CN110457794A - A kind of reservoir area three-dimensional stability of slope method under the conditions of water-level fluctuation - Google Patents
A kind of reservoir area three-dimensional stability of slope method under the conditions of water-level fluctuation Download PDFInfo
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Abstract
The invention discloses a kind of reservoir area three-dimensional stability of slope methods under the conditions of water-level fluctuation, comprising the following steps: the selected specific slip mass to be analyzed of S1. determines its slip-crack surface, slip mass is separated into a column；S2. the basic assumption of stability analysis is provided；S3. it is write the functional relation of basic assumption in step S2 as incremental form, and introduces correction factor c, assign each initial parameter values；S4. according to the equilibrium equation of three power, the equilibrium equation and boundary condition of three torque, the correction factor and parameter of safety coefficient and introducing are solved；Whether the correction factor and parameter of the safety coefficient and introducing that S5. solve in comparison step S4 meet the requirements, and are such as unsatisfactory for, then with solution by iterative method to meeting the requirements.The present invention effectively increases the computational efficiency of safety coefficient and the reliability of analysis.
Description
Technical field
The present invention relates to geological disaster Control Technology fields, three-dimensional more particularly to the reservoir area under the conditions of a kind of water-level fluctuation
Method for Slope Stability Analysis.
Background technique
Area landslide refers to the Rock And Soil that hydraulics variation is sensitive on slope, is easy under the effect of extraneous hydrodynamic factor
Cause and integrally or hierarchically slide.Reservoir area landform is precipitous, geological environment is fragile, is unloaded by long-term geological structure and weathering
Lotus effect etc. leads to mountain area superficial part rock crushing and joints development.Simultaneously as frequent proluvial effect, rain product are made in history
With, colluviation and ancient slide movement, loosely-packed layer abundant is generally covered in slope surface.Therefore, the safety on reservoir area slope
Stability is relatively poor, easily lures under the driving of the hydrodynamic factors such as heavy rainfall, fluctuation of water table, rainwash and groundwater activities
The generation on the catastrophic landslide of hair, constitutes great threat to the safety of life and property of the people.Especially for Southwest China
Reservoir area, with the iterative method of Hydroelectric Cascade Development of River Basin, the landslide induced disaster to take place frequently seriously affects southwestern water power and opens
Hair and the engineering safety in operational process and reservoir area safety.Research slope stability in reservoir region has become Chinese Economy Development and west
One of the vital task of southern hydroelectric development.
Existing patent document is dedicated to improving three-dimensional stability of slope from criterion of strength, Strength Reduction Method etc.
Method, or extend three-dimensional stability of slope method to operating conditions such as earthquake, rainfall and explosions.However, in engineering practice
The soil encountered is usually unsaturated, but Method for Slope Stability Analysis is usually based on saturation shearing.Especially for
Side reservoir slope, since the operation of engineering needs water level to dispatch, the saturation state of soil changes frequent occurrence, while also along with soil
The variation of earth suction.Soil suction is factor very important in reservoir stability stability analysis.Therefore, it introduces using based on three
The stability that waterpower response under the conditions of the analysis means evaluation water-level fluctuation of dimension limit equilibrium method influences reservoir stability still has
To be developed and research.
Summary of the invention
It is an object of the invention to overcome the deficiencies of the prior art and provide the reservoir area three-dimensional sides under the conditions of a kind of water-level fluctuation
Analysis of Stability of Front Slope method.
The purpose of the present invention is achieved through the following technical solutions: the reservoir area three-dimensional side under the conditions of a kind of water-level fluctuation
Analysis of Stability of Front Slope method, comprising the following steps:
S1. specific slip mass to be analyzed is selected, its slip-crack surface is determined, slip mass is separated into a column；
S2. the basic assumption of stability analysis is carried out；
S3. it is write the functional relation of basic assumption in step S2 as incremental form, and introduces correction factor c, assign each ginseng
Number initial value；
S4. according to the equilibrium equation of three power, the equilibrium equation and boundary condition of three torque, solve safety coefficient and
The correction factor and parameter of introducing；
Whether the correction factor and parameter of the safety coefficient and introducing that S5. solve in comparison step S4 meet the requirements, such as
It is unsatisfactory for, then with solution by iterative method to meeting the requirements.
