CN113607770A - Stability analysis method for geotechnical engineering structure in bedding rock in seasonal frozen region - Google Patents

Stability analysis method for geotechnical engineering structure in bedding rock in seasonal frozen region Download PDF

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CN113607770A
CN113607770A CN202110874031.XA CN202110874031A CN113607770A CN 113607770 A CN113607770 A CN 113607770A CN 202110874031 A CN202110874031 A CN 202110874031A CN 113607770 A CN113607770 A CN 113607770A
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bedding
freeze
damage
strain
coupling
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CN113607770B (en
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王子利
逄明卿
姜谙男
张霄汉
周立飞
李忠海
马超
侯拉平
马新彪
刘林涛
毕建成
唐卫平
黄健铭
杨秀荣
郑帅
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China Railway North Investment Co ltd
Dalian Maritime University
China Railway First Engineering Group Co Ltd
Second Engineering Co Ltd of China Railway First Engineering Group Co Ltd
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China Railway North Investment Co ltd
Dalian Maritime University
China Railway First Engineering Group Co Ltd
Second Engineering Co Ltd of China Railway First Engineering Group Co Ltd
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Abstract

The invention discloses a stability analysis method of a rock engineering structure in bedding rock in a season freezing region, which comprises the following steps of S1: defining a bedding-freeze thawing coupling damage variable of a rock mass; s2: establishing a nonlinear viscoelastic-elastic plastic creep constitutive model; s3: establishing a three-dimensional creep equation, and programming the nonlinear viscoelastic-plastic creep constitutive model; s4: verifying the correctness and the applicability of the nonlinear viscoelastic-plastic creep constitutive model according to the results of triaxial creep tests of rocks under different bedding angles and different freeze-thaw times; s5: and calculating the freeze-thaw slope stability coefficient under different freeze-thaw times by adopting the nonlinear viscoelastic-plastic creep constitutive model. The established nonlinear viscoelastic-plastic creep constitutive model considering the bedding-freezing-thawing coupled damage variable can better reflect the freezing-thawing-bedding damage based on the rock freezing-thawing-bedding damage to reflect the freezing-thawing-bedding coupled damage and the creep characteristic of the bedding rock body generated due to the freezing-thawing-bedding influence and the time effect.

Description

Stability analysis method for geotechnical engineering structure in bedding rock in seasonal frozen region
Technical Field
The invention relates to the field of geotechnical engineering in bedding rocks in a seasonal frozen region, in particular to a stability analysis method for a geotechnical engineering structure in the bedding rocks in the seasonal frozen region.
Background
The freeze-thaw creep characteristic of the rock mass is one of important mechanical characteristics of the bedding rock mass engineering and is closely related to the long-term stability of the bedding rock mass engineering. In the projects of slope treatment, tunnel construction, mine exploitation and the like, the damage of the bedding rock mass due to freezing and thawing and long-term load action is one of the main damage forms. Particularly, with the development of cold region rock engineering construction, the damage of the physical rock is seriously deteriorated under the action of freeze-thaw cycles, and the creep property is more remarkable, which can generate adverse effect on the long-term stability of the cold region engineering.
Disclosure of Invention
The invention provides a stability analysis method for a geotechnical engineering structure in bedding rocks in a freezing and thawing area, which aims to solve the technical problems that the bedding rocks are seriously damaged and deteriorated under the action of freezing and thawing cycles, and the creep characteristic has adverse effect on the long-term stability of cold area engineering.
In order to achieve the purpose, the technical scheme of the invention is as follows:
a method for analyzing the stability of a geotechnical engineering structure in bedding rocks in a freezing region comprises the following steps:
s1: defining a bedding-freeze-thaw coupled damage variable D of a rockβ,nThe bedding-freeze-thaw coupled lesion variable Dβ，nRepresenting the damage of the rock caused by different bedding angles and different freezing-thawing cycle times;
s2: establishing a variable D considering bedding-freeze thawing coupling damageβ，nA nonlinear viscoelastic-plastic creep constitutive model is used for representing stress and strain relations under the influence of different bedding angles and different freezing-thawing cycle times on the rock;
s3: establishing a three-dimensional creep equation to analyze the stability of geotechnical engineering in anisotropic rocks;
s4: verifying the correctness and the applicability of the nonlinear viscoelastic-plastic creep constitutive model according to the results of triaxial creep tests of rocks under different bedding angles and different freeze-thaw times;
s5: and calculating freeze-thaw slope stability coefficients under different freeze-thaw times by adopting a verified nonlinear viscoelastic-plastic creep constitutive model so as to determine the sliding surface position and short-term stability of rock-soil critical failure state in the slope rock.
