratio of the upper wall height is small; obtaining a first fracture surface shear angle exertion coefficient eta and a slope height h (m) through multiple regression analysis, wherein the first fracture surface shear angle exertion coefficient eta and the slope height h (m) satisfy an exponential function relation formula eta taking a natural logarithm e as a base, and the exponential function relation formula eta is 0.841-0.478e -0.505h And the eta values under the influence of different factor levels can be accurately predicted.
Therefore, when the active soil pressure of the balance weight type retaining wall is determined, firstly, the eta value is determined according to the height of the side slope, so that the shear angle zeta is obtained, and then, the wall back soil pressure value is obtained by the method for determining the active soil pressure of the balance weight type retaining wall. The method improves the determination precision of the soil pressure of the balance weight type retaining wall, perfects the soil pressure calculation method, reduces the cracking risk of the upper wall structure, and enhances the safety of the retaining wall structure.
While the embodiments of the invention have been described in detail in connection with the accompanying drawings, it is not intended to limit the scope of the invention. Various modifications and changes may be made by those skilled in the art without inventive step within the scope of the appended claims.

Claims (6)

1. An active soil pressure determination method for a balance weight retaining wall is characterized by comprising the following steps:
s1, determining the structure of the constant weight retaining wall and the filling parameters of the wall back;
s2, calculating a first fracture surface shear angle of a fracture prism of the wall on the balance weight type retaining wall according to the structure of the balance weight type retaining wall;
s3, constructing a force polygon closed static balance equation according to the structure of the balance weight type retaining wall, the wall back filling parameters and the first fracture surface shear angle, and calculating to obtain a first fracture surface inclination angle and a second fracture surface inclination angle of the fracture prism of the wall on the balance weight type retaining wall;
s4, calculating to obtain a first fracture surface soil pressure and a second fracture surface soil pressure based on the calculated first fracture surface inclination angle and second fracture surface inclination angle of the fracture prism of the balance weight type retaining wall;
s5, calculating the back soil pressure of the upper wall of the balance weight type retaining wall and the soil pressure of the balance weight platform according to the self weight of the soil on the balance weight platform between the second fracture surface and the upper wall back;
and S6, calculating the tilt angle of the lower wall fracture surface of the balance weight retaining wall and the back soil pressure of the lower wall according to the self weight of the lower wall fracture prism.
2. The active soil pressure determination method of a balanced weight retaining wall according to claim 1, wherein the determining of the balanced weight retaining wall structure and the wall back filling parameters in step S1 comprises:
upper wall height H of measured and determined balance weight type retaining wall 1 Height of lower wall H 2 Width L of the weighing platform and back inclination angle alpha of the upper wall 1 And the back inclination angle alpha of the lower wall 2 The height h of the side slope of the embankment above the wall top and the inclination angle lambda of the side slope;
and the volume weight gamma and the comprehensive internal friction angle of the wall back soil body obtained by adopting the geotechnical test
Figure FDA0003623064660000011
Wall soil friction angle delta.
3. The active soil pressure determination method of a balanced weight retaining wall of claim 2 wherein the step of calculating a first fracture surface shear angle of a balanced weight retaining wall fracture prism in step S2 comprises:
according to the height h of the embankment side slope above the wall top, calculating a first fracture surface shear angle exertion coefficient eta of the upper wall fracture prism body:
η＝0.841-0.478e -0.505h
according to the angle of comprehensive internal friction
Figure FDA0003623064660000021
First fracture surface shear angle ζ of upper wall fracture prism:
Figure FDA0003623064660000022
and h is less than or equal to 8 m.
4. The active soil pressure determination method of a balanced weight retaining wall according to claim 3 wherein the step S3 of constructing a static equilibrium equation of force polygon closure and calculating the first and second slope angles of the fracture surface of the fracture prism of the balanced weight retaining wall comprises:
constructing a static equilibrium equation of force polygon closure:
Figure FDA0003623064660000023
wherein W' is based on the dead weight of the broken prism, R 1 Is the first fracture surface soil pressure, E' is the second fracture surface soil pressure, and zeta is the first fracture surface soil pressure R 1 And the included angle between the normal line and the normal line,
Figure FDA0003623064660000024
the second fracture surface soil pressure E' and the included angle with the normal line are adopted, and beta and alpha are respectively a first fracture surface inclined angle and a second fracture surface inclined angle of the fracture prism body of the wall on the balance weight type retaining wall;
and (4) deriving the static equilibrium equation for beta and alpha to obtain a limit equation, and solving the limit equation to obtain the beta and the alpha.
5. The active soil pressure determination method of a balanced weight retaining wall according to claim 4, wherein the step of calculating the back soil pressure and the balanced weight table soil pressure of the balanced weight retaining wall in step S5 comprises:
according to the self weight W of the soil body on the weighing platform between the second fracture surface and the upper wall back, the soil pressure E' of the second fracture surface and the included angle with the normal line
Figure FDA0003623064660000025
Soil pressure P of weighing platform and soil pressure E of upper wall 1 And constructing a static balance equation system of force polygon closure:
Figure FDA0003623064660000026
solving the force polygon closed static equilibrium equation set to obtain the upper wall back earth pressure E 1 And a counter-weight earth pressure P.
6. The active soil pressure determination method of a balanced weight retaining wall according to claim 5 wherein the tilt angle θ of the lower wall cracking surface of the balanced weight retaining wall and the lower wall back soil pressure E are calculated in step S6 2 The method comprises the following steps:
according to the self weight W' of the lower wall fracture prism body and the first fracture surface soil pressure R 1 And angle zeta with the normal, lower wall cracking surface soil pressure R 2 And angle theta from normal, lower wall back earth pressure E 2 And angle delta from normal 2 And constructing a static balance equation system of force polygon closure:
Figure FDA0003623064660000031
derivation is carried out on theta of the force polygon closed static equilibrium equation set to obtain a limit equation, the limit equation is solved to obtain a lower wall fracture surface inclination angle theta, and the lower wall fracture surface inclination angle theta is substituted into the static equilibrium equation set to obtain a lower wall back earth pressure E 2 。
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