CN115828377A - Equal shear strength slope stability calculation method - Google Patents
Equal shear strength slope stability calculation method Download PDFInfo
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- CN115828377A CN115828377A CN202211432702.8A CN202211432702A CN115828377A CN 115828377 A CN115828377 A CN 115828377A CN 202211432702 A CN202211432702 A CN 202211432702A CN 115828377 A CN115828377 A CN 115828377A
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Abstract
The invention provides a method for calculating the stability of a side slope with equal shear strength, which comprises the following steps: dividing a region, namely dividing the composite foundation filling side slope into a first region, a second region and a third region; a model conversion step, namely dividing each pile body into a plurality of repeated unit bodies with square cross sections in the first area, converting the cross sections of the pile bodies from circular shapes into rectangular cross sections with the same area, and converting the pile bodies from cylindrical piles into rectangular piles; a re-modeling step, namely dividing the slope filling in the second area into areas with different gravities, obtaining the equivalent gravities of the second area for modeling, and re-establishing a second area model above the first area; and calculating a slope stability coefficient, namely acquiring the height of the slope in the second area and the pile length to determine the range of the third area, establishing a finished two-dimensional limit balance method analysis model, and calculating the slope stability coefficient in the second area.
Description
Technical Field
The invention relates to the field of rock-soil shear strength calculation, in particular to a method for calculating the stability of a side slope with equal shear strength.
Background
In slope engineering, a limit balance method is usually adopted when calculating the stability of a filling slope of a composite foundation, and commercial calculation software (such as rational rock-soil software, GEO5 rock-soil software and the like) adopting a two-dimensional limit balance method is adopted for auxiliary calculation nowadays. When the slope stability of the composite foundation fill slope is calculated, the composite shear strength parameters of the piles and the soil are usually calculated through the replacement rate, the piles and the foundation soil in the reinforced area are simplified into a composite material, but the difference of the loads borne by the piles and the foundation soil under the influence of the pile-soil stress ratio is ignored, and the two materials have larger difference and are inconsistent with the actual situation.
Disclosure of Invention
The invention aims to provide a method for calculating the stability of a side slope with equal shear strength, which is used for modeling a composite foundation filling side slope by using a two-dimensional limit balancing method and fully considering the difference of the load borne by a pile body and foundation soil, so that the calculation result is fitted to the actual situation as much as possible.
In order to solve the above problems, the invention provides a method for calculating the stability of a side slope with equal shear strength, which comprises the following steps: dividing the composite foundation filling side slope into a first area, a second area and a third area, wherein the first area is a piling area, the second area is an area formed above the piling area, and the third area is the rest area of the composite foundation filling side slope; a model conversion step, wherein each pile body in the first region is divided into a plurality of repeated unit bodies with square cross sections, each unit body comprises a pile body and foundation soil, the pile body in each unit body is converted into a rectangular pile from a cylindrical pile, and the cross section area of the rectangular pile is equal to that of the cylindrical pile; a re-modeling step, namely dividing the slope filling in the second area into areas with different gravities, obtaining the equivalent gravities of the second area for modeling, and re-establishing a second area model above the first area; and calculating a slope stability coefficient, namely acquiring the height of the slope in the second area and the pile length to determine the range of a third area, establishing a finished two-dimensional limit balance method analysis model, and calculating to obtain the slope stability coefficient.
Further, the step of converting the model in the equal shear strength slope stability calculation method further includes: a data measurement step: acquiring the pile diameter d and the pile spacing s of the pile body and the heavy gamma of the pile body p C, cohesion force p Pile body internal friction angle phi p Obtaining the gravity gamma of the foundation soil s C, cohesion force s Internal friction angle phi of foundation soil s (ii) a In the step of converting the model, the width b of the converted rectangular section of the pile body 0 Comprises the following steps:
wherein s is the cross-sectional width of the unit body.