According to the stability analysis method for the geotechnical engineering structure in the bedding rock in the seasonal freezing region, the nonlinear viscoelastic-plastic creep constitutive model is established when the bedding-freeze thawing coupling damage variable is considered, and the freeze-thaw-bedding coupling damage and the creep characteristic of the bedding rock body due to freeze-thaw-bedding influence and time effect can be reflected better based on the rock freeze-thaw-bedding damage. The technical problems that the damage of the physical rock is seriously deteriorated under the action of freeze-thaw cycles, and the creep property has adverse effect on the long-term stability of cold region engineering are solved.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the description of the embodiments or the prior art will be briefly introduced below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to these drawings without creative efforts.
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a diagram of the bedding-freeze-thaw coupled damaged software elements of the present invention;
FIG. 3 is a diagram of a bedding-freeze-thaw coupled damaged elastic element of the present invention;
FIG. 4 is a schematic diagram of a Kelvin bulk device assembly for delamination-freeze-thaw coupling damage in accordance with the present invention;
FIG. 5 is a diagram of a delamination-freeze-thaw coupling damageable adhesive element of the present invention;
FIG. 6 is a diagram of a non-linear viscoelastic creep model element assembly according to the present invention;
FIG. 7(a) is a graph comparing the experimental and calculated values for rocks according to the invention for a freeze-thaw cycle of 0 times at a bedding angle of 0 °;
FIG. 7(b) is a graph comparing the experimental and calculated values for rocks of the present invention for 20 freeze-thaw cycles at a bedding angle of 0 °;
FIG. 7(c) is a graph comparing the experimental and calculated values for rocks of the present invention for 40 freeze-thaw cycles at a bedding angle of 0 °;
FIG. 7(d) is a graph comparing the experimental and calculated values for rocks of the present invention for 60 freeze-thaw cycles at a bedding angle of 0 °;
FIG. 7(e) is a graph comparing the test values and calculated values for a freeze-thaw cycle of 80 times with a bedding angle of 0 in accordance with the present invention;
FIG. 8(a) is a slope shear strain cloud of 80 freeze-thaw cycles at a bedding angle of 0 ° in accordance with the present invention;
FIG. 8(b) is a slope shear strain cloud of the present invention with 80 freeze-thaw cycles at a bedding angle of 30 °;
FIG. 8(c) is a slope shear strain cloud of 80 freeze-thaw cycles at a bedding angle of 45 ° in accordance with the present invention;
FIG. 8(d) is a slope shear strain cloud of the present invention with 80 freeze-thaw cycles at a bedding angle of 60 °;
FIG. 8(e) is a slope shear strain cloud of the present invention with 80 freeze-thaw cycles at a bedding angle of 90 °;
FIG. 9 is a graph showing the relationship between the times of freezing and thawing of the rock mass and the safety coefficient of the rock mass side slope when the bedding angle is 0 degree.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The embodiment provides a stability analysis method for a geotechnical engineering structure in bedding rocks in a freezing region, which comprises the following steps: as shown in figure 1:
s1: defining a bedding-freeze-thaw coupled damage variable D of a rockβ，nThe bedding-freeze-thaw coupled lesion variable Dβ，nRepresenting the damage of the rock caused by different bedding angles and different freezing-thawing cycle times;
the bedding-freeze thawing coupled damage variable Dβ，nThe establishment method comprises the following steps:
according to the principle of strain equivalence proposed by lemitare, the strain induced by the action of the stress σ on the damaged material is equivalent to the strain induced by the action of the effective stress σ' on the undamaged material, namely:
Figure RE-GDA0003247243090000031
in the formula: e is the elastic modulus of the undamaged material, and E' is the elastic modulus of the damaged material;
variable D for coupling bedding-freeze thawing damage of rockβ,nIs defined as:
Figure RE-GDA0003247243090000032
in the formula: wβ,nThe elastic modulus of the rock with the bedding angle of beta and the freezing and thawing times of n; wβ,0The elastic modulus of the rock with the bedding angle of beta and the freezing-thawing frequency of 0.
