CN111324942B - Seismic slope stability analysis method considering progressive damage of sliding surface power - Google Patents
Seismic slope stability analysis method considering progressive damage of sliding surface power Download PDFInfo
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Abstract
The invention relates to an earthquake slope stability analysis method considering progressive damage of sliding surface power, and belongs to the technical field of slope stability. According to the method, according to the slope landslide surface damage evolution rule under the earthquake action, the mechanical test is adopted to obtain the strength parameter characteristics and the dynamic attenuation rule of the slope rock-soil material, a characteristic material strength parameter attenuation strain softening model and a fracture surface vibration degradation model are constructed, the position of the slide surface in the critical state under the slope static state is determined based on the dichotomy strength reduction method and the maximum shear strain increment, then the earthquake slope safety coefficient time-course curve is solved in numerical calculation by combining the slide surface dynamic progressive damage theory and the vector sum method, the stability state under the slope earthquake action is truly reflected, and the accuracy and the reliability of the numerical calculation result are improved.
Description
Technical Field
The invention relates to an earthquake slope stability analysis method considering progressive damage of sliding surface power, and belongs to the technical field of slope stability.
Background
The severe destructive earthquake above grade 6 causes fast damage to the side slope, has large damage degree, is very easy to induce serious landslide disasters, and causes huge casualties and economic losses. The method has the advantages that the slope stability under the earthquake action is accurately analyzed, the theoretical basis of the design of the disaster prevention and reduction and earthquake-proof support system is provided, and landslide disasters caused by earthquakes can be effectively avoided or reduced.
When the traditional elastic-plastic model is used for analyzing the stability of the earthquake slope, the phenomenon of attenuation of strength parameters of rock-soil materials is difficult to characterize, so that the calculation result is unsafe, and adverse effects on landslide disaster prevention are achieved. However, the earthquake slope instability process shows obvious dynamic progressive failure characteristics, the stability state often depends on the progressive failure process and the damage degree of the sliding surface, and the phenomenon represented by an ideal elastic-plastic model has certain limitations. Therefore, it is urgently needed to construct an intensity parameter attenuation model capable of describing the dynamic gradual failure characteristics of the earthquake slope, establish a numerical calculation method for truly reflecting the dynamic stability state of the earthquake slope, and improve the accuracy and reliability of the numerical calculation result.
Disclosure of Invention
The invention provides an earthquake slope stability analysis method considering progressive damage of sliding surface power, aiming at the defect that a traditional elastic-plastic model is difficult to represent the dynamic attenuation characteristics of rock-soil material parameters under the action of an earthquake, the invention adopts a mechanical test to obtain the strength parameter characteristics and the dynamic attenuation rules of the rock-soil material parameters of the slope according to the evolution rules of the slope sliding surface damage under the action of the earthquake, constructs a model representing the strength parameter attenuation strain softening and a fracture surface vibration degradation model, determines the position of the sliding surface of the slope in a static state based on a dichotomy strength reduction method and a maximum shear strain increment, further combines a sliding surface dynamic progressive damage theory and a vector sum method, solves an earthquake slope safety coefficient time-course curve in numerical calculation, truly reflects the state under the action of the earthquake, and improves the accuracy and the reliability of numerical calculation results.
An earthquake slope stability analysis method considering sliding surface dynamic progressive damage comprises the following specific steps:
(1) Establishing a slope numerical calculation model based on geometric parameters of slope height, slope angle and step width of the field region, determining mechanical parameters of slope rock-soil materials through a mechanical test, and establishing a strength parameter attenuation strain softening model and a fracture surface vibration degradation model; the mechanical parameters of the slope rock-soil material comprise density, elastic modulus, poisson ratio, cohesive force, internal friction angle, shear expansion angle and tensile strength;
(2) According to the intensity parameter attenuation strain softening model, calculating the slope stability by adopting a dichotomy intensity reduction method static force, and determining the slide surface position in a critical state based on the maximum shear strain increment;
(3) Solving the safety coefficient of each power moment according to the slope internal stress distribution state at each power moment based on the vector sum method by taking the slide surface in the critical state as a basis, and solving a safety coefficient time course curve;
(4) And evaluating the overall stability state of the earthquake slope by using the average safety coefficient according to the safety coefficient time-course curve.
The construction method of the intensity parameter attenuation strain softening model in the step (1) comprises the following steps
The attenuation law of the strength parameter of the rock-soil material is approximately represented by adopting a linear piecewise function, and the accumulated plastic shear strain epsilon is established s And tensile strain ε t As independent variable, cohesion c, internal angle of friction
Shear expansion angle psi and tensile strength sigma t Is a strain softening model relation of dependent variable.
