CN113836616B - Rock slope wedge body sliding stability analysis method based on coordinate system conversion method - Google Patents

Rock slope wedge body sliding stability analysis method based on coordinate system conversion method Download PDF

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CN113836616B
CN113836616B CN202110995218.5A CN202110995218A CN113836616B CN 113836616 B CN113836616 B CN 113836616B CN 202110995218 A CN202110995218 A CN 202110995218A CN 113836616 B CN113836616 B CN 113836616B
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slope
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CN113836616A (en
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安彩龙
王亮清
孙自豪
田建林
牛奕凯
王子宜
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China University of Geosciences
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    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/13—Architectural design, e.g. computer-aided architectural design [CAAD] related to design of buildings, bridges, landscapes, production plants or roads
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
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    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/02—Reliability analysis or reliability optimisation; Failure analysis, e.g. worst case scenario performance, failure mode and effects analysis [FMEA]
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
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Abstract

The invention provides a rock slope wedge body sliding stability analysis method based on a coordinate system conversion method, which is characterized in that a three-dimensional geological analysis model of a wedge body slope is established by taking various factors such as rock structure characteristic parameters, geometric characteristic parameters, anchor cable support parameters and the like of a sliding body and a sliding bed into consideration, a calculation formula of partial dimension parameters and spatial arrangement parameters of the model is deduced by a spatial geometric analysis method, the gravity G borne by the wedge body slope sliding body and the pretension force T under three-dimensional support of an anchor cable are effectively decomposed into the normal directions of two groups of sliding surfaces and the sliding direction of the sliding body by adopting a coordinate system conversion method, a tensor analysis method and the like, and the gliding force F borne by the wedge body slope before and after anchoring is further calculated by a limit balance methodLower partAnd a sliding resistance FResist againstThe method improves the solving formula of the stability coefficient before and after the traditional wedge-shaped slope is anchored, and effectively improves the precision of the stability analysis of the wedge-shaped slope.

Description

Rock slope wedge body sliding stability analysis method based on coordinate system conversion method
Technical Field
The invention relates to the technical field of geological disaster prevention and control, in particular to a rock slope wedge body sliding stability analysis method based on a coordinate system transformation method.
Background
Wedge-shaped landslides are one of the common rock slope failure types, the sliding surface of the landslides consists of two crossed weak surfaces, and the landslides belong to a relatively complex space subject in stability analysis. At present, wedge slope stability analysis methods are very many, including a bathochromic projection method, an engineering class ratio method, a block theory method, a fuzzy set theory method, an integral method, a vector analysis method, a limit balance method, a numerical analysis method and the like. The extreme balance method is used for judging the stability of the side slope by using the ratio (stability coefficient) of the anti-sliding force generated by the sliding body on the sliding surface, has higher accuracy compared with other analysis methods, and is widely applied and practiced in a large number of side slope projects for a long time.
According to previous research results, the most common model for wedge slope stability analysis is shown in fig. 1, and the stability coefficient solving formula is as follows:
Figure BDA0003233621750000011
wherein:
Figure BDA0003233621750000012
θ1and theta2Respectively are the included angles between N and the normal directions of the two sliding surfaces; s. the1And S2The areas of the two sliding surfaces are respectively;
Figure BDA0003233621750000013
according to the above formula, the following incompleteness exists in the current wedge slope stability coefficient solving formula: firstly, the space geometric analysis of the wedge-shaped body slope generalized model is not systematic, the included angle beta between the intersection line of two sliding surfaces and the horizontal plane and the area S of the top (delta ABC) of the sliding bodyΔABCAnd the contact area S between the two sliding surfaces and the slider bed1And S2The solution formula of (2) needs to be further indicated; ② in practical engineering application, the normal included angle theta between N and two sliding surfaces1And theta2The solution of (2) is very difficult, and when the sliding body gravity G is decomposed towards the normal direction of the two sliding surfaces, a certain error exists in the solution result, so that the solution result of the wedge-shaped body slope stability coefficient is inaccurate.
In addition, the two-dimensional reinforcing mode that the reinforcing direction is perpendicular to the slope direction is mainly adopted when anchor cable supporting is carried out on the existing rock slope, analysis is carried out based on the two-dimensional supporting mode when anchor slope stability analysis is carried out, and the result is directly applied to the wedge-shaped slope, so that the optimal anchoring performance of the anchor cable is difficult to exert, and the cost of slope supporting is increased. In order to solve the problem, currently, researchers have developed a study on a three-dimensional optimization mode when the reinforcing direction of the anchor cable is not limited, and the anchoring direction angle of the three-dimensional optimization mode includes not only an anchoring downward inclination angle in the traditional design, but also an anchoring horizontal angle. Therefore, when the stability of the anchored slope is analyzed, the anti-slip effect of the anchor cable under three-dimensional support needs to be further considered, and the traditional solving formula of the stability coefficient of the anchored slope is perfected.
Disclosure of Invention
In view of this, the embodiment of the invention provides a rock slope wedge sliding stability analysis method based on a coordinate system conversion method, aiming at the problems that the solving formula of the stability coefficient before and after the wedge slope is anchored is not perfect and the solving result has certain error in the prior art.