S2: establishing a variable D considering bedding-freeze thawing coupling damageβ,nA time nonlinear viscoelastic-plastic creep constitutive model is used for representing stress and strain relations under the influence of different bedding angles and different freezing-thawing cycle times on the rock; and (3) obtaining that rock and soil in the bedding rock after freeze-thaw cycling successively undergoes a deceleration creep stage, a stable creep stage and an acceleration creep stage through triaxial creep tests of the rock under different bedding angles and different freeze-thaw times. The classical creep model can well describe the deceleration creep and steady-state creep stages in the creep test of the bedding rock, but cannot reflect the acceleration creep characteristics of the bedding rock. Thus, it is possible to provideThe method is based on a classical creep model, replaces viscous elements in a viscoplastomer with freeze-thaw damage viscous elements, considers the influence of freeze-thaw cycles on model parameters, and establishes a laminated slate freeze-thaw creep constitutive model.
The nonlinear viscoelastic-plastic creep constitutive model is created based on a classical creep model combination; the classical creep model combination comprises a bedding-freeze-thaw coupling damage Maxwell body, a bedding-freeze-thaw coupling damage Kelvin body and a bedding-freeze-thaw coupling damage Binham body; the bedding-freezing-thawing coupled damage Maxwell surface represents instantaneous elastic deformation and viscous deformation of a rock mass material in a creep process, and comprises a bedding-freezing-thawing coupled damage elastic element and a bedding-freezing-thawing coupled damage viscous element which are connected in series; the bedding-freeze thawing coupled damage Kelvin body represents viscoelastic deformation of a rock mass material in a creep process, and comprises a bedding-freeze thawing coupled damage elastic element and a bedding-freeze thawing coupled damage soft element which are connected in parallel; the bedding-freeze-thaw coupling damage Binham body represents the viscoplasticity deformation of the rock mass material in the creep process and comprises a bedding-freeze-thaw coupling damage plastic element and a bedding-freeze-thaw coupling damage soft element which are connected in parallel; according to the invention, the viscous elements in the traditional viscoplastic body are replaced by the bedding-freeze thawing damage soft elements, so that the rock mass model can be closer to the state of real rock, as shown in the attached figures 2-5.
The method for establishing the nonlinear viscoelastic-elastic plastic creep constitutive model comprises the following steps:
s21: the soft body element represents the stress strain characteristic between an ideal elastomer and an ideal fluid or expresses the accelerated creep state of the material, the damaged soft body element under the freezing and thawing condition is the soft body under the effect of the bedding-freezing and thawing coupling, and the constitutive relation of the damaged soft body element under the bedding-freezing and thawing coupling is established as follows:
Figure RE-GDA0003247243090000041
in the formula: t is time; σ (t) represents the corresponding stress at time t; ε (t) represents the corresponding strain at time t; eta is the viscosity coefficient of the soft element; m is a grading order number, m is more than or equal to 0 and less than or equal to 1, when m is 0, the formula (3) is degraded into a Hooke bulk stress-strain relation, when m is 1, the formula (3) is degraded into a Newton bulk stress-strain relation, and when m is more than 0 and less than 1, the stress-strain characteristic between an ideal elastomer and an ideal fluid is represented; when m is more than 1, expressing the accelerated creep state of the material;
s22: the constitutive relation of the bedding-freeze thawing coupling damage elastic element is established as follows:
Figure RE-GDA0003247243090000051
the constitutive relation of the Maxwell body considering the bedding-freeze-thaw coupling damage is as follows:
Figure RE-GDA0003247243090000052