The fracture surface vibration degradation model in the step (1) quantitatively describes the shear strength parameter degradation characteristics of the slope fracture surface under the action of earthquake by using a vibration degradation coefficient D (t) changing along with the force time, and establishes a vibration degradation coefficient expression with a power cycle shear amplitude J (t), a frequency K (t) and a relative motion speed V (t):
D(t)＝[P 0 +(1-P 0 )e -mV(t) ][R 0 +(1-R 0 )e bJ(t) +(1-R 0 )(1-e bJ(t) )e -aK(t) ]
in the formula: p 0 Attenuation convergence values are the relative motion speed influence coefficients; r 0 The attenuation convergence value is a cyclic shear amplitude influence coefficient; a. b and m are undetermined coefficients; p 0 、R 0 、a、b、m is obtained through a structural surface vibration table cyclic wear test;
at any power moment, a fracture surface shear strength parameter c (t),
Represented by the fracture surface vibration degradation model:
in the formula: c. C f 、
The residual cohesion and internal friction angle in the strain-softening model are respectively.
The method for calculating the slope stability by adopting the dichotomy strength reduction method in the step (2) comprises the following steps
1) Preset safety factor K s Maximum value of (K) max And a minimum value K min ；
2) Let K s ＝(K max +K min ) And/2, judging whether the slope numerical model considering the strength parameter strain softening model converges, if so, K min ＝K s ，K max ＝K max (ii) a If not, then K max ＝K s ，K min ＝K min ；
3) Judgment of K max —K min If the value of (A) is less than the preset limit value difference, returning to the first step to preset the safety coefficient K again s Maximum value of (K) max And a minimum value K min (ii) a If the difference is less than the preset limit value, the safety factor K is used s Calculating the strength parameter strain softening model for the reduction coefficient and judging whether convergence occurs, if yes, increasing K s The value is then determined by a safety factor K s Calculating the strength parameter strain softening model for the reduction coefficient and judging whether the stress softening model is converged; if not, obtaining the maximum shear strain increment, and determining the position of the slide surface in the critical state according to the position of the maximum shear strain increment.
The step (3) is based on the slide surface in the critical state, based on a vector sum method, solving the safety coefficient at each power moment according to the internal stress distribution state of the slope at each power moment, and solving a safety coefficient time course curve by using a specific method
1) Dispersing the slip surface in a critical state into a plurality of slip surface unit bodies, simultaneously considering an intensity parameter attenuation strain softening model and a fracture surface vibration degradation model, and giving corresponding material intensity parameters to the unit bodies according to the states of the slip surface unit bodies;
2) Taking the displacement and gliding direction of the nodes on the sliding surface unit as the unit shear stress direction, and calculating the stress vector sigma of each sliding surface unit on the critical sliding surface s Tangential stress σ t And normal stress sigma n ，σ t And σ n Are respectively sigma s The cell tangential and normal components of (1), wherein the cell stress vector σ s Comprises the following steps:
σ s ＝σ·n
in the formula: σ is the stress tensor of the cell; n is a unit vector of the normal direction of the unit shear stress direction;
3) Calculating the integral downward-sliding trend direction d of the slope, wherein d is the shear stress sigma of each unit on the critical sliding surface t Vector sum direction, expressed as:
in the formula: ds is each unit on the sliding surface;
4) Calculating tangential anti-sliding force vector sigma 'of each unit of sliding surface' t 'Normal anti-slip vector σ' n And slip resistance vector σ' s ：
σ′ n ＝-σ n
σ′ s ＝σ′ t +σ′ n
In the formula: c.
respectively corresponding cohesive force and internal friction angle of the unit; d t Is unit vector of unit anti-sliding shear stress direction; sigma n The normal stress of the unit is the magnitude, and the pressure is negative; when sigma is n >At 0, take σ n ＝0；
5) Defining vector sum method safety factor F s Algebraic sum ^ integral number of projection of total anti-slip vector of each unit on potential slip surface in integral potential slip trend direction of side slope s [σ′ s ·(-d)]Algebraic sum ^ integral of ds and total lower sliding vector projected in the direction s (σ s D) ds, namely, obtaining a power safety coefficient time course curve, wherein the expression is as follows:
further, the step 1) considers the strength parameter attenuation strain softening model and the fracture surface vibration degradation model simultaneously, and the method for endowing the corresponding material strength parameters of the unit bodies according to the states of the slip surface unit bodies comprises the following steps
When the sliding surface unit bodies in the earthquake side slope obey an ideal elastic-plastic model in the elastic stage, the strength parameters of the unit bodies are kept unchanged; when the slide surface unit bodies in the earthquake slope are subjected to plastic deformation, the strength parameters are attenuated according to a strain softening model; after the earthquake slope inner slide surface unit body reaches the ultimate plastic strain, namely the failure stage, the unit strength parameters of the failure stage are attenuated according to the vibration degradation model under the action of earthquake load.