Further, in the step of re-modeling in the equal shear strength slope stability calculation method, the second region equivalent severe degree γ 'corresponding to the rectangular piles in the unit bodies' pi Comprises the following steps:
wherein m is the replacement rate, n is the stress ratio of the pile soil, and gamma is the filling weight; in the modeling step again, the equivalent weight gamma of a second area corresponding to the foundation soil in the unit body' si Comprises the following steps:
wherein m is the replacement rate, n is the pile-soil stress ratio, and gamma is the filling weight.
Further, in the equal shear strength slope stability calculation method, the pile-soil stress ratio calculation formula is as follows:
n＝p pi /p si
wherein p is pi For the stress shared by the piles, p si Is the stress shared by the foundation soil;
further, the stress p shared by the piles in the equal shear strength slope stability calculation method pi The calculation formula is as follows:
stress p shared by foundation soil si The calculation formula is:
wherein h is i Is the fill height.
According to the method for realizing equal shear strength slope model establishment in the two-dimensional limit balancing method software provided by the embodiment of the invention, an analysis model in the two-dimensional limit balancing method software is established by dividing into 3 regions with different properties according to the characteristics of the analysis model; the method comprises the steps of converting a three-dimensional model of a circular pile composite foundation into a three-dimensional model of a rectangular pile composite foundation by eliminating shape difference between a pile body and foundation soil in the longitudinal direction to meet plane strain assumption, and analyzing a two-dimensional profile of the three-dimensional model to establish a composite foundation area model; regarding the filling side slope on the composite foundation as a load, considering the influence of pile-soil stress ratio, dividing the side slope filling on the upper part of the composite foundation into areas with different gravities for simulating the effect of pile-soil stress ratio, calculating the equivalent gravities of the filling side slope area on the composite foundation for modeling, and establishing a filling side slope area model on the composite foundation; determining other area ranges according to the height of the slope and the pile length, giving original parameters, establishing a complete two-dimensional extreme balance method analysis model, and enabling software to automatically search the most dangerous sliding surface so as to calculate the stability coefficient of the slope. The invention provides a more practical method for realizing the establishment of the equal shear strength slope model in the two-dimensional limit balance method software based on the equal shear strength substitution principle and the slope filling equivalent weight calculation principle considering the pile-soil stress ratio.
Drawings
FIG. 1 is a flow diagram of a method according to an embodiment of the invention;
FIG. 2 is a schematic diagram of a three-dimensional model of a composite foundation fill side slope before equivalence according to an embodiment of the invention;
fig. 3 is a composite ground area floor plan view according to an embodiment of the present invention;
FIG. 4 is a schematic cross-sectional view of an equivalent front cell body according to an embodiment of the present invention;
FIG. 5 is a schematic cross-sectional view of an equivalent rear cell body according to an embodiment of the present invention;
FIG. 6 is a schematic diagram of an equivalent post-composite foundation fill slope three-dimensional model according to an embodiment of the invention;
FIG. 7 is an equivalent rear slope two-dimensional cross-sectional view according to an embodiment of the invention;
FIG. 8 is a schematic diagram of calculation of equivalent weight of a fill slope area on a composite foundation according to an embodiment of the invention;
FIG. 9 is another schematic diagram of calculating equivalent weight of a fill slope area on a composite foundation according to an embodiment of the invention;
FIG. 10 is a schematic diagram of a complete two-dimensional extreme balance analysis model of a composite foundation fill slope according to an embodiment of the invention;
FIG. 11 is a schematic diagram of a computing software interface used in accordance with an embodiment of the present invention;
FIG. 12 is a schematic diagram of another interface of computing software for use in accordance with an embodiment of the present invention;
FIG. 13 is a schematic diagram of another interface of computing software for use in accordance with an embodiment of the present invention;
FIG. 14 is a schematic diagram of another interface for computing software used in accordance with an embodiment of the present invention.