in the formula: epsilonMStrain components generated for the Maxwell body damaged by the bedding-freeze thawing coupling; eMThe elastic modulus of the Maxwell body is damaged by the coupling of bedding and freezing thawing;
s23: establishing the constitutive relation of the layering-freeze thawing coupling damage Kelvin body as follows:
Figure RE-GDA0003247243090000053
in the formula: epsilonHStrain components of the elastic elements are damaged by the delamination-freeze thawing coupling in the Kelvin body; epsilonNStrain components of the bedding-freeze thawing coupling damage software elements in the bedding-freeze thawing coupling damage Kelvin body; ekThe elastic modulus of a Kelvin body is damaged by a bedding-freeze thawing coupling mode; epsilonkIs a strain component, eta, of a stratigraphically-freeze-thaw coupled lesion Kelvin bodykThe viscosity coefficient of the bedding-freeze thawing coupling damage software element is shown, m1 is the fractional order number in the bedding-freeze thawing coupling damage Kelvin body, and m1 is more than or equal to 0 and less than or equal to 1;
from equation (6):
Figure RE-GDA0003247243090000054
when t is 0,. epsilonk(t) is 0, assuming
Figure RE-GDA0003247243090000055
Equation (7) is rewritten as:
Figure RE-GDA0003247243090000056
the main advantage of the Caputo method is that the initial condition of the fractional order differential equation can take the same form as the integer order differential equation; therefore, according to the fractional calculus theory, the conversion of the Riemann-Liouville fractional derivative into the Caputo fractional derivative is as follows:
Figure RE-GDA0003247243090000057
in the formula: c represents the Caputo fractional derivative; k is a positive integer; dt m(t) is the fractional derivative of Riemann-Liouville;
when epsilonk(0) When equal to 0, Dm[εK(t)]＝CDm[εK(t)]Then equation (8) is rewritten as:
b＝aεK+CDm[εK(t)] (10)
laplace transform is carried out on two sides of the formula (9) to obtain
Figure RE-GDA0003247243090000061
In the formula: s ═ σ + j ω is a complex parametric variable;
therefore, the temperature of the molten metal is controlled,
Figure RE-GDA0003247243090000062
continuing to perform Laplace transform to obtain
Figure RE-GDA0003247243090000063
Wherein,
Figure RE-GDA0003247243090000064
then the process of the first step is carried out,
Figure RE-GDA0003247243090000065
will be provided with
Figure RE-GDA0003247243090000066
The constitutive relation of the modified smectic-freeze-thaw coupling damage Kelvin body obtained by substitution is as follows:
Figure RE-GDA0003247243090000067
s24: establishing a constitutive relation of the layering-freeze thawing coupling damage viscous element:
Figure RE-GDA0003247243090000068
in the formula:
Figure RE-GDA0003247243090000069
is the strain rate, η, of the Newton bodyMThe Newton body viscosity coefficient;
s25: establishing a constitutive relation of the bedding-freeze thawing coupled damage Binham;
Figure RE-GDA00032472430900000610
in the formula: etaBThe viscosity coefficient of the damaged Binham body by adopting the coupling of bedding and freeze thawing; m is2The number of fractional orders in the Binham body is damaged by bedding-freeze thawing coupling; sigmasThe stress threshold of a plastic element in the Binham body is damaged by the coupling of bedding and freezing thawing;
s26: fig. 6 shows a non-linear viscoelastic-plastic creep model element combination diagram comprehensively considering a bedding-freeze-thaw coupling damage Maxwell body, a bedding-freeze-thaw coupling damage Kelvin body and a bedding-freeze-thaw coupling damage Binham body, and a non-linear viscoelastic-plastic creep constitutive model is established as follows:
Figure RE-GDA0003247243090000071
s3: in order to conveniently realize the programming of the nonlinear viscoelastic-plastic creep constitutive model by adopting a secondary development platform, a three-dimensional creep equation is established so as to analyze the stability of geotechnical engineering in anisotropic rocks in the subsequent process; the three-dimensional creep equation is established by the following steps; the equations are derived by a finite difference method: the invention adopts FLAC3DAnd a secondary development platform is used for realizing the programming of the nonlinear viscoelastic-plastic creep constitutive model.