Adopting an average safety factor in the overall stability state of the earthquake slope in the step (4)
Evaluation, average safety factor
Taking an average value after discretizing the power safety coefficient time course curve in the step (3), wherein the expression is as follows:
in the formula: n is the total discrete number of curves; f si The ith safety factor after the dispersion.
Further, the evaluation method of the overall stability state of the earthquake slope comprises the following steps
If the average safety coefficient is larger than 1, judging that the whole earthquake side slope is in a relatively stable state; if the average safety coefficient is equal to 1, judging that the whole earthquake side slope is in a critical state; and if the average safety coefficient is less than 1, judging that the whole earthquake slope is in a destabilization state.
The invention has the beneficial effects that:
(1) The invention relates to an earthquake slope stability analysis method considering sliding surface dynamic progressive damage, which considers the earthquake slope dynamic progressive damage process in the numerical calculation process, introduces a strain softening model and a vibration degradation model, represents the attenuation characteristics of rock and soil material strength parameters under the action of an earthquake, and overcomes the defect that the calculation result is unsafe because the strength parameters are unchanged in the calculation process of the traditional elastic-plastic model;
(2) The earthquake slope stability analysis method considering the progressive damage of the sliding surface power has the advantages of clear physical significance, simple principle and high reliability, can obtain a relatively real earthquake slope stability coefficient, can provide theoretical basis for researching earthquake landslide disaster forming mechanism, disaster prevention and reduction and earthquake-proof support system design, and has good practical engineering application prospect.
Drawings
FIG. 1 is a flow chart of an earthquake slope stability analysis method considering progressive failure of sliding surface dynamics;
FIG. 2 is a schematic diagram of the attenuation of the strength parameters of a slope strain softening model;
FIG. 3 is a graph of the vibration degradation coefficient of the strength parameter of the fracture surface under the action of power;
FIG. 4 is a flowchart of a slide surface search for a critical side slope condition;
FIG. 5 is a diagram of critical slide position for a slope numerical model and search under different model conditions;
FIG. 6 is a strength parameter selection diagram of an earthquake slope numerical simulation unit considering progressive dynamic destruction of a sliding surface;
FIG. 7 is a cloud of maximum shear strain increment calculated for an earthquake slope under different model conditions;
FIG. 8 is a safety coefficient time-course curve calculated by earthquake slopes under different model conditions.
Detailed Description
The present invention will be described in further detail with reference to specific embodiments, but the scope of the present invention is not limited to the description.
Example 1: an earthquake slope stability analysis method considering slide surface dynamic progressive failure (see figure 1) comprises the following specific steps:
(1) Establishing a slope numerical calculation model by adopting simulation software based on geometric parameters of slope height, slope angle and step width of a slope in the field, determining mechanical parameters of slope rock and soil materials through a mechanical test, and establishing a strength parameter attenuation strain softening model and a fracture surface vibration degradation model; the mechanical parameters of the slope rock-soil material comprise density, elastic modulus, poisson ratio, cohesive force, internal friction angle, shear expansion angle and tensile strength;
the construction method of the intensity parameter attenuation strain softening model comprises the following steps
The attenuation rule of the strength parameter of the rock-soil material is approximately represented by adopting a linear piecewise function, and the accumulated plastic shear strain epsilon is established s And tensile strain ε t As independent variable, cohesion c, internal angle of friction
Shear expansion angle psi and tensile strength sigma t Strain softening model relation for dependent variable:
in the process of slope progressive failure, a potential sliding surface is locally damaged, a large number of joint cracks are generated in a rock-soil body to form a fracture surface, part of bearing capacity of the rock-soil body is provided by a fracture surface strength parameter, the fracture surface is subjected to dislocation under the action of cyclic shearing of earthquake load, the fracture surface is subjected to abrasion and passivation, and the fracture surface shear strength parameter is further attenuated; through developing the structural plane shaking table cycle wear test, obtain the decay law of rock-soil mass structural plane shear strength parameter under power cycle load, establish fracture face vibrations degradation model, fracture face vibrations degradation model for with follow power time variation's vibrations degradation coefficient D (t) quantitative description slope fracture face shear strength parameter degradation characteristic under the earthquake action, construct with the vibrations degradation coefficient expression of power cycle shear amplitude J (t), number of times K (t) and relative motion speed V (t):
D(t)＝[P 0 +(1-P 0 )e -mV(t) ][R 0 +(1-R 0 )e bJ(t) +(1-R 0 )(1-e bJ(t) )e -aK(t) ]
in the formula: p is 0 Attenuating convergence values for the relative motion velocity influence coefficients; r is 0 The attenuation convergence value is a cyclic shear amplitude influence coefficient; a. b and m are undetermined coefficients; p 0 、R 0 A, b and m are obtained through a structural surface vibration table cyclic wear test;
at any power moment, a fracture surface shear strength parameter c (t),