The embodiment of the invention provides a rock slope wedge body sliding stability analysis method based on a coordinate system conversion method, which comprises the following steps of:
l1 establishes a generalized wedge-shaped body side slope three-dimensional geological model and obtains the structural characteristic parameters of the side slope rock mass, the side slope rock mass comprises a slope surface, a first sliding surface and a second sliding surface which are opposite, and the normal direction of the first sliding surface
Figure BDA0003233621750000021
Normal to said second sliding surface
Figure BDA0003233621750000022
An intersection of the first sliding surface and the second sliding surface
Figure BDA0003233621750000023
Respectively serving as coordinate axes, and establishing a group of space conversion coordinate systems related to the original geodetic coordinate system by adopting a tensor analysis method;
l2, based on the transformation coordinate system and the original geodetic coordinate system established in the step L1, decomposing the acting force F borne by the sliding body in the wedge slope model by adopting a coordinate system transformation method and a tensor analysis method into the acting force F in the same sliding direction as the sliding direction of the sliding bodyz`And positive pressure F acting on both sliding surfacesx`And Fy`；
L3 respectively deduces two rock masses through space geometric analysis according to the structural characteristic parameters and the geometric characteristic parameters of the slope rock massesAn included angle beta between an intersection line BO of the sliding surface and a projection line of the sliding surface on a horizontal plane, an included angle psi between the projection line and a slope surface inclination, a length l of the wedge slope model calculation region, a width d of the wedge slope model calculation region, and a top area S of the sliding body0The contact area S between the first sliding surface and the sliding body and the contact area S between the second sliding surface and the sliding body1And S2The expression of (2);
l4 deducing an expression of the gravity G of the sliding body by combining the data in the step L3 and the weight gamma of the sliding body, and introducing the pretension T and the anchoring direction angle of a single anchor rope during anchor rope supporting;
l5 according to the decomposition method of the acting force F applied to the sliding body in the step L2, combining the expression of the sliding body gravity G deduced in the step L4 and the introduced pretension force T of a single anchor cable, the sliding body gravity G is decomposed into the sliding force G in the sliding direction of the sliding bodyz`Positive pressure G acting on both sliding surfacesx`、Gy`The pretension force T of a single anchor cable is decomposed into the anti-sliding force T with the sliding direction of the sliding body opposite to that of the sliding bodyz`And positive pressure T acting on both sliding surfacesx`、Ty`Calculating the gliding force F borne by the wedge-shaped slope before and after anchoringLower partAnd a sliding resistance FResist against；
L6 combines the sliding force F of the wedge slope under natural conditions estimated in the step L5 according to the limit balance methodLower partAnd a sliding resistance FResist againstDeducing a stability coefficient expression of the strain under a natural working condition;
l7 is based on the limit balance method, and combines the gliding force F of the wedge-shaped slope after anchoring calculated in the step L5Lower partAnd a sliding resistance FResist againstDeducing a stability coefficient expression of the anchor-added stability coefficient;
l8, compiling a corresponding wedge sliding slope stability analysis system by combining the theoretical formulas obtained in the steps L1-L7;
and L9, aiming at the concrete wedge body side slope case, analyzing the stability of the selected wedge body sliding side slope before and after anchoring by adopting the wedge body sliding side slope stability analysis system compiled in the step L8, and optimally designing the arrangement number of the anchor cables.
Further, the step L1 is to establish a space transformation coordinate system to
Figure BDA0003233621750000031
Is taken as the x and the axis,
Figure BDA0003233621750000032
is a Y-axis and a Z-axis,
Figure BDA0003233621750000041
is the z ' axis, and the unit vector of the x ' axis and the y ' axis is
Figure BDA0003233621750000042
Figure BDA0003233621750000043
Unit vector of z' axis
Figure BDA0003233621750000044
Is composed of
Figure BDA0003233621750000045
Wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003233621750000046
Figure BDA0003233621750000047
tendency of the first sliding surface, β1Is the inclination of the first sliding surface,
Figure BDA0003233621750000048
tendency of the second sliding surface, β2Is the angle of inclination of the second sliding surface,
Figure BDA0003233621750000049
further, the expression of the acting force F on the slider in the original geodetic coordinate system in step L2 is
Figure BDA00032336217500000410
The expression in the transformed coordinate system is
Figure BDA00032336217500000411
The acting force F after decomposition is the same as the sliding direction of the sliding bodyz`And a positive pressure F acting on the two sliding surfacesx`And Fy`The expression of (c) is: :
Figure BDA00032336217500000412
wherein:
Figure BDA00032336217500000413
alpha is a horizontal included angle between the acting force F and the inclination of the slope surface of the side slope, theta is a vertical included angle between the acting force F and the horizontal plane,
Figure BDA00032336217500000414
is a tendency of slope surface.