Suppose that the rock strain ε ij consists of three components, namely: strain of Maxwell body damaged by bedding-freeze thawing coupling
Figure RE-GDA0003247243090000072
Strain of Kelvin body damaged by bedding-freeze thawing coupling
Figure RE-GDA0003247243090000073
And strain of bedding-freeze thawing coupled damaged Binham body
Figure RE-GDA0003247243090000074
Namely, it is
Figure RE-GDA0003247243090000075
The form of the offset strain is as follows:
Figure RE-GDA0003247243090000076
in the formula
Figure RE-GDA0003247243090000077
In order to be subjected to a bias strain,
Figure RE-GDA0003247243090000078
damage the partial strain of Maxwell body for the coupling of bedding-freeze thawing,
Figure RE-GDA0003247243090000079
Is a laminated-freeze-thaw coupled damage on the partial strain of Kelvin body,
Figure RE-GDA00032472430900000710
The bias strain of Binham body is damaged by bedding-freeze thawing coupling;
writing the bias strain in increments yields the relationship between bias strain increments:
Figure RE-GDA00032472430900000711
in the formula: Δ eijIn order to be the offset strain increment,
Figure RE-GDA00032472430900000712
the strain deflection increment of Maxwell body is damaged by the coupling of bedding and freeze thawing,
Figure RE-GDA00032472430900000713
Offset strain increment and for damage of Kelvin body by bedding-freeze thawing coupling
Figure RE-GDA00032472430900000714
The method comprises the following steps of (1) damaging the bias strain increment of a Binham body by adopting a bedding-freeze thawing coupling manner;
continuing with the formula derivation, we find: bedding-freeze-thaw coupling damage elastic element:
Figure RE-GDA00032472430900000715
bedding-freeze thawing coupled damage Kelvin body:
Figure RE-GDA00032472430900000716
formula (I) of Chinese SijBias stress, G shear modulus; etaKThe viscosity coefficient of a delamination-freeze thawing coupling damage Kelvin body;
the strain rate of a bedding-freeze-thaw coupled damaged Binham body can be written as follows
Figure RE-GDA0003247243090000081
Wherein g is the plastic yield potential function, ηBIs a viscosity coefficient of a bedding-freeze thawing coupling damaged Binham body,<F>expressed as a switch function, as follows:
Figure RE-GDA0003247243090000082
writing equation (25) in the form of the bias strain rate:
Figure RE-GDA0003247243090000083
in the formula:
Figure RE-GDA0003247243090000084
damaging the volume strain of the Binham body by adopting a bedding-freeze thawing coupling mode;
the total strain delta can be obtained from equation (26):
Figure RE-GDA0003247243090000085
by adopting a central differential mode, the bedding-freeze thawing coupling damage elastic element can be written into
Figure RE-GDA0003247243090000086
In the formula
Figure RE-GDA0003247243090000087
Is an offset stress in the form of a central differential,
Figure RE-GDA0003247243090000088
the strain bias is a difference mode of the central of a Maxwell body damaged by bedding-freeze thawing coupling; Δ t is the time increment;
by adopting a central difference mode, a Kelvin body with a bedding-freeze-thawing coupling damage can be written
Figure RE-GDA0003247243090000089
In the formula
Figure RE-GDA00032472430900000810
Bias strain in the form of difference in the Kelvin body center for bedding-freeze-thaw coupled lesions. Δ t is the time increment. EtaKIs the viscosity coefficient of the Kelvin body of the bedding-freeze thawing coupling damage,
wherein:
Figure RE-GDA00032472430900000811
Figure RE-GDA00032472430900000812
in the formula,
Figure RE-GDA00032472430900000813
representing stress offset in a time incrementThe old value of (c);
Figure RE-GDA00032472430900000814
representing a new value of the stress offset in a time increment,
Figure RE-GDA00032472430900000815
an old value representing a stress offset in a time increment;
Figure RE-GDA00032472430900000816
is a new value of the strain offset in a time increment;
shift strain of Kelvin body of bedding-freeze thawing coupling damage
Figure RE-GDA0003247243090000091
In the formula:
Figure RE-GDA0003247243090000092
is an old value of Kelvin bulk partial strain of bedding-freeze thawing coupled damage,
Figure RE-GDA0003247243090000093
The new value of Kelvin bulk bias strain of the bedding-freeze-thaw coupling damage is obtained.