In the step S1, row interface is parallel to xoz plane, and column interface is parallel to yoz plane, is indicated using subscript i and j
This column is ith row and jth column in the position of entire gliding mass,WithTo act on a load in capital face, make
It is the geometric center of top surface with point
NI, jFor bottom surface normal force, ruFor pore pressure coefficient；WI, jFor column gravity；WithRespectively bottom sliding surface shearing is flat
Row is in the component of xoz and yoz plane；SI, jForWithResultant force；WithRespectively colonnade interface and row interface
Normal force；WithVertical shear and horizontal shear on respectively 4 sides；WithRespectively
For the angle of bottom sliding surface and x and y-axis；Width of the column in the direction x and y is respectively Δ x and Δ y.
Basic assumption in the step S2 includes:
The first, the action direction of column bottom sliding surface normal force is determined by the plane normal vector of its fitting, is denoted asPosition is the geometric center of bottom sliding surfaceGravity direction is also by sliding surface geometry
The heart；
The second, shearing meets following relationship with normal force between hypothesis item:
Hx=η1λ1(x, y) Ex (1)
Hy=η2λ2(x, y) Ey (2)
Ty=η3λ3(x, y) Ex (3)
Tx=η4λ4(x, y) Ey (4)
In formula: λ1(x, y), λ2(x, y), λ3(x, y) and λ4(x, y) is the continuous function assumed in advance, claims lateral shearing
Distribution function；η1, η2, η3And η4It is constant undetermined, the referred to as lateral coefficient of shear；
Known to the borderline thrust of third, gliding mass or so and front and back and shearing；
It is 4th, identical with the safety coefficient of each article of column in the x-direction in a line, it may be assumed that
The safety coefficient of each column in the y-direction is identical in same row, it may be assumed that
The step S3 includes:
It is write functional relation (1)~(4) in step S2 as incremental form, and introduces correction factor c, at the beginning of assigning each parameter
Value, obtains:
Wherein:
In formula:WithRespectively λm(x, y) is in the native column of ith row and jth column
Value corresponding to the side of left, right, front and rear,For λm(x, y) is in the corresponding value in this column bottom surface midpoint； To make inter-slice force meet the constant of reasonability restrictive condition introducing, 0 is taken as when calculating for the first time；0 is also taken in first calculate.
The step S4 includes following sub-step:
Give each column bottom surface skid resistance calculation formula:
In formula:For bottom surface skid resistance；NI, jFor bottom surface normal force；cI, j, AI, jAnd φI, jRespectively article column bottom (i, j)
Cohesion, area and the angle of friction of sliding surface；Formula (10) is to predict Rock And Soil by the Mohr Coulomb's theory of effective stress state
Shearing strength, form of calculation is only applicable to the soil body of saturation state.By introducing unsaturated soils theory, it is extended to both
It is applicable in saturated soil, and is applicable in the form of calculation of unsaturated soil；
Provide the semiempirical model of prediction unsaturation soil classifiction:
Formula (11) is one of Vanapalli proposition for predicting the semiempirical model of unsaturation soil classifiction,
Assuming that the air of solid particle skeleton is communicated with the atmosphere in side slope, i.e. ua=0, formula (11) is expanded into three-dimensional coordinate, and write
At the form of formula (10), following formula is obtained:
Wherein, s is substrate suction, it is believed that it is equal to negative pore water pressure, i.e. s=-uw；SrFor saturation degree；Substrate is inhaled
Power s and saturation degree SrAs hydraulic characteristic data；
S403. 2 safety coefficients of each column in the direction x and the direction y are
Wherein, the safety coefficient of each column is
Entirely the safety coefficient of slip mass is
The equilibrium equation of single column is
Formula (10) are substituted into formula (13), then substitute into formula (15)~(17)；Formula (5)~(8) are also substituted into formula (15)~(17),
Then, formula (15)~(17) are write as:
Using formula (15a), (16a) is obtainedWithFormula (17a) is substituted into, bottom surface normal force is obtained are as follows:
Wherein,
Formula (18) is entered formula (10) to obtain:
Formula (13) are substituted into formula (15)~(17)；Formula (5)~(8) are also substituted into formula (15)~(17), are obtained