Further, the expression of each parameter in step L3 is:
the expression of β is: beta is arcsin | n33|；
The expression of ψ is:
Figure BDA0003233621750000051
wherein: when in use
Figure BDA0003233621750000052
When n is 0; when in use
Figure BDA0003233621750000053
When n is 1;
the expressions for l and d are:
Figure BDA0003233621750000054
wherein: h is the height of the wedge slope model calculation area,
Figure BDA0003233621750000055
δ1is the angle between the inclination of the first sliding surface and the inclination of the sloping surface, delta2Angle between the inclination of the second sliding surface and the inclination of the sloping surface, beta0The inclination angle of the slope surface of the side slope;
S0the expression of (c) is:
Figure BDA0003233621750000056
S1and S2Are respectively:
Figure BDA0003233621750000057
wherein:
Figure BDA0003233621750000061
Figure BDA0003233621750000062
further, the expression of the weight G of the slider in step L4 is:
Figure BDA0003233621750000063
wherein d is the width of the calculation area of the wedge slope model, h is the height of the calculation area of the wedge slope model, l is the length of the calculation area of the wedge slope model, gamma is the weight of the slider, and beta is0Is the inclination angle of the slope surface of the side slope.
Further, in step L5, the pretensioning force T of the single anchor cable acts on the positive pressure T on the two sliding surfacesx`、Ty`Anti-slip force T opposite to sliding direction of sliding bodyz`Are respectively:
Figure BDA0003233621750000064
wherein T is the pretension force of the introduced single anchor cable, and thetamIs a vertical included angle between the T action line and the horizontal plane,
Figure BDA0003233621750000066
inclination of the slope surface, αmThe horizontal included angle between the acting direction of the pretensioning force T of the single anchor cable and the slope inclination is formed;
positive pressure G of gravity G acting on two sliding surfacesx`、＝Gy`And the sliding force G in the sliding direction of the sliding bodyz`The expressions are:
Figure BDA0003233621750000065
further, the downward sliding force F generated by the gravity G in the step L5Lower partAnd a sliding resistance FResist againstAre respectively:
Figure BDA0003233621750000071
wherein phi isj1Is the internal friction angle of the first sliding surface, phij2Is the internal friction angle, S, of the second sliding surface1Is the area of the first sliding surface, Cj1Is the cohesion of the first sliding surface, S2Is the area of the second sliding surface, Cj2Is the cohesion of the second sliding surface.
Further, in the step L6, the stability coefficient expression of the wedge slope under the natural condition is as follows:
Figure BDA0003233621750000072
further, the step L5 is performed by a single anchor cable pretension force TResistance to sliding Fm. reactanceThe expression of (a) is:
Figure BDA0003233621750000073
further, in step L7, the stability coefficient expression of the wedge slope after anchoring is:
Figure BDA0003233621750000074
wherein: and m is the number of the anchor cables on the wedge-shaped slope.
The technical scheme provided by the embodiment of the invention has the following beneficial effects: taking a plurality of factors such as structural characteristic parameters, geometric characteristic parameters, anchor rope support parameters and the like of a sliding body and a sliding bed rock body as optimization control independent variables, taking stability coefficients of a wedge body side slope before and after anchoring as target control variables, establishing a three-dimensional geological analysis model of the wedge body side slope, adopting methods such as a coordinate system conversion method, a tensor analysis method, a limit balance method, a geometric analysis method and the like, effectively decomposing gravity G borne by the wedge body side slope sliding body and pretension force T under three-dimensional support of an anchor rope into normal directions of two groups of sliding surfaces and sliding directions of the sliding body, and further calculating gliding force F borne by the wedge body side slope before and after anchoring by the limit balance methodLower partAnd a sliding resistance FIs resistant toAnd the three-dimensional reinforcing mode of the anchor cable in the rock slope is further considered, the solving formula of the stability coefficient before and after the traditional wedge-shaped slope anchoring is completed, the precision of the stability analysis of the wedge-shaped slope is effectively improved, and the prediction result is more reliable. And partial size parameters and spatial arrangement parameter calculation formulas of the wedge slope model are deduced, so that a foundation is laid for setting the size of a model box and constructing a template system when a wedge slope model test is developed in subsequent researches.
Drawings
FIG. 1 is a conventional wedge slope stability analysis model;
FIG. 2 is a schematic flow chart of an embodiment of a method for analyzing sliding stability of a rock slope wedge based on a coordinate system transformation method;
FIG. 3 is a wedge slope model and a transformed coordinate system analysis model of the present invention;
FIG. 4 is a decomposition analysis model of the acting force applied to the wedge-shaped body slope slide body according to the present invention;
FIG. 5 is a wedge slope space geometric analysis model of the present invention;
fig. 6 is an analysis model of the wedge-shaped body side slope anchor cable support.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, embodiments of the present invention will be further described with reference to the accompanying drawings.
Referring to fig. 2, an embodiment of the present invention provides a method for analyzing sliding stability of a rock slope wedge based on a coordinate system transformation method, including the following steps:
s1, establishing a generalized wedge-shaped body side slope three-dimensional geological model and obtaining structural characteristic parameters of side slope rock mass, wherein the side slope rock mass comprises a slope surface AOC, a first sliding surface AOB and a second sliding surface BOC which are opposite, and the normal direction of the first sliding surface is
Figure BDA0003233621750000081
Normal to said second sliding surface
Figure BDA0003233621750000082
An intersection of the first sliding surface and the second sliding surface
Figure BDA0003233621750000083
And respectively taking the coordinate axes as a group of space conversion coordinate systems related to the original geodetic coordinate system by adopting a tensor analysis method.