Represented by fracture surface vibration degradation model:
in the formula: c. C f 、
Respectively representing residual cohesive force and internal friction angle in the strain softening model;
(2) According to the intensity parameter attenuation strain softening model, calculating the slope stability by adopting a dichotomy intensity reduction method static force, and determining the slide surface position in a critical state based on the maximum shear strain increment;
the method for calculating the slope stability by adopting the dichotomy strength reduction method comprises the following steps
1) Preset safety factor K s Upper limit safety factor of (2), i.e. maximum value K max And a lower safety factor, i.e. minimum value K min ；
2) Let K s ＝(K max +K min ) And/2, judging whether the slope numerical model considering the strength parameter strain softening model converges, if so, K min ＝K s ，K max ＝K max (ii) a If not, then K max ＝K s ，K min ＝K min ；
3) Judgment of K max —K min Whether the value of (A) is less than a preset limit value difference (such as 0.02) or not, if not, returning to the first step to preset the safety coefficient K again s Maximum value of (K) max And a minimum value K min (ii) a If the difference is less than the preset limit value, the safety factor K is used s Calculating the intensity parameter strain softening model for the reduction coefficient and judging whether convergence occurs, if yes, increasing K s The value is then determined by a safety factor K s Calculating the strength parameter strain softening model for the reduction coefficient and judging whether the stress softening model is converged; if not, obtaining the maximum shear strain increment, and determining the position of the slip surface in the critical state according to the position of the maximum shear strain increment, wherein the shear strain increment is the accumulated increment of strain in the shear deformation process of the side slope;
(3) Based on a critical state sliding surface and based on a vector sum method, solving the safety coefficient of each power moment according to the internal stress distribution state of the slope at each power moment to obtain a safety coefficient time-course curve, wherein the specific steps are as follows
1) Dispersing the slip surface in a critical state into a plurality of slip surface unit bodies, in the process of solving the power safety coefficient by a vector sum method, simultaneously considering a strength parameter attenuation strain softening model and a fracture surface vibration degradation model, and giving corresponding material strength parameters (shown in figure 6) to the unit bodies according to the states of the slip surface unit bodies, namely, the slip surface unit bodies in the earthquake side slope obey an ideal elastoplasticity model in an elastic stage, and the strength parameters are kept unchanged; when the slide surface unit bodies in the earthquake slope are subjected to plastic deformation, the strength parameters are attenuated according to a strain softening model; after the earthquake slope inner slide surface unit body reaches the limit plastic strain, namely a damage stage, attenuating the unit strength parameters in the damage stage according to a vibration degradation model under the action of earthquake load;
2) Taking the displacement and gliding direction of the nodes on the sliding surface unit as the unit shear stress direction, and calculating the stress vector sigma of each sliding surface unit on the critical sliding surface s Tangential stress σ t And normal stress sigma n ，σ t And σ n Are respectively sigma s The cell tangential and normal components of (1), wherein the cell stress vector σ s Comprises the following steps:
σ s ＝σ·n
in the formula: σ is the stress tensor of the cell; n is a unit vector of the normal direction of the unit shear stress direction;
3) Calculating the integral downward-sliding trend direction d of the slope, wherein d is the shear stress sigma of each unit on the critical sliding surface t Vector sum direction, expressed as:
in the formula: ds is each unit on the sliding surface;
4) Calculating tangential slip resistance vector sigma 'of each unit of slip surface' t 'Normal anti-slip vector σ' n And anti-slip vector σ' s ：
σ′ n ＝-σ n
σ′ s ＝σ′ t +σ′ n
In the formula: c.
respectively corresponding cohesive force and internal friction angle of the unit; d t Is a sheetThe unit vector of the element anti-sliding shear stress direction; sigma n The normal stress of the unit is the magnitude, and the pressure is negative; when σ is n >At 0, take σ n ＝0；
5) Defining vector sum law factor of safety F s Algebraic sum ^ integral number of projection of total anti-slip vector of each unit on potential slip surface in integral potential slip trend direction of side slope s [σ′ s ·(-d)]Algebraic sum ^ integral of ds and total lower sliding vector projected in the direction s (σ s D) ds, namely, obtaining a power safety coefficient time course curve, wherein the expression is as follows:
(4) According to the safety coefficient time course curve, evaluating the integral stability state of the earthquake slope by using the average safety coefficient:
average safety factor is adopted in the overall stability state of the earthquake slope
Evaluation, mean safety factor->
Obtaining the integral safety coefficient of the earthquake slope by taking an average value after discretizing the power safety coefficient time course curve in the step (3), and judging the slope stability, wherein the expression is as follows:
in the formula: n is the total discrete number of curves; f si The ith safety coefficient after dispersion;
the concrete method for judging the stability state of the earthquake slope comprises the following steps: if the average safety coefficient is larger than 1, judging that the whole earthquake side slope is in a relatively stable state; if the average safety coefficient is equal to 1, judging that the whole earthquake side slope is in a critical state; and if the average safety coefficient is less than 1, judging that the whole earthquake slope is in a destabilization state.