N is obtained using formula (17b)I, j+ruWI, jAnd substituted into formula (15b), (16b)；Solution formula (15b), (16b)
Wherein,
The borderline horizontal thrust of slopes is it is known that have
It substitutes into boundary condition formula (22) respectively according to hypothesis (4) and by formula (20) and (21) and (23) obtains
Wherein,
The borderline horizontal and vertical shearing of slopes is it is known that have
In formula:Vertical shear on respectively the i-th row right side, left margin；WithRespectively jth column are upper and lower
Borderline vertical shear；Vertical shear on respectively the i-th row right side, left margin；WithRespectively jth arranges
Upper and lower borderline horizontal shear；
(5)~(8) are substituted into formula (26)~(29) to obtain
Actually only λ to be givenI, jMeet boundary condition, takes ξI, jWhen=0, formula (30)~(33) are to meet automatically
's；Moment equilibrium condition of the entire gliding mass around 3 axis
Wherein,
Write formula (34)~(36) as following form in convolution (15)~(17):
ax1η1+ax2η2+ax3η3=ax (37)
ay1η1+ay2η2+ay4η4=ay (38)
az3η3+az4η4=az (39)
Wherein,
Formula (35)~(37) contain 4 unknown quantitys, but only 3 equations, according to the property of slip mass, give one reasonably
η4, to acquire other 3 unknown quantitys, obtain:
η3=(az-az4η4)/az3 (39a)
So far, all unknown quantitys must solve, whenAnd η1, η2, η3After acquiring according to the above method,NI, j
WithAccording to formula (11), (16), (17) obtain, using the geometric properties of sliding surface, acquire
The safety coefficient that formula (40) substitution formula (14a) is acquired to each column is solved the safety system of entire gliding mass by formula (14b)
Number.
The step S5 includes:
Whether the correction factor and parameter of the safety coefficient and introducing that solve in comparison step S4 meet the requirementsWith
Respectively less than 0.0001, be such as unsatisfactory for, then with solution by iterative method to meeting the requirements:
It is calculated newly according to hypothesisIn result generation, is gone back to formula (18) and (19) to be iterated, it is desirable that meet:
According to it is assumed that when meeting above-mentioned condition,Also a numerical value is converged to automatically；
New inter-slice force mobilization factor η is calculated according to formula (37)~(39)m(m=1~3), by result generation return formula (18) and
(19) it is iterated, it is desirable that Δ ηm(m=1~3) are less than 0.000 1；
Safety coefficient is solved respectively by formula (14a) and (14b)；
The reasonability restrictive condition assumed according to inter-slice force:
Judge whether inter-slice force meets the requirements, if met the requirements, calculates success；For being unsatisfactory for the item of this requirement
Column gives constant ξI, jMeet above formula equal sign, while the additional out-of-balance force of introducing being pressed to a column for same a line or same row
The proportional distribution of pillar height degree, makes boundary condition formula (30)~(33) also be met, and recalculate safety coefficient.
The beneficial effects of the present invention are: slip mass has been carried out discretization by the present invention, and consider multiple dynamic balances, torque
Balance and boundary condition, two-dimensional Morgenstern-Price method is expanded to three-dimensional, improves the calculating effect of safety coefficient
The reliability of rate and analysis；In addition, all calculating process can sequencing, convenient for operation and programming, base is realized by computer
In the three-dimensional stability of slope that Morgenstern-Price method assumes, safety coefficient is solved, artificial calculating is greatly reduced
Amount, improves the computational efficiency and precision of safety coefficient；Also, soil saturation when hydraulics variation is considered in calculating process
The change of state and substrate suction can be adapted for the calculating of reservoir stability stability in the case of water-level fluctuation.
Detailed description of the invention
Fig. 1 is flow chart of the method for the present invention；
Fig. 2 is the stress condition schematic diagram of discrete and single column of a column.
Specific embodiment
Technical solution of the present invention is described in further detail with reference to the accompanying drawing, but protection scope of the present invention is not limited to
It is as described below.