Reference numerals:
1: a first region;
11: a pile body;
11a: rectangular piles;
12: a unit body;
13 foundation soil
2: a second region;
21: filling soil on the side slope;
22: filling soil in the side slope on the upper part of the pile;
23: a side slope filling area on the upper part of the foundation soil;
3: a third region;
4: the original ground.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail with reference to the accompanying drawings in conjunction with the following detailed description. It should be understood that the description is intended to be exemplary only, and is not intended to limit the scope of the present invention. Moreover, in the following description, descriptions of well-known structures and techniques are omitted so as to not unnecessarily obscure the concepts of the present invention.
The illustrated embodiments of the present invention and the principles of the calculations are described below with reference to the accompanying drawings.
Referring to fig. 1, the illustrated embodiment of the present invention may be broadly divided into the following steps: dividing regions, converting models, rebuilding models and calculating slope stability coefficients.
Referring to fig. 2, after pile driving is completed, the regions are divided, and the pile driving region is a composite foundation region, i.e., a first region, on which a slope filling side slope region, i.e., a second region, is formed, and the other regions are third regions.
Then, starting to convert the model, the first area may be divided into a plurality of groups of repeated unit bodies with square cross sections according to each pile body, each group of unit bodies includes a pile body and foundation soil, and the unit bodies do not conform to the plane strain assumption in the longitudinal direction due to the shape difference between the pile body and the foundation soil, so that the shape difference between the pile body and the foundation soil in the longitudinal direction needs to be eliminated to conform to the plane strain assumption.
Referring to fig. 3, the piles arranged in a square shape in the plane are round piles, the diameter of each pile is d, the distance between every two adjacent piles is s, and the weight of each pile is gamma p A cohesion of c p The internal friction angle of the pile body is
The gravity of the foundation soil is gamma s A cohesion of c s The internal friction angle of the foundation soil is
Taking a unit body for analysis, as shown in FIG. 4, the length and width of the unit body are s, the pile diameter is d, and the area of the pile is A p ，A p ＝πd 2 (ii) in pile area A p Under the condition of no change, the circular area is equivalent to the length s and the width b 0 I.e. the cylindrical pile is converted into a rectangular pile, while the cross-sectional area of the cylindrical pile is equal to the cross-sectional area of the rectangular pile, as shown in fig. 5, then b 0 The calculation formula is as follows:
the transformed model is shown in FIG. 6.
Referring to fig. 7, after the conversion is completed, only the cross-sectional shape of the pile body is changed, that is, the pile body is converted from a circular shape to a rectangular shape, but the volume of the pile body remains unchanged, and the original cylindrical pile body is converted into a rectangular pile, so that the pile body and the foundation soil weight and shear strength parameters in the first region are unchanged and meet the plane strain assumption. At the moment, the related parameters of the model composite foundation area, namely the weight of the pile body in the first area is gamma, can be given in the calculation software adopting the two-dimensional limit balance method p A cohesion of c p The internal friction angle of the pile body is
The gravity of the foundation soil is gamma s A cohesion of c s The ground soil internal friction angle is
Referring to fig. 8, the fill side slope in the second area may be regarded as a load, the influence of pile-soil stress ratio is considered, the side slope fill at the upper portion of the first area is divided into areas with different weights for simulating the effect of pile-soil stress ratio, the equivalent weight of the fill side slope area on the composite foundation for modeling is calculated, and a fill side slope area model on the first area is established.
When a certain load acts on the first area, due to the influence of the pile-soil stress ratio, the actual load shared by the pile body and the foundation soil is different, one unit body i and the filling soil on the upper slope are taken from the two-dimensional section of the filling side slope of the composite foundation shown in fig. 7 for analysis, and the filling soil on the side slope above the unit body i is regarded as the load acting on the unit body i of the composite foundation.