Example 2: an earthquake slope stability analysis method considering slide surface dynamic progressive damage (see figure 1) comprises the following specific steps:
(1) Establishing a slope numerical calculation model by adopting simulation software based on geometric parameters of slope height, slope angle and step width of a slope in the field, determining mechanical parameters of slope rock and soil materials through a mechanical test, and establishing a strength parameter attenuation strain softening model and a fracture surface vibration degradation model; the mechanical parameters of the slope rock-soil material comprise density, elastic modulus, poisson ratio, cohesive force, internal friction angle, shear expansion angle and tensile strength; the method comprises the following specific steps:
1) Engineering geology is adopted to investigate the stratum occurrence condition of a certain slope field region, and FLAC is adopted 3D Establishing a slope numerical calculation model, wherein the slope height of a slope is 10m and the slope angle is 60 degrees as shown in fig. 5 (a);
2) Determining the mechanical parameters of the slope rock-soil material through a mechanical test (see table 1),
TABLE 1 geotechnical parameters
The attenuation law of the strength parameter of the geotechnical material is approximately represented by adopting a linear piecewise function (see figure 2), and the accumulated plastic shear strain epsilon is established s And tensile strain ε t As independent variable, cohesion c, internal angle of friction
Shear expansion angle psi and tensile strength sigma t Strain softening model relationship for dependent variables: />
3) In the process of slope progressive failure, a potential sliding surface is locally damaged, a large number of joint cracks are generated in the rock-soil body to form a fracture surface, partial bearing capacity of the rock-soil body is provided by strength parameters of the fracture surface, and the fracture surface is subjected to cyclic shearing action of earthquake loadThe dislocation is generated, so that the phenomena of abrasion and passivation of the fracture surface are caused, and the shear strength parameter of the fracture surface is further attenuated; through developing a structural surface vibration table cyclic wear test, obtaining the attenuation rule of the shear strength parameter of the rock-soil mass structural surface under a power cyclic load, and establishing a fracture surface vibration degradation model, wherein the power load is simulated by adopting simple harmonic vibration waves, the acceleration time course is a = lambda cos (2 pi ft), and lambda =1.25m/s 2 Equivalent to VII-degree seismic intensity acceleration amplitude, seismic wave frequency f =2H Z The duration is 5s;
the fracture surface vibration degradation model is used for quantitatively describing the degradation characteristics of the slope fracture surface shear strength parameters under the action of earthquake by using a vibration degradation coefficient D (t) changing along with the time of force (see fig. 3), and a vibration degradation coefficient expression with a power cycle shear amplitude J (t), a frequency K (t) and a relative motion speed V (t) is established:
D(t)＝[P 0 +(1-P 0 )e -mV(t) ][R 0 +(1-R 0 )e bJ(t) +(1-R 0 )(1-e bJ(t) )e -aK(t) ]
in the formula: p is 0 Attenuation convergence values are the relative motion speed influence coefficients; r is 0 Attenuating the convergence value for the cyclic shear amplitude influence coefficient; a. b and m are undetermined coefficients; p is 0 、R 0 A, b and m are obtained through a structural surface vibration table cyclic wear test;
at any power moment, a fracture surface shear strength parameter c (t),
Represented by the fracture surface vibration degradation model:
in the formula: c. C f 、
Respectively representing residual cohesive force and internal friction angle in the strain softening model;
(2) According to the intensity parameter attenuation strain softening model, calculating the slope stability by adopting a dichotomy intensity reduction method static force, and determining the slide surface position in a critical state based on the maximum shear strain increment;
the method for calculating the slope stability by adopting the bisection strength reduction method and the static force (see figure 4) is
1) Preset safety factor K s Upper limit safety factor of (i.e. maximum value K) max And a lower safety factor, i.e. minimum value K min ；
2) Let K s ＝(K max +K min ) And/2, judging whether the slope numerical model considering the intensity parameter strain softening model converges, if so, K min ＝K s ，K max ＝K max (ii) a If not, then K max ＝K s ，K min ＝K min ；
3) Judgment of K max —K min If the value of (A) is less than the preset limit value difference (0.02), returning to the first step to preset the safety coefficient K again s Maximum value of (K) max And a minimum value K min (ii) a If the difference is less than the preset limit value, the safety factor K is used s Calculating the strength parameter strain softening model for the reduction coefficient and judging whether convergence occurs, if yes, increasing K s The value is then determined by a safety factor K s Calculating the strength parameter strain softening model for the reduction coefficient and judging whether convergence occurs; if not, obtaining the maximum shear strain increment, and determining the position of the slip surface in the critical state according to the position of the maximum shear strain increment, wherein the shear strain increment is the accumulated increment of strain in the shear deformation process of the side slope; the critical state sliding surface of the slope calculated by adopting an ideal elastoplasticity and strain softening model is shown in fig. 5, and the calculated static safety coefficients are 1.26 and 1.06 respectively;