As shown in Figure 1, a kind of reservoir area three-dimensional stability of slope method under the conditions of water-level fluctuation, including following step
It is rapid:
S1. specific slip mass to be analyzed is selected, its slip-crack surface is determined, slip mass is separated into a column；
S2. the basic assumption of stability analysis is carried out；
S3. it is write the functional relation of basic assumption in step S2 as incremental form, and introduces correction factor c, assign each ginseng
Number initial value；
S4. according to the equilibrium equation of three power, the equilibrium equation and boundary condition of three torque, solve safety coefficient and
The correction factor and parameter of introducing；
Whether the correction factor and parameter of the safety coefficient and introducing that S5. solve in comparison step S4 meet the requirements, such as
It is unsatisfactory for, then with solution by iterative method to meeting the requirements.
As shown in Fig. 2, in the step S1, row interface is parallel to xoz plane, and column interface is parallel to yoz plane, in use
Mark i and j indicate this column the position of entire gliding mass be ith row and jth column,WithTo act on a capital face
Load, position be top surface geometric center
NI, jFor bottom surface normal force, ruFor pore pressure coefficient；WI, jFor column gravity；WithRespectively bottom sliding surface shearing is flat
Row is in the component of xoz and yoz plane；SI, jForWithResultant force；WithRespectively colonnade interface and row interface
Normal force；WithVertical shear and horizontal shear on respectively 4 sides；WithRespectively
For the angle of bottom sliding surface and x and y-axis；Width of the column in the direction x and y is respectively Δ x and Δ y.
Basic assumption in the step S2 includes:
The first, the action direction of column bottom sliding surface normal force is determined by the plane normal vector of its fitting, is denoted asPosition is the geometric center of bottom sliding surfaceGravity direction is also by sliding surface geometry
The heart；
The second, shearing meets following relationship with normal force between hypothesis item:
Hx=η1λ1(x, y) Ex (1)
Hy=η2λ2(x, y) Ey (2)
Ty=η3λ3(x, y) Ex (3)
Tx=η4λ4(x, y) Ey (4)
In formula: λ1(x, y), λ2(x, y), λ3(x, y) and λ4(x, y) is the continuous function assumed in advance, claims lateral shearing
Distribution function；η1, η2, η3And η4It is constant undetermined, the referred to as lateral coefficient of shear；
Known to the borderline thrust of third, gliding mass or so and front and back and shearing；
It is 4th, identical with the safety coefficient of each article of column in the x-direction in a line, it may be assumed that
The safety coefficient of each column in the y-direction is identical in same row, it may be assumed that
The step S3 includes:
It is write functional relation (1)~(4) in step S2 as incremental form, and introduces correction factor c, at the beginning of assigning each parameter
Value, obtains:
Wherein:
In formula:WithRespectively λm(x, y) is in the native column of ith row and jth column
Value corresponding to the side of left, right, front and rear,For λm(x, y) is in the corresponding value in this column bottom surface midpoint； To make inter-slice force meet the constant of reasonability restrictive condition introducing, 0 is taken as when calculating for the first time；0 is also taken in first calculate.
The step S4 includes following sub-step:
Give each column bottom surface skid resistance calculation formula:
In formula:For bottom surface skid resistance；NI, jFor bottom surface normal force；cI, j, AI, jAnd φI, jRespectively article column bottom (i, j)
Cohesion, area and the angle of friction of sliding surface；Formula (10) is to predict Rock And Soil by the Mohr Coulomb's theory of effective stress state
Shearing strength, form of calculation is only applicable to the soil body of saturation state.By introducing unsaturated soils theory, it is extended to both
It is applicable in saturated soil, and is applicable in the form of calculation of unsaturated soil.
Provide the semiempirical model of prediction unsaturation soil classifiction:
Formula (11) is one of Vanapalli proposition for predicting the semiempirical model of unsaturation soil classifiction,
Assuming that the air of solid particle skeleton is communicated with the atmosphere in side slope, i.e. ua=0, formula (11) is expanded into three-dimensional coordinate, and write
At the form of formula (10), following formula is obtained:
Wherein, s is substrate suction, it is believed that it is equal to negative pore water pressure, i.e. s=-uw；SrFor saturation degree；Substrate is inhaled
Power s and saturation degree SrAs hydraulic characteristic data；
In embodiments herein, substrate suction s and saturation degree SrApparatus measures or FEM calculation can be passed through
It obtains；For instrument measuring method, the data of pore water pressure are measured by pressure sensor, and saturation degree is measured by water-level gauge
Data；For Finite Element, pore water pressure and saturation degree carry out calculating acquisition as follows:
Mass conservation law shows the rate of quality inflow characterization unit body and the difference of discharge rate is equal to characterization list
Member is intracorporal of poor quality, is shown below:
In formula, MsIt is previously stored the intracorporal quality of characterization unit；minIt is to be transported quality by characterization unit body surface face
The middle quality for flowing into characterization unit body；moutIt is to be transported by flowing out characterization unit body in the bright quality of characterization unit body surface
Quality；MstIt is existing quality or the quality lost in characterization unit body.Subscript dot indicates that the time-derivative of these variables (becomes
Rate).