Specifically, referring to FIG. 3, the inclination and inclination of the wedge slope AOC are
Figure BDA0003233621750000085
And beta0(ii) a The inclination and inclination of the first sliding surface AOB (sliding surface:) are respectively
Figure BDA0003233621750000086
And beta1The included angle between the inclination of the slope surface and the inclination of the slope surface is delta 1 (when the included angle is larger than the inclination of the slope surface, the included angle is positive), and the normal direction is
Figure BDA0003233621750000084
The inclination and inclination of the second sliding surface BOC (sliding surface:) are respectively
Figure BDA00032336217500000920
And beta2And the included angle delta between the inclination angle delta and the slope surface2Normal direction is
Figure BDA0003233621750000091
The intersection line between the two groups of sliding surfaces is OB, and the relationship between the two groups of sliding surfaces and the slope inclination satisfies the following conditions:
Figure BDA0003233621750000092
to be provided with
Figure BDA0003233621750000093
Is an x' axis and is a linear axis,
Figure BDA0003233621750000094
is the axis of the y' axis,
Figure BDA0003233621750000095
establishing a group of space conversion coordinate systems related to an original geodetic coordinate system xyz for a z' axis;
specifically, the unit vector of the x 'axis and the y' axis is
Figure BDA0003233621750000096
Wherein the content of the first and second substances,
Figure BDA0003233621750000097
Figure BDA0003233621750000098
tendency of the first sliding surface, β1Is the inclination of the first sliding surface,
Figure BDA00032336217500000919
tendency of the second sliding surface, β2Is the inclination of the second sliding surface;
and BO is the intersection between two sets of sliding surfaces, which must satisfy:
Figure BDA0003233621750000099
and is
Figure BDA00032336217500000910
Then
Figure BDA00032336217500000911
Can be expressed as:
Figure BDA00032336217500000912
Figure BDA00032336217500000913
order to
Figure BDA00032336217500000914
Unit vector of z' axis
Figure BDA00032336217500000915
Is composed of
Figure BDA00032336217500000916
S2, based on the transformation coordinate system and the original geodetic coordinate system established in the step S1, the acting force F (which can be any force acting on the sliding body) borne by the sliding body in the wedge slope model is decomposed by adopting a coordinate system transformation method and a tensor analysis method and is decomposed into the acting force F in the same sliding direction as the sliding bodyz`And a positive pressure F acting on the two sliding surfacesx`And Fy`。
Work on sliding bodyExerting force
Figure BDA00032336217500000917
When decomposed, acting force
Figure BDA00032336217500000918
The expression in the original geodetic coordinate system is:
Figure BDA0003233621750000101
acting force
Figure BDA0003233621750000102
The expression in the transformed coordinate system is:
Figure BDA0003233621750000103
by combining the two formulas, the following results can be obtained:
Figure BDA0003233621750000104
according to the Clarmer's rule, the equation coefficient F of the above-mentioned linear equation set can be obtainedx`、Fy`And Fz`Respectively as follows:
Figure BDA0003233621750000105
wherein:
Figure BDA0003233621750000106
alpha is a horizontal included angle between the acting force F and the inclination of the slope surface of the side slope, theta is a vertical included angle between the acting force F and the horizontal plane,
Figure BDA0003233621750000107
is a tendency of slope surface.
S3 according to the side slopeThe structural characteristic parameters and the geometric characteristic parameters of the rock mass are respectively deduced through space geometric analysis to obtain an included angle beta between an intersection line BO of two sliding surfaces and a projection line of the intersection line BO on a horizontal plane, an included angle psi between the projection line and slope inclination, the length l of a wedge slope model calculation region, the width d of the wedge slope model calculation region and the top area S of a sliding body0The contact area S between the first sliding surface and the sliding body and the contact area S between the second sliding surface and the sliding body1And S2Is described in (1).
The expression of the included angle β between the intersection line BO of the two sliding surfaces and the projection line on the horizontal plane is: beta is arcsin | n33|；
The expression for the angle ψ between the projection line and the slope inclination is:
Figure BDA0003233621750000111
wherein: when the temperature is higher than the set temperature
Figure BDA0003233621750000115
When n is 0; when in use
Figure BDA0003233621750000116
When n is 1.
Suppose usingijThe side lengths of the line segments between two characters in fig. 5 are respectively shown, and through the spatial geometric analysis, the length of the line segment between CFs is:
Figure BDA0003233621750000112
the expressions of the length l of the wedge slope model calculation area and the width d of the wedge slope model calculation area are respectively:
Figure BDA0003233621750000113
wherein: h is the height of the wedge slope model calculation area,
Figure BDA0003233621750000114
δ1is the angle between the inclination of the first sliding surface and the inclination of the sloping surface, delta2Angle between the inclination of the second sliding surface and the inclination of the sloping surface, beta0Is the inclination angle of the slope surface of the side slope.
Area S of slider tip (Δ ABC)0The expression of (a) is:
Figure BDA0003233621750000121
through the spatial geometry analysis, it can be obtained:
Figure BDA0003233621750000122
Figure BDA0003233621750000123
the edge lengths of the three sides of the first sliding surface (Δ OAB) and the second sliding surface (Δ OBC) are:
Figure BDA0003233621750000124
according to the Helen formula, the contact area S of the first sliding surface and the sliding body1The contact area S between the second sliding surface and the sliding body2Are respectively:
Figure BDA0003233621750000125
wherein:
Figure BDA0003233621750000126
the deduced space geometric analysis formulas can lay a foundation for setting the size of a model box and constructing a template system in the test process when a typical wedge slope model test is developed in subsequent researches.