(3) Based on a critical state sliding surface and based on a vector sum method, solving the safety coefficient of each power moment according to the internal stress distribution state of the slope at each power moment to obtain a safety coefficient time-course curve, wherein the specific steps are as follows
1) Dispersing the slip surface in a critical state into a plurality of slip surface unit bodies, solving a dynamic safety coefficient process by a vector sum method, simultaneously considering a strength parameter attenuation strain softening model and a fracture surface vibration degradation model, and giving corresponding material strength parameters to the unit bodies according to the states of the slip surface unit bodies, namely, the slip surface unit bodies in the earthquake slope obey an ideal elastoplasticity model in an elastic stage, and the strength parameters are kept unchanged; when the slide surface unit bodies in the earthquake slope are subjected to plastic deformation, the strength parameters are attenuated according to a strain softening model; after the earthquake slope inner slide surface unit body reaches the ultimate plastic strain, namely a failure stage, attenuating the unit strength parameters of the failure stage according to a vibration degradation model under the action of earthquake load; the process of selecting the rock-soil body unit strength parameters is shown in figure 6;
2) Taking the displacement and gliding direction of the nodes on the sliding surface unit as the unit shear stress direction, and calculating the stress vector sigma of each sliding surface unit on the critical sliding surface s Tangential stress σ t And normal stress sigma n ，σ t And σ n Are respectively sigma s The cell tangential and normal components of (1), wherein the cell stress vector σ s Comprises the following steps:
σ s ＝σ·n
in the formula: σ is the stress tensor of the cell; n is a unit vector of the normal direction of the unit shear stress direction;
3) Calculating the integral downward-sliding trend direction d of the slope, wherein d is the shear stress sigma of each unit on the critical sliding surface t Vector sum direction, expressed as:
in the formula: ds is each unit on the sliding surface;
4) Calculating tangential slip resistance vector sigma 'of each unit of slip surface' t 'Normal anti-slip vector σ' n And slip resistance vector σ' s ：
σ′ n ＝-σ n
σ′ s ＝σ′ t +σ′ n
In the formula: c.
respectively corresponding cohesive force and internal friction angle of the unit; d t Is unit vector of unit anti-sliding shear stress direction; sigma n The normal stress of the unit is the magnitude, and the pressure is negative; when sigma is n >At 0, take σ n ＝0；
5) Defining vector sum law factor of safety F s Algebraic sum ^ integral number of projection of total anti-slip vector of each unit on potential slip surface in integral potential slip trend direction of side slope s [σ′ s ·(-d)]Algebraic sum ^ integral of ds and total gliding vector projected in the direction s (σ s D) ds, namely, obtaining a power safety coefficient time course curve, wherein the expression is as follows:
in order to reflect the dynamic stability characteristics of the side slope when progressive damage is considered, three models of ideal elastoplasticity, strain softening and strain softening + vibration degradation are respectively adopted for the earthquake side slope to carry out dynamic analysis; under the action of dynamic load, the local damage of the side slope gradually expands towards the inside of the side slope, the maximum shear strain increment of the earthquake side slope calculated by adopting different models and a safety coefficient time course curve are shown in fig. 7-8, the maximum shear strain increment is 60.75mm when the traditional elastic-plastic model is adopted for calculation, the minimum safety coefficient of the dynamic side slope is 0.30, the maximum safety coefficient is 2.40, after the dynamic load, the safety coefficient of the side slope tends to be stable, the final safety coefficient is 1.19, and the difference between the final safety coefficient and the safety coefficient before the dynamic load is not large; when a strain softening model is adopted for calculation, the maximum shear strain increment is increased to 588.40mm, the minimum safety coefficient and the maximum safety coefficient of the side slope in the power process are respectively 0.29 and 2.52, and finally the safety coefficient of the side slope approaches to 1.03 and approaches to a critical failure state; when double factors of strain softening and vibration degradation of the dynamic slope are considered, the shear plastic yield surface of the slope is further expanded, the maximum shear strain increment reaches 602.70mm, the minimum safety coefficient and the maximum safety coefficient are respectively 0.27 and 2.45, and the final safety coefficient approaches 0.67, which indicates that the final slope is in a destabilization state;