It is stored in the mass change of water in characterization unit body are as follows:
In formula, MwIt is previously stored the quality of liquid water in characterization unit body；MwIt is previously stored vapor in characterization unit body
Quality.The possible dissolved solid of liquid water, therefore its density is different from fresh water.The quality for being stored in liquid water in characterization unit body becomes
Rate is shown below:
Above formula can be extended are as follows:
In formula, ρwIt is the density of water；θwIt is volumetric(al) moisture content；βwIt is that the isothermal compressibility of water (is approximately equal at 10 DEG C
4.8E-10m2/N)uwIt is pore water pressure；β is soil texture compressibility；mwIt is the slope of volume of aqueous flow function；αwIt is constant pressure
The volume factor of lower thermal expansion.It is substrate suction, is the difference of pore air pressure and pore water pressure
Soil structures compressibility is equal to the inverse (1/K) of bulk modulus, by the bulk strain of soil structures and pore water pressure
The variation of power connects.Specific soil body compressibility must have loading condition that could embody.For example, in three-dimensional loading condition
Under, bulk modulus must be related with elastic modulus E and Poisson's ratio μ, as shown in formula K=E/ [3 (1-2 μ)].It is answered in two-dimensional surface
Under the conditions of time dependent loading, the expression formula of bulk modulus is K=E/ (1+ μ) (1-2 μ)].Under one-dimensional loading condition, compressibility is equivalent
In volume change Coefficient mv.And bulk modulus, the restraint modulus of loading condition is typically referred to, is had with elasticity modulus and Poisson's ratio
It closes, such as formula K=E (1- μ)/[(1+ μ) (1-2 μ)].
It is using the mass change that perfect gas law calculating is stored in vapor in characterization unit body
In formula, M is molal weight；R is gas constant (8.314472JK-1·mol-1)；pvIt is atmospheric pressure；VaIt is gas
Volume is equal to volume air content (θa=n- θw-θice) multiplied by the volume (dx dy dz) of characterization unit body.
The gross mass change rate that water is stored in characterization unit body is equal to quality rate of inflowWith quality discharge rateThe change rate of mass flow describes transmission process of the water (liquid or gaseous state) in characterization unit body surface face.Flowing is rung
It answers energy gradient and occurs.For liquid water, flowing be can be since (elastic potential energy, gravitional force move mechanical energy
Can), electric energy, thermal energy or chemical energy gradient, however general only consider mechanical energy gradient.Steam flowing can be by partial gas pressure power ladder
Degree occurs or is transported by total pressure gradient and the moving air of density-driven by advection in volume gas phase to send out by diffusive transport
It is raw.
The quality stream change rate of liquid water caused by mechanical energy gradient can be described with the Darcy's law of Variable Density Fluid:
In formula, qwIt is the flux of water；KwIt is the hydraulic conductivity of isothermal liquid water；G is acceleration of gravity.
The quality stream change rate of vapor can be described with Fick's law:
The diffusion coefficient of vapor is obtained by following formula in the soil body:
In formula, τ is bending coefficient；DvapIt is the diffusivity of vapor under kelvin degree.