S4 combines the data in step S3 and the weight gamma of the sliding body, deduces the expression of the gravity G of the sliding body, and introduces the pretension force T and the anchoring direction angle (horizontal angle alpha) of a single anchor rope during anchor rope supportmVertical angle θm)。
The expression of the weight G of the slider is:
Figure BDA0003233621750000131
wherein d is the width of the calculation area of the wedge slope model, h is the height of the calculation area of the wedge slope model, l is the length of the calculation area of the wedge slope model, gamma is the weight of the slider, and beta is0Is the inclination angle of the slope surface of the side slope.
S5 according to the decomposition method of the acting force F applied to the sliding body in the step S2, combining the expression of the sliding body gravity G deduced in the step S4 and the introduced pretension force T of a single anchor cable, the sliding body gravity G is decomposed into the sliding force G in the sliding direction of the sliding bodyz`And a positive pressure G acting on the two sliding surfacesx`、Gy`The pretension force T of a single anchor cable is decomposed into the anti-sliding force T with the opposite sliding direction of the sliding bodyz`And a positive pressure T acting on the two sliding surfacesx`、Ty`Calculating the gliding force F borne by the wedge-shaped slope before and after anchoringLower partAnd a sliding resistance FResist against。
When the gravity G of the sliding body and the pretension force T of a single anchor cable are decomposed, the horizontal included angle alpha between the action direction of the gravity G of the sliding body and the inclination of the slope surface is 0, the vertical included angle theta between the action force F and the horizontal plane is 90 degrees, and then the positive pressure (G) is generated on the two sliding surfacesx`、Gy`) And a downward sliding force (G) in the sliding direction of the sliding bodyz`) Respectively as follows:
Figure BDA0003233621750000132
between the acting direction of the pretensioning force T of the single anchor cable and the slope inclinationHas a horizontal included angle of alphamThe vertical angle between the force F and the horizontal plane is thetamThe pretension force T of a single anchor cable acts on the positive pressure T on the two sliding surfacesx`、Ty`Sliding resistance T opposite to sliding direction of sliding bodyz`Are respectively:
Figure BDA0003233621750000133
wherein T is the pretension force of the introduced single anchor cable, and thetamIs a vertical included angle between the T action line and the horizontal plane,
Figure BDA0003233621750000134
inclination of the slope surface, αmThe horizontal included angle between the acting direction of the pretensioning force T of the single anchor cable and the slope inclination is formed.
Positive pressure G of gravity G of sliding body acting on two sliding surfacesx`、＝Gy`And the sliding force G in the sliding direction of the sliding bodyz`The expressions are:
Figure BDA0003233621750000141
down-sliding force F generated by gravity GLower partAnd a sliding resistance FIs resistant toAre respectively:
Figure BDA0003233621750000142
wherein phi isj1Is the internal friction angle of the first sliding surface, phij2Is the internal friction angle, S, of the second sliding surface1Is the area of the first sliding surface, Cj1Is the cohesion of the first sliding surface, S2Is the area of the second sliding surface, Cj2Is the cohesion of the second sliding surface.
Anti-sliding force F generated by single anchor cable pretension force Tm. reactanceThe expression of (a) is:
Figure BDA0003233621750000143
s6 according to the limit balance method, combining the sliding force F of the wedge slope under the natural condition (before anchoring) estimated in the step S5Lower partAnd a sliding resistance FResist againstAnd deducing the stability coefficient expression of the steel wire rope under the natural working condition (before anchoring).
The stability coefficient expression of the wedge-shaped body slope under the natural working condition (before anchor addition) is as follows:
Figure BDA0003233621750000144
s7 according to the limit balance method, combining the gliding force F of the wedge-shaped slope after anchoring calculated in the step S5Lower partAnd a sliding resistance FResist againstAnd deriving a stability coefficient expression of the stability coefficient after anchoring.
The stability coefficient expression of the wedge-shaped slope after anchoring is as follows:
Figure BDA0003233621750000151
wherein: m is the number of the anchor cables supported on the wedge-shaped slope.
S8, compiling a corresponding wedge sliding slope stability analysis system by combining the theoretical formulas obtained in the steps S1-S7;
s9, aiming at the concrete wedge body side slope case, the stability of the selected wedge body sliding side slope before and after anchoring is analyzed by adopting the wedge body sliding side slope stability analysis system compiled in the step S8, and the arrangement number of the anchor cables is optimally designed.