(4) According to the safety coefficient time course curve, evaluating the integral stability state of the earthquake slope by using the average safety coefficient:
average safety factor is adopted in the overall stability state of the earthquake slope
Evaluation, mean safety factor->
Obtaining the integral safety coefficient of the earthquake slope by taking an average value after discretizing the power safety coefficient time course curve in the step (3), and judging the slope stability, wherein the expression is as follows:
in the formula: n is the total discrete number of curves; f si The ith safety coefficient after dispersion;
wherein the average safety factors under different models are shown in a table 2;
TABLE 2 average safety factor under different models
The concrete method for judging the stability state of the earthquake slope comprises the following steps: if the average safety coefficient is larger than 1, judging that the whole earthquake side slope is in a relatively stable state; if the average safety coefficient is equal to 1, judging that the whole earthquake side slope is in a critical state; if the average safety coefficient is less than 1, judging that the whole earthquake side slope is in a destabilization state; from table 2, it can be seen that the dynamic safety coefficient calculated by using the ideal elastic-plastic model is 1.11, which still can meet the engineering requirements, and when the strain softening and fracture surface vibration degradation of the rock-soil material under the action of the earthquake are considered, the calculated safety coefficient is 0.88, the side slope is already in the instability state, which indicates that the calculation result by using the traditional elastic-plastic model is unsafe, and the influence of the dynamic progressive damage on the earthquake side slope is not negligible, so the earthquake side slope stability analysis method considering the sliding surface dynamic progressive damage can truly reflect the earthquake side slope stability state.
While the present invention has been described in detail with reference to the specific embodiments thereof, it will be apparent to those skilled in the art that the present invention is not limited to the embodiments described above, and that various changes and modifications can be made without departing from the spirit and scope of the invention.
Claims (2)
1. An earthquake slope stability analysis method considering sliding surface dynamic progressive failure is characterized by comprising the following specific steps:
(1) Establishing a slope numerical calculation model based on geometric parameters of slope height, slope angle and step width of a side slope in a field region, determining mechanical parameters of rock and soil materials of the side slope through a mechanical test, and establishing a strength parameter attenuation strain softening model and a fracture surface vibration degradation model; the mechanical parameters of the slope rock-soil material comprise density, elastic modulus, poisson ratio, cohesive force, internal friction angle, shear expansion angle and tensile strength;
(2) According to the intensity parameter attenuation strain softening model, calculating the slope stability by adopting a dichotomy intensity reduction method static force, and determining the slide surface position in a critical state based on the maximum shear strain increment;
(3) Dispersing the slide surface in the critical state into a plurality of slide surface unit bodies by taking the slide surface in the critical state as a basis, simultaneously considering a strength parameter attenuation strain softening model and a fracture surface vibration degradation model, giving corresponding material strength parameters to the unit bodies according to the states of the slide surface unit bodies, solving the safety coefficient at each power moment according to the internal stress distribution state of the slope at each power moment on the basis of a vector sum method, and solving a safety coefficient time course curve;
the specific method for solving the safety coefficient time course curve is
1) Dispersing the slip surface in a critical state into a plurality of slip surface unit bodies, simultaneously considering an intensity parameter attenuation strain softening model and a fracture surface vibration degradation model, and giving corresponding material intensity parameters to the unit bodies according to the states of the slip surface unit bodies;
2) Taking the displacement and gliding direction of the nodes on the sliding surface unit as the unit shear stress direction, and calculating the stress vector sigma of each sliding surface unit on the critical sliding surface s Tangential stress σ t And normal stress σ n ，σ t And σ n Are respectively sigma s The cell tangential and normal components of (1), wherein the cell stress vector σ s Comprises the following steps:
σ s ＝σ·n
in the formula: σ is the stress tensor of the cell; n is a unit vector of the normal direction of the unit shear stress direction;
3) Calculating the integral downward-sliding trend direction d of the slope, wherein d is the shear stress sigma of each unit on the critical sliding surface t Vector sum direction, expressed as:
in the formula: ds is each unit on the sliding surface;
4) Calculating tangential anti-sliding force vector sigma of each unit of the sliding surface t ', normal anti-slip vector σ' n And the slip resistance vector sigma s '：
σ′ n ＝-σ n
σ′ s ＝σ′ t +σ′ n
In the formula: c.