As shown in fig. 8, the unit i corresponds to the upper slope filling area with a filling weight γ, a cohesive force c, and a third internal friction angle
(ii) a The filling height is h i The fill stress p acting on the unit body i i Comprises the following steps:
p i ＝γh i (1)
the stress shared by the pile body is p due to the influence of the stress ratio of the pile soil pi The foundation soil shares a stress of p si The substitution rate is m, and the principle of the substitution rate shows that:
p i ＝mp pi +(1-m)p si (2)
the stress ratio of the pile soil is as follows: n = p pi /p si According to the formulas (1) and (2), the corresponding stress p shared by the piles can be obtained pi Comprises the following steps:
corresponding stress p shared by foundation soil si Comprises the following steps:
therefore, if the calculation of the original soil gravity using the side slope fill is continued, the effect of the pile-soil stress ratio cannot be exhibited. In order to enable the calculation result to be more in line with the actual situation, the slope filling weight needs to be equivalent, the total weight of the filling above the piles and the foundation soil is enabled to be consistent with the actual load shared by the piles and the foundation soil, and therefore equivalent weight parameters required to be given to the second area on the first area can be calculated.
Keeping the height h of the slope fill i Equivalent conversion is carried out on the filling load without change to obtain equivalent severe gamma 'of the upper side slope filling area corresponding to the pile in the unit body i' pi Comprises the following steps:
substituting equation (3) into equation (5) yields:
equivalent gravity gamma 'of upper slope soil filling area corresponding to foundation soil in unit body i' si Comprises the following steps:
substituting equation (4) into equation (7) yields:
and respectively calculating the equivalent weight of the slope soil filling area above each strip block according to the method, and endowing the equivalent weight to the model.
And then, determining the range of other areas in the third area according to the height of the side slope and the pile length, giving original parameters, establishing a complete two-dimensional limit balance method analysis model, and automatically searching the most dangerous sliding surface function by using two-dimensional limit balance method software (such as rational rock and soil) so as to calculate the stability coefficient of the side slope.
Referring to fig. 10, for a composite foundation fill side slope with a height of h and a length of l, the range of the complete model can respectively extend 1 time of the height of the slope from the top of the slope and the bottom of the slope, and the thickness of the soil body of the foundation is taken 2 times of the length of the pile from the original ground. So far, the Auto CAD software can be adopted to establish a complete composite foundation filling slope model.
Referring to fig. 11, selecting a slope stability analysis module in the ideal geotechnical software, importing the CAD model of the composite foundation fill slope into the module, setting basic information, referring to fig. 12, selecting a simplified Bishop method recommended by the specification by adopting the specification of 'construction slope engineering technical specification', automatically searching a most dangerous slip crack surface by selecting an arc stability calculation target, and selecting the specification by using the arc stability analysis method; the parameters of each region of the composite foundation fill slope obtained in the above steps are set in software as shown in fig. 13. Pile severity in area one is gamma p A cohesion of c p An internal angle of friction of
The gravity of the foundation soil is gamma s A cohesion of c s An internal angle of friction of
The equivalent gravity of the upper slope soil filling area corresponding to the piles in the strip block in the second area is gamma' pi C cohesive force and internal friction angle
The equivalent gravity of an upper side slope soil filling area corresponding to the foundation soil in the strip is gamma' si C cohesive force and internal friction angle
In the third area, the original foundation soil parameters are taken from the foundation soil, and the gravity of the foundation soil is gamma s A cohesive force cs and an internal friction angle
Taking original side slope filling parameters for side slope filling, wherein the side slope filling has the weight of gamma, the cohesive force of c and internal frictionThe angle is
After the parameter setting is completed, the sliding safety coefficient of the composite foundation fill slope is calculated, as shown in fig. 14.