Selecting a local side slope near a dam site left bank adit (PDZ05) in a hydropower station as a specific embodiment:
l1, establishing a generalized wedge-shaped body side slope three-dimensional geological model, wherein the inclination/inclination angle of the slope surface of the side slope is 205 degrees/48 degrees, and when the wedge body slides, the inclination/inclination angle of the sliding surface (the first sliding surface) is 158 degrees/53 degrees respectively; the inclination/inclination angle of the sliding surface (second sliding surface) was 228 °/28 °, respectively. Then the unit vectors of the x ', y ', and z ' axes in the transformed coordinate system constructed with reference to fig. 3 are:
Figure BDA0003233621750000152
l2, please refer to fig. 4, assuming that the slide of the wedge slope model receives the acting force F, the horizontal angle between the acting line of the acting force F and the slope inclination is α (positive when the clockwise rotation is larger than the slope inclination), and the vertical angle between the acting line of the acting force F and the horizontal plane is θ (positive when the acting direction of the force is declined), based on the transformed coordinate system and the original terrestrial coordinate system established in step L1, the force F received by the slide is decomposed by the coordinate system transformation method and the tensor analysis method into the force F having the same acting line with the sliding direction of the slidez`And positive pressure F acting on both sliding surfacesx`And Fy`Respectively is as follows:
Figure BDA0003233621750000153
l3, please refer to fig. 5, suppose the height of the wedge slope calculation region is 50 m; the weight of the slide was 26.3kN/m3(ii) a The shape of the slope and the two sets of sliding surfaces is the same as that in step L1; the friction angle of the sliding surface I is 18 degrees, and the cohesive force is 30 kPa; the friction angle of the sliding surface II is 23 degrees, the cohesive force is 40kPa, the calculated length l of the wedge-shaped slope is 88.85m, and the calculated width l is 144.14 m; the included angle between the intersection line of the two sliding surfaces and the projection line on the horizontal plane is beta, and the included angle between the projection line and the slope inclination is psi, which are respectively: 27.95 ° and 19.43 °; the area of the top of the slider (Delta ABC) is S0Is 3159.18m2(ii) a Sliding surface (I) and contact area (S) between sliding surface (II) and sliding body1And S2Respectively as follows: 1979.75m2And 5642.35m2. The obtained parameters can also be used for setting the size of a model box and a template system in the test process when a typical wedge slope model test is carried out in subsequent researchesAnd a foundation is laid for the construction of the system.
L4, combining area S of slider top (Δ ABC) obtained in step L30Calculating a value, calculating the height h of the area by the model and the gravity gamma of the slider, and calculating the gravity G of the slider as follows:
Figure BDA0003233621750000161
referring to fig. 6, when the anchor cable is introduced for supporting, the pretensioning force T of a single anchor cable is 500 kN; horizontal angle alpha in anchoring direction anglemIs 9.70 degrees and has a vertical angle thetamIs 18.75 degrees.
L5, according to the decomposition method of the acting force F applied to the sliding body in the step L2, when the gravity G of the sliding body is decomposed, the horizontal included angle alpha between the acting direction and the slope inclination is 0, the vertical included angle theta between the acting line and the horizontal plane is 90 degrees, and then the gravity G of the sliding body is in the positive pressure (G) on the two sliding surfacesx`、Gy`) And a downward sliding force (G) in the sliding direction of the sliding bodyz`) Respectively as follows:
Figure BDA0003233621750000162
downward sliding force F generated by sliding body gravity GLower partAnd a sliding resistance FResist againstComprises the following steps:
Figure BDA0003233621750000163
when the pretensioning force T of the single anchor cable is decomposed, the horizontal included angle alpha between the acting direction and the slope inclination is 9.70 degrees, the vertical included angle theta between the acting line and the horizontal plane is 18.75 degrees, and then the pretensioning force T of the single anchor cable is in positive pressure (T) on the two sliding surfacesx`、Ty`) Sliding resistance (T) opposite to sliding direction of sliding bodyz`) Respectively as follows:
Figure BDA0003233621750000171
anti-sliding force F generated by single anchor cable pretension force Tm antibodyComprises the following steps:
Fm. reactance＝Tx`tanφj1+Ty`tanφj2+Tz`＝494.35kN。
L6, according to the limit balance method, combining the downward sliding force F generated by the weight G of the sliding body of the wedge-shaped slope under the natural working condition calculated in the step L5Lower partAnd a sliding resistance FResist againstThe stability coefficient under the natural working condition is as follows:
Figure BDA0003233621750000172
l7, according to a limit balance method, combining the downward sliding force and the anti-sliding force borne by the wedge-shaped body side slope after the anchor is added, which are calculated in the step L5, assuming that 10 anchor cables are supported on the side slope in total, the stability coefficient after the anchor is added is as follows:
Figure BDA0003233621750000173
l8, compiling a corresponding wedge sliding slope stability analysis system by using Microsoft Excel, and realizing the operation of the steps L1-L7;
l9, aiming at the landslide case, the stability coefficient of the wedge-shaped slope under the natural working condition in the step L6 is 1.24202 which is smaller than the standard (1.25-1.30) of the safety coefficient of the anti-skid stability specified by the specification, so that the treatment is needed; in the step L7, it is assumed that 10 anchor cables are supported on the slope, and the stability coefficient after anchoring is 1.24963, which is still less than the standard of the safety coefficient of anti-skid stability specified by the specification, so that the number of the anchor cables supported under the supporting scheme is insufficient, and further optimization is needed; if the final stability coefficient required by the wedge-shaped body side slope reaches more than 1.28, the number m of the support of the anchor cables required in the step L7 can be deduced reversely, the minimum number of the support is 50, and the stability coefficient after the anchor is added to the wedge-shaped body side slope is about 1.28010 (more than 1.28), so that the design requirement of side slope support is met.