It brings the conservation of mass after spreading rate equation into quantify, and divided by the dimension of control volume, obtains:
Ignore gas transfer and thermal expansion, above formula can be reduced to more conventional Groundwater Flow equation and divided by being assumed to be
The water density of space-time constant:
For the porous media of saturation state, can be further simplified by ignoring Section 2 above formula:
S403. 2 safety coefficients of each column in the direction x and the direction y are
Wherein, the safety coefficient of each column is
Entirely the safety coefficient of slip mass is
The equilibrium equation of single column is
Formula (10) are substituted into formula (13), then substitute into formula (15)~(17)；Formula (5)~(8) are also substituted into formula (15)~(17),
Then, formula (15)~(17) are write as:
Using formula (15a), (16a) is obtainedWithFormula (17a) is substituted into, bottom surface normal force is obtained are as follows:
Wherein,
Formula (18) is entered formula (10) to obtain:
Formula (13) are substituted into formula (15)~(17)；Formula (5)~(8) are also substituted into formula (15)~(17), are obtained
N is obtained using formula (17b)I, j+ruWI, jAnd substituted into formula (15b), (16b)；Solution formula (15b), (16b)
Wherein,
The borderline horizontal thrust of slopes is it is known that have
It substitutes into boundary condition formula (22) respectively according to hypothesis (4) and by formula (20) and (21) and (23) obtains
Wherein,
The borderline horizontal and vertical shearing of slopes is it is known that have
In formula:Vertical shear on respectively the i-th row right side, left margin；WithRespectively jth column are upper and lower
Borderline vertical shear；Vertical shear on respectively the i-th row right side, left margin；WithRespectively on jth column,
Horizontal shear on lower boundary；
(5)~(8) are substituted into formula (26)~(29) to obtain
Actually only λ to be givenI, jMeet boundary condition, takes ξI, jWhen=0, formula (30)~(33) are to meet automatically
's；
Moment equilibrium condition of the entire gliding mass around 3 axis
Wherein,
Write formula (34)~(36) as following form in convolution (15)~(17):
ax1η1+ax2η2+ax3η3=ax (37)
ay1η1+ay2η2+ay4η4=ay (38)
az3η3+az4η4=az (39)
Wherein,
Formula (35)~(37) contain 4 unknown quantitys, but only 3 equations, according to the property of slip mass, give one reasonably
η4, to acquire other 3 unknown quantitys, obtain:
η3=(az-az4η4)/az3 (39a)
So far, all unknown quantitys must solve, whenAnd η1, η2, η3After acquiring according to the above method,NI, j
WithAccording to formula (11), (16), (17) obtain, using the geometric properties of sliding surface, acquire
The safety coefficient that formula (40) substitution formula (14a) is acquired to each column is solved the safety system of entire gliding mass by formula (14b)
Number.
The step S5 includes:
Whether the correction factor and parameter of the safety coefficient and introducing that solve in comparison step S4 meet the requirementsWithRespectively less than 0.0001, be such as unsatisfactory for, then with solution by iterative method to meeting the requirements:
It is calculated newly according to hypothesisIn result generation, is gone back to formula (18) and (19) to be iterated, it is desirable that meet:
According to it is assumed that when meeting above-mentioned condition,Also a numerical value is converged to automatically；
New inter-slice force mobilization factor η is calculated according to formula (37)~(39)m(m=1~3), by result generation return formula (18) and
(19) it is iterated, it is desirable that Δ ηm(m=1~3) are less than 0.000 1；
Safety coefficient is solved respectively by formula (14a) and (14b)；
The reasonability restrictive condition assumed according to inter-slice force:
Judge whether inter-slice force meets the requirements, if met the requirements, calculates success；For being unsatisfactory for the item of this requirement
Column gives constant ξI, jMeet above formula equal sign, while the additional out-of-balance force of introducing being pressed to a column for same a line or same row
The proportional distribution of pillar height degree, makes boundary condition formula (30)~(33) also be met, and recalculate safety coefficient.
To sum up, slip mass has been carried out discretization by the present invention, and considers multiple dynamic balances, equalising torque and perimeter strip
Part expands two-dimensional Morgenstern-Price method to three-dimensional, improve safety coefficient computational efficiency and analysis it is reliable
Property；In addition, all calculating process can sequencing, convenient for operation and programming, by computer realize be based on Morgenstern-
The three-dimensional stability of slope that Price method assumes solves safety coefficient, greatly reduces artificial calculation amount, improve safety
The computational efficiency and precision of coefficient；Also, consider that soil saturation state and substrate are inhaled when hydraulics variation in calculating process
The change of power can be adapted for the calculating of reservoir stability stability in the case of water-level fluctuation.