According to the method for realizing equal shear strength slope stability calculation in the physical and positive geotechnical software, provided by the embodiment of the invention, an analysis model in the physical and positive geotechnical software is divided into 3 regions with different properties according to the characteristics of the analysis model to be established; the method comprises the steps of converting a three-dimensional model of a circular pile composite foundation into a three-dimensional model of a rectangular pile composite foundation by eliminating shape difference between a pile body and foundation soil in the longitudinal direction to meet plane strain assumption, and analyzing a two-dimensional profile of the three-dimensional model to establish a composite foundation area model; regarding the filling side slope on the composite foundation as a load, considering the influence of pile-soil stress ratio, dividing the side slope filling on the upper part of the composite foundation into areas with different gravities for simulating the effect of pile-soil stress ratio, calculating the equivalent weight of the filling side slope area on the composite foundation for modeling, and establishing a filling side slope area model on the composite foundation; determining the range of other areas according to the height of the side slope and the pile length, giving original parameters, establishing a complete two-dimensional extreme balance method analysis model, and enabling software to automatically search the most dangerous sliding surface so as to calculate the sliding safety coefficient of the side slope. The method is based on the equal shear strength substitution principle and the side slope filling equivalent weight calculation principle considering the pile-soil stress ratio, and provides a more practical method for realizing the establishment of the equal shear strength side slope model and the stability calculation in the regular rock software.
It is to be understood that the above-described embodiments of the present invention are merely illustrative of or explaining the principles of the invention and are not to be construed as limiting the invention. Therefore, any modification, equivalent replacement, improvement and the like made without departing from the spirit and scope of the present invention should be included in the protection scope of the present invention. Further, it is intended that the appended claims cover all such variations and modifications as fall within the scope and boundaries of the appended claims or the equivalents of such scope and boundaries.
Claims (5)
1. A method for calculating the stability of a side slope with equal shear strength is characterized by comprising the following steps:
dividing a region, namely dividing the composite foundation fill side slope into a first region, a second region and a third region, wherein the first region is a piling region, the second region is a region formed above the piling region, and the third region is the rest region of the composite foundation fill side slope;
a model conversion step, wherein each pile body in the first region is divided into a plurality of repeated unit bodies with square cross sections, each unit body comprises one pile body and foundation soil, the pile body in each unit body is converted into a rectangular pile from a cylindrical pile, and the cross section area of the rectangular pile is equal to that of the cylindrical pile; a re-modeling step, namely dividing the slope filling of a second area into areas with different gravities, obtaining the equivalent gravities of the second area for modeling, and re-establishing a model of the second area above the first area;
and calculating a slope stability coefficient, namely acquiring the height of the slope in the second region and the length of the pile body to determine the range of the third region, establishing a finished two-dimensional limit balance method analysis model, and calculating to obtain the slope stability coefficient.
2. The equal shear strength slope stability calculation method of claim 1, characterized in that:
the step of transforming the model further comprises:
a data measurement step: acquiring the pile diameter d and the pile distance s of the pile body and the weight gamma of the pile body p C, cohesion force p Pile body internal friction angle phi p Obtaining the gravity gamma of the foundation soil s C, cohesion force s Internal friction angle phi of foundation soil s ；
In the step of converting the model, the width b of the converted rectangular section of the pile body 0 Comprises the following steps:
wherein s is the cross-sectional width of the unit body.
3. The equal shear strength slope stability calculation method of claim 1, characterized in that:
in the modeling step, the second area equivalent weight gamma 'corresponding to the rectangular piles in the unit body' pi Comprises the following steps:
wherein m is the replacement rate, n is the stress ratio of the pile soil, and gamma is the filling weight;
in the modeling step, the second area equivalent weight gamma 'corresponding to the foundation soil in the unit body' si Comprises the following steps:
wherein m is the replacement rate, n is the stress ratio of the pile soil, and gamma is the filling weight.
4. The equal shear strength slope stability calculation method of claim 3, characterized in that:
the pile-soil stress ratio calculation formula is as follows:
n＝p pi /p si
wherein p is pi For the stress shared by the piles, p si Is the stress shared by the foundation soil.
5. The equal shear strength slope stability calculation method of claim 4, characterized in that:
the stress p shared by the piles pi Is calculated as：
The stress p shared by the foundation soil si The calculation formula is as follows:
wherein h is i The filling height.
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