The present invention providesThe technical scheme includes that multiple factors such as structural characteristic parameters, geometric characteristic parameters and anchor cable support parameters of a sliding body and a sliding bed rock body are used as optimization control independent variables, stability coefficients of a wedge body side slope before and after anchoring are used as target control variables, a three-dimensional geological analysis model of the wedge body side slope is built, the gravity G borne by the wedge body side slope sliding body and the pre-tensioning force T under three-dimensional support of an anchor cable are effectively decomposed to the normal directions of two sliding surfaces and the sliding direction of the sliding body by adopting methods such as a coordinate system conversion method, a tensor analysis method, a limit balance method and a geometric analysis method, and the sliding force F borne by the wedge body side slope before and after anchoring is calculated through the limit balance methodLower partAnd a sliding resistance FResist againstAnd the three-dimensional reinforcing mode of the anchor cable in the rock slope is further considered, the solving formula of the stability coefficient before and after the traditional wedge-shaped slope anchoring is completed, the precision of the stability analysis of the wedge-shaped slope is effectively improved, and the prediction result is more reliable. And partial size parameters and spatial arrangement parameter calculation formulas of the wedge slope model are deduced, so that a foundation is laid for setting the size of a model box and constructing a template system when a wedge slope model test is developed in subsequent researches.
In this document, the terms front, back, upper, lower and the like in the drawings are used for the sake of clarity and convenience only for the components are located in the drawings and the positions of the components relative to each other. It is to be understood that the use of the directional terms should not be taken to limit the scope of the claims.
The features of the embodiments and embodiments described herein above may be combined with each other without conflict.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.

Claims (1)

1. A rock slope wedge body sliding stability analysis method based on a coordinate system conversion method is characterized by comprising the following steps:
l1 establishmentGeneralizing a wedge-shaped body side slope three-dimensional geological model and acquiring structural characteristic parameters of a side slope rock mass, wherein the side slope rock mass comprises a slope surface, a first relative sliding surface and a second sliding surface, and the normal direction of the first sliding surface
Figure FDA0003616277090000011
Normal to said second sliding surface
Figure FDA0003616277090000012
An intersection of the first sliding surface and the second sliding surface
Figure FDA0003616277090000013
Respectively serving as coordinate axes, and establishing a group of space conversion coordinate systems related to the original geodetic coordinate system by adopting a tensor analysis method;
l2 based on the transformation coordinate system and the original geodetic coordinate system established in the step L1, decomposing the acting force F borne by the sliding body in the wedge slope model by adopting a coordinate system transformation method and a tensor analysis method into the acting force F in the same sliding direction as the sliding direction of the sliding bodyz`And positive pressure F acting on both sliding surfacesx`And Fy`；
L3 respectively deducing an included angle beta between an intersection line BO of two sliding surfaces and a projection line of the intersection line BO on a horizontal plane, an included angle psi between the projection line and slope surface inclination, the length L of a wedge body slope model calculation area, the width d of the wedge body slope model calculation area, and the top area S of a sliding body through space geometric analysis according to the structural characteristic parameters and the geometric characteristic parameters of the slope rock mass0The contact area S between the first sliding surface and the sliding body and the contact area S between the second sliding surface and the sliding body1And S2The expression of (2);
l4 deducing an expression of the gravity G of the sliding body by combining the data in the step L3 and the weight gamma of the sliding body, and introducing the pretension T and the anchoring direction angle of a single anchor rope during anchor rope supporting;
l5 according to the decomposition method of the acting force F applied to the sliding body in the step L2, combining the expression of the gravity G of the sliding body deduced in the step L4 and the introduced pretension force T of the single anchor cable, the sliding body is subjected toThe gravity G is decomposed into a gliding force G in the gliding direction of the sliderz`And positive pressure G acting on both sliding surfacesx`、Gy`The pretension force T of a single anchor cable is decomposed into the anti-sliding force T with the opposite sliding direction of the sliding bodyz`And a positive pressure T acting on the two sliding surfacesx`、Ty`Calculating the gliding force F borne by the wedge-shaped slope before and after anchoringLower partAnd a sliding resistance FResist against；
L6 is based on the limit balance method, and combines the sliding force F of the wedge slope calculated in the step L5 under the natural working conditionLower partAnd a sliding resistance FResist againstDeducing a stability coefficient expression of the strain under a natural working condition;
l7 is based on the limit balance method, and combines the gliding force F of the wedge-shaped slope after anchoring calculated in the step L5Lower partAnd a sliding resistance FIs resistant toDeducing a stability coefficient expression of the anchor-added stability coefficient;
l8, compiling a corresponding wedge sliding slope stability analysis system by combining the theoretical formulas obtained in the steps L1-L7;
l9, aiming at a concrete wedge body side slope case, analyzing the stability of the selected wedge body sliding side slope before and after anchoring by adopting the wedge body sliding side slope stability analysis system compiled in the step L8, and optimally designing the arrangement number of anchor cables;