The above is a preferred embodiment of the present invention, it should be understood that the present invention is not limited to shape described herein
Formula should not be viewed as excluding other embodiments, and can be used for other combinations, modification and environment, and can be in this paper institute
It states in contemplated scope, modifications can be made through the above teachings or related fields of technology or knowledge.And what those skilled in the art were carried out
Modifications and changes do not depart from the spirit and scope of the present invention, then all should be within the scope of protection of the appended claims of the present invention.
Claims (6)
1. a kind of reservoir area three-dimensional stability of slope method under the conditions of water-level fluctuation, it is characterised in that: the following steps are included:
S1. specific slip mass to be analyzed is selected, its slip-crack surface is determined, slip mass is separated into a column；
S2. the basic assumption of stability analysis is provided；
S3. it is write the functional relation of basic assumption in step S2 as incremental form, and introduces correction factor c, at the beginning of assigning each parameter
Value；
S4. according to the equilibrium equation of three power, the equilibrium equation and boundary condition of three torque, safety coefficient and introducing are solved
Correction factor and parameter；
Whether the correction factor and parameter of the safety coefficient and introducing that S5. solve in comparison step S4 meet the requirements, such as discontented
Foot, then with solution by iterative method to meeting the requirements.
2. the reservoir area three-dimensional stability of slope method under the conditions of a kind of water-level fluctuation according to claim 1, special
Sign is:
In the step S1, row interface is parallel to xoz plane, and column interface is parallel to yoz plane, indicates this using subscript i and j
Column is ith row and jth column in the position of entire gliding mass,WithTo act on a load in capital face, position is
The geometric center of top surface
NI, jFor bottom surface normal force, ruFor pore pressure coefficient；WI, jFor column gravity；WithRespectively bottom sliding surface shearing is parallel to
The component of xoz and yoz plane；SI, jForWithResultant force；WithThe respectively normal direction at colonnade interface and row interface
Power；WithVertical shear and horizontal shear on respectively 4 sides；WithRespectively bottom is sliding
The angle in face and x and y-axis；Width of the column in the direction x and y is respectively Δ x and Δ y.
3. the reservoir area three-dimensional stability of slope method under the conditions of a kind of water-level fluctuation according to claim 2, special
Sign is: the basic assumption in the step S2 includes:
The first, the action direction of column bottom sliding surface normal force is determined by the plane normal vector of its fitting, is denoted asPosition is the geometric center of bottom sliding surfaceGravity direction is also by sliding surface geometry
The heart；
The second, shearing meets following relationship with normal force between hypothesis item:
Hx=η1λ1(x, y) Ex (1)
Hy=η2λ2(x, y) Ey (2)
Ty=η3λ3(x, y) Ex (3)
Tx=η4λ4(x, y) Ey (4)
In formula: λ1(x, y), λ2(x, y), λ3(x, y) and λ4(x, y) is the continuous function assumed in advance, claims lateral shearing distribution
Function；η1, η2, η3And η4It is constant undetermined, the referred to as lateral coefficient of shear；
Known to the borderline thrust of third, gliding mass or so and front and back and shearing；
It is 4th, identical with the safety coefficient of each article of column in the x-direction in a line, it may be assumed that
The safety coefficient of each column in the y-direction is identical in same row, it may be assumed that
4. the reservoir area three-dimensional stability of slope method under the conditions of a kind of water-level fluctuation according to claim 3, special
Sign is: the step S3 includes:
It is write functional relation (1)~(4) in step S2 as incremental form, and introduces correction factor c, assign each initial parameter values,
It obtains:
Wherein:
In formula:WithRespectively λm(x, y) the native column left side of ith row and jth column,
Value corresponding to right, forward and backward side,For λm(x, y) is in the corresponding value in this column bottom surface midpoint； To make inter-slice force meet the constant of reasonability restrictive condition introducing, 0 is taken as when calculating for the first time；0 is also taken in first calculate.