respectively corresponding cohesive force and internal friction angle of the unit; d is a radical of t Is unit vector of unit anti-sliding shear stress direction; sigma n The normal stress of the unit is the magnitude, and the pressure is negative; when sigma is n >At 0, take σ n ＝0；
5) Defining vector sum method safety factor F s For the cell assembly on a potential sliding surfaceAlgebraic sum ^ integral factor of projection of antiskid vector on integral potential sliding trend direction of side slope s [σ' s ·(-d)]Algebraic sum ^ integral of ds and total lower sliding vector projected in the direction s (σ s D) the ratio of ds, namely, obtaining a power safety coefficient time course curve, wherein the expression is as follows:
the method for simultaneously considering the strength parameter attenuation strain softening model and the fracture surface vibration degradation model and giving the corresponding material strength parameters to the unit bodies according to the states of the sliding surface unit bodies comprises the following steps of
When the slide surface unit bodies in the earthquake slope obey an ideal elastic-plastic model in the elastic stage, the strength parameters of the slide surface unit bodies are kept unchanged; when the slide surface unit bodies in the earthquake slope are subjected to plastic deformation, the strength parameters are attenuated according to a strain softening model; after the earthquake slope inner slide surface unit body reaches the ultimate plastic strain, namely a failure stage, attenuating the unit strength parameters of the failure stage according to a vibration degradation model under the action of earthquake load;
(4) Evaluating the overall stability state of the earthquake slope by using the average safety coefficient according to the safety coefficient time-course curve; the average safety factor is adopted in the overall stability state of the earthquake slope
Evaluation, mean factor of safety>
Taking an average value after discretizing the power safety coefficient time course curve in the step (3), wherein the expression is as follows:
in the formula: n is the total discrete number of curves; f si The ith safety coefficient after dispersion;
the evaluation method of the overall stability state of the earthquake slope comprises the following steps
If the average safety coefficient is larger than 1, judging that the whole earthquake side slope is in a relatively stable state; if the average safety coefficient is equal to 1, judging that the whole earthquake side slope is in a critical state; if the average safety coefficient is less than 1, judging that the whole earthquake side slope is in a destabilization state;
the construction method of the intensity parameter attenuation strain softening model in the step (1) comprises the following steps
The attenuation rule of the strength parameter of the rock-soil material is approximately represented by adopting a linear piecewise function, and the accumulated plastic shear strain epsilon is established s And tensile strain ε t As independent variable, cohesion c, internal angle of friction
Shear expansion angle psi and tensile strength sigma t A strain softening model relation as a dependent variable;
the fracture surface vibration degradation model in the step (1) quantitatively describes the shear strength parameter degradation characteristics of the slope fracture surface under the action of earthquake by using a vibration degradation coefficient D (t) changing along with the force time, and establishes a vibration degradation coefficient expression with a power cycle shear amplitude J (t), a frequency K (t) and a relative motion speed V (t):
D(t)＝[P 0 +(1-P 0 )e -mV(t) ][R 0 +(1-R 0 )e bJ(t) +(1-R 0 )(1-e bJ(t) )e -aK(t) ]
in the formula: p 0 Attenuation convergence values are the relative motion speed influence coefficients; r is 0 The attenuation convergence value is a cyclic shear amplitude influence coefficient; a. b and m are undetermined coefficients; p 0 、R 0 A, b and m are obtained through a structural surface vibration table cyclic wear test;
at any power moment, a fracture surface shear strength parameter c (t),
Represented by fracture surface vibration degradation model:
in the formula: c. C f 、
Respectively, the residual cohesion and the internal friction angle in the strain softening model.
2. The method for analyzing the stability of an earthquake slope considering progressive failure of sliding surface dynamics as claimed in claim 1, wherein: the method for calculating the slope stability by adopting the dichotomy strength reduction method comprises the following steps
1) Preset safety factor K s Maximum value of (K) max And a minimum value K min ；
2) Let K s ＝(K max +K min ) And/2, judging whether the slope numerical model considering the intensity parameter strain softening model converges, if so, K min ＝K s ，K max ＝K max (ii) a If not, then K max ＝K s ，
K min ＝K min ；
3) Judgment of K max —K min If the value of (A) is less than the preset limit value difference, returning to the first step to preset the safety factor K again s Maximum value of (K) max And minimum value K min (ii) a If the difference is less than the preset limit value, the safety factor K is used s Calculating the strength parameter strain softening model for the reduction coefficient and judging whether convergence occurs, if yes, increasing K s Value again with a safety factor K s Calculating the strength parameter strain softening model for the reduction coefficient and judging whether the stress softening model is converged; and if not, obtaining the maximum shear strain increment, and determining the position of the slide surface in the critical state according to the position of the maximum shear strain increment.
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