in the space transformation coordinate system established by the step L1 to
Figure FDA0003616277090000021
Is an x' axis and is a linear axis,
Figure FDA0003616277090000022
is the axis of the y' axis,
Figure FDA0003616277090000023
is the z ' axis, and the unit vector of the x ' axis and the y ' axis is
Figure FDA0003616277090000024
Figure FDA0003616277090000025
Unit vector of z' axis
Figure FDA0003616277090000026
Is composed of
Figure FDA0003616277090000027
Wherein the content of the first and second substances,
Figure FDA0003616277090000028
Figure FDA0003616277090000029
tendency of the first sliding surface, β1Is the inclination of the first sliding surface,
Figure FDA00036162770900000210
tendency of the second sliding surface, β2Is the angle of inclination of the second sliding surface,
Figure FDA00036162770900000211
the expression of the acting force F on the sliding body in the original geodetic coordinate system in the step L2 is
Figure FDA0003616277090000031
The expression in the transformed coordinate system is
Figure FDA0003616277090000032
The acting force F after decomposition is the same as the sliding direction of the sliding bodyz`And a positive pressure F acting on the two sliding surfacesx`And Fy`The expression of (a) is:
Figure FDA0003616277090000033
wherein:
Figure FDA0003616277090000034
alpha is a horizontal included angle between the acting force F and the inclination of the slope surface of the side slope, theta is a vertical included angle between the acting force F and the horizontal plane,
Figure FDA0003616277090000035
the inclination of the slope surface of the side slope;
the expression of each parameter in step L3 is:
the expression of β is: beta is arcsin | n33|；
The expression of ψ is:
Figure FDA0003616277090000036
wherein: when in use
Figure FDA0003616277090000037
When n is 0; when in use
Figure FDA0003616277090000038
When n is 1;
the expressions of l and d are respectively:
Figure FDA0003616277090000041
wherein: h is the height of the wedge slope model calculation area,
Figure FDA0003616277090000042
δ1is the angle between the inclination of the first sliding surface and the inclination of the sloping surface, delta2Is the angle between the inclination of the second sliding surface and the inclination of the sloping surface, beta0The inclination angle of the slope surface of the side slope;
S0the expression of (a) is:
Figure FDA0003616277090000043
S1and S2Are respectively:
Figure FDA0003616277090000044
wherein:
Figure FDA0003616277090000045
Figure FDA0003616277090000046
the expression of the weight G of the slider in step L4 is:
Figure FDA0003616277090000047
wherein d is the width of the wedge slope model calculation area, h is the height of the wedge slope model calculation area, l is the length of the wedge slope model calculation area, gamma is the weight of the sliding mass, and beta is0The inclination angle of the slope surface of the side slope;
in the step L5, the pretension force T of a single anchor cable acts on the positive pressure T on the two sliding surfacesx`、Ty`Sliding resistance T opposite to sliding direction of sliding bodyz`Are respectively:
Figure FDA0003616277090000051
wherein T is the pretension force of the introduced single anchor cable, and thetamIs a vertical included angle between the T action line and the horizontal plane,
Figure FDA0003616277090000052
is a side slopeTendency of face, αmThe horizontal included angle between the acting direction of the pretensioning force T of the single anchor cable and the slope inclination is formed;
positive pressure G of gravity G of sliding body acting on two sliding surfacesx`、Gy`And the sliding force G in the sliding direction of the sliding bodyz`Are respectively:
Figure FDA0003616277090000053
the gliding force F generated by the gravity G in the step L5Lower partAnd a sliding resistance FResist againstAre respectively:
Figure FDA0003616277090000054
wherein phij1Is the internal friction angle of the first sliding surface, phij2Is the internal friction angle, S, of the second sliding surface1Is the area of the first sliding surface, Cj1Is the cohesion of the first sliding surface, S2Is the area of the second sliding surface, Cj2Is the cohesion of the second sliding surface;
in the step L6, the stability coefficient expression of the wedge slope under natural conditions is:
Figure FDA0003616277090000055
the anti-skid force F generated by the single anchor cable pre-tensioning force T in the step L5m antibodyThe expression of (a) is:
Figure FDA0003616277090000056
in the step L7, the stability coefficient expression of the wedge-shaped slope after anchoring is:
Figure FDA0003616277090000061
wherein: and m is the number of the anchor cables on the wedge-shaped slope.
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Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103266617A (en) * 2013-05-30 2013-08-28 昆明理工大学 Method for computing optimal anchoring angle of rock slope wedge
CN106844927A (en) * 2017-01-13 2017-06-13 青岛理工大学 A kind of double glide face rock mass slope anchors the assay method of Optimal Parameters
CN107330224A (en) * 2017-07-24 2017-11-07 中国地质大学（武汉） A kind of Analysis of Slope Stability slices method of the non-hypothesis in slitting intermolecular forces inclination angle
CN108563608A (en) * 2018-03-16 2018-09-21 重庆交通大学 Sphenoid method for analyzing stability based on equatorial horizon projection and deformation analysis

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US6607332B2 (en) * 2001-08-30 2003-08-19 Soo-Yong Kang Method of reinforcing slope reverse analysis technique

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103266617A (en) * 2013-05-30 2013-08-28 昆明理工大学 Method for computing optimal anchoring angle of rock slope wedge
CN106844927A (en) * 2017-01-13 2017-06-13 青岛理工大学 A kind of double glide face rock mass slope anchors the assay method of Optimal Parameters
CN107330224A (en) * 2017-07-24 2017-11-07 中国地质大学（武汉） A kind of Analysis of Slope Stability slices method of the non-hypothesis in slitting intermolecular forces inclination angle
CN108563608A (en) * 2018-03-16 2018-09-21 重庆交通大学 Sphenoid method for analyzing stability based on equatorial horizon projection and deformation analysis

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