5. the reservoir area three-dimensional stability of slope method under the conditions of a kind of water-level fluctuation according to claim 4, special
Sign is: the step S4 includes following sub-step:
Give each column bottom surface skid resistance calculation formula:
In formula:For bottom surface skid resistance；NI, jFor bottom surface normal force；cI, j, AI, jAnd φI, jRespectively (i, j) article column bottom sliding surface
Cohesion, area and angle of friction；
Provide the semiempirical model of prediction unsaturation soil classifiction:
Assuming that the air of solid particle skeleton is communicated with the atmosphere in side slope, i.e. ua=0, formula (11) is expanded into three-dimensional coordinate, and
The form for being write as formula (10), obtains following formula:
Wherein, s is substrate suction, it is believed that it is equal to negative pore water pressure, i.e. s=-uw；SrFor saturation degree；Substrate suction s
With saturation degree SrAs hydraulic characteristic data；
S403. 2 safety coefficients of each column in the direction x and the direction y are
Wherein, the safety coefficient of each column is
Entirely the safety coefficient of slip mass is
The equilibrium equation of single column is
Formula (10) are substituted into formula (13), then substitute into formula (15)~(17)；Formula (5)~(8) are also substituted into formula (15)~(17), then,
It is write as formula (15)~(17):
Using formula (15a), (16a) is obtainedWithFormula (17a) is substituted into, bottom surface normal force is obtained are as follows:
Wherein,
Formula (18) is entered formula (10) to obtain:
Formula (13) are substituted into formula (15)~(17)；Formula (5)~(8) are also substituted into formula (15)~(17), are obtained
N is obtained using formula (17b)I, j+ruWI, jAnd substituted into formula (15b), (16b)；Solution formula (15b), (16b)
Wherein,
The borderline horizontal thrust of slopes is it is known that have
It substitutes into boundary condition formula (22) respectively according to hypothesis (4) and by formula (20) and (21) and (23) obtains
Wherein,
The borderline horizontal and vertical shearing of slopes is it is known that have
In formula:Vertical shear on respectively the i-th row right side, left margin；WithRespectively jth arranges upper and lower boundary
On vertical shear；Vertical shear on respectively the i-th row right side, left margin；WithRespectively jth arranges upper and lower side
Horizontal shear in boundary；
(5)~(8) are substituted into formula (26)~(29) to obtain
Actually only λ to be givenI, jMeet boundary condition, takes ξI, jWhen=0, formula (30)~(33) meet automatically；
Moment equilibrium condition of the entire gliding mass around 3 axis
Wherein,
Write formula (34)~(36) as following form in convolution (15)~(17):
ax1η1+ax2η2+ax3η3=ax (37)
ay1η1+ay2η2+ay4η4=ay (38)
az3η3+az4η4=az (39)
Wherein,
Formula (35)~(37) contain 4 unknown quantitys, but only 3 equations, according to the property of slip mass, give a reasonable η4, from
And other 3 unknown quantitys are acquired, it obtains:
η3=(az-az4η4)/az3 (39a)
So far, all unknown quantitys must solve, whenAnd η1, η2, η3After acquiring according to the above method,NI, jWith
According to formula (11), (16), (17) obtain, using the geometric properties of sliding surface, acquire
The safety coefficient that formula (40) substitution formula (14a) is acquired to each column is solved the safety coefficient of entire gliding mass by formula (14b).
6. the reservoir area three-dimensional stability of slope method under the conditions of a kind of water-level fluctuation according to claim 5, special
Sign is: the step S5 includes:
Whether the correction factor and parameter of the safety coefficient and introducing that solve in comparison step S4 meet the requirementsWithIt is small
In 0.0001, be such as unsatisfactory for, then with solution by iterative method to meeting the requirements:
It is calculated newly according to hypothesisIn result generation, is gone back to formula (18) and (19) to be iterated, it is desirable that meet:
According to it is assumed that when meeting above-mentioned condition,Also a numerical value is converged to automatically；
New inter-slice force mobilization factor η is calculated according to formula (37)~(39)m(m=1~3), by result generation return formula (18) and (19) into
Row iteration, it is desirable that Δ ηm(m=1~3) are less than 0.0001；
Safety coefficient is solved respectively by formula (14a) and (14b)；
The reasonability restrictive condition assumed according to inter-slice force:
Judge whether inter-slice force meets the requirements, if met the requirements, calculates success；For being unsatisfactory for the column of this requirement, give
Permanent several ξI, jMeet above formula equal sign, while the additional out-of-balance force of introducing is pressed into column to the column of same a line or same row
Highly proportional distribution makes boundary condition formula (30)~(33) also be met, and recalculate safety coefficient.
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