Wherein:
Figure RE-GDA0003247243090000094
finally obtaining updated bias stress
Figure RE-GDA0003247243090000095
In the formula: Δ eijIn order to be the offset strain increment,
Figure RE-GDA0003247243090000096
and
Figure RE-GDA0003247243090000097
respectively adopting partial strain increments of a bedding-freeze thawing coupling damage Binham body and a bedding-freeze thawing coupling damage Maxwell body;
wherein:
Figure RE-GDA0003247243090000098
Figure RE-GDA0003247243090000099
according to the knowledge of plastic mechanics, the ball stress is not considered to generate plastic deformation, so the ball stress of the whole bedding-freeze-thaw damage creep model is written as follows:
Figure RE-GDA00032472430900000910
in the formula
Figure RE-GDA00032472430900000911
Is a new value of the ball stress;
Figure RE-GDA00032472430900000912
is the old value of the ball stress, K is the bulk modulus,. DELTA.. di-elect consvolIs the volume strain increment;
Figure RE-GDA00032472430900000913
the volume strain increment of the Binham body is damaged by bedding-freeze thawing coupling;
in the molar coulombic destabilization criterion:
Figure RE-GDA00032472430900000914
in the formula:
Figure RE-GDA00032472430900000915
is a layerThe strain increment of the physical-freeze thawing coupled damage Binham body, g infinity is a long-term yield potential function,<F>as a function of switching, tcAlpha is the coefficient of the adjustment time dimension for the initial time of entering the accelerated creep phase;
the principal stress space is a cartesian space coordinate system composed of three principal stress components σ 1, σ 2, σ 3 as coordinate axes, and in the three-dimensional principal stress space, the principal stress vector of any point can be represented as a linear superposition of unit vectors of three principal stress axes, so that under the principal stress space:
Figure RE-GDA0003247243090000101
stress tensor
Figure RE-GDA0003247243090000102
Can be decomposed into stress deflection numbers
Figure RE-GDA0003247243090000103
And ball stress tensor
Figure RE-GDA0003247243090000104
Figure RE-GDA0003247243090000105
For shear yield, one can obtain:
Figure RE-GDA0003247243090000106
in the formula
Figure RE-GDA0003247243090000107
As a function of the long-term yield strength at shear yield,
Figure RE-GDA0003247243090000108
is an intermediate variable;
the following can be obtained:
Figure RE-GDA0003247243090000109
wherein:
Figure RE-GDA00032472430900001010
in the formula of∞Is a plastic hardening factor, c∞In order to ensure the long-term cohesion of the material,
Figure RE-GDA00032472430900001011
is the long-term rubbing angle;
for tensile yield:
Figure RE-GDA00032472430900001012
in the formula
Figure RE-GDA00032472430900001013
Is a long-term yield potential function of tensile yield;
the three-dimensional creep equation is jointly derived from equation (20) to equation (45) as follows:
Figure RE-GDA00032472430900001014
s4: verifying the correctness and the applicability of the nonlinear viscoelastic-plastic creep constitutive model according to the results of triaxial creep tests of rocks under different bedding angles and different freeze-thaw times;
the three-dimensional creep equation is in FLAC3DConverting the secondary development platform into a dll file, calling the dll file for calculation to obtain a graph of the rock calculated by the nonlinear viscoelastic-plastic creep constitutive model established by the invention under different bedding angles and different freeze-thaw cycle times, and comparing the graph with the result obtained according to the triaxial creep test to verify that the nonlinear viscoelastic-plastic creep established by the invention is subjected to creep testCorrectness and applicability of the constitutive model.
As can be seen from the attached drawings 7(a) -7 (e), the coincidence effect of the two is good, the model fitting curve can well reflect the characteristics of deceleration creep, stable creep and accelerated creep of the bedding rock under different freezing and thawing cycle times, and the correctness and the applicability of the freeze-thaw damage and bedding damage creep constitutive model established in the method are shown.
Fig. 8 is a shear strain increment cloud chart of rock mass side slopes with different bedding angles, wherein fig. 8(a) is the shear strain increment cloud chart of the rock mass side slopes with the bedding angle of 0 degrees, the maximum shear strain of the side slope appears in the area near the slope surface above the slope foot of the side slope, a potential slip surface is not formed yet, and the stability of the rock mass side slope is better; fig. 8(b) is a shear strain cloud chart of a rock mass side slope with a bedding angle of 30 degrees, and compared with fig. 8(a), fig. 8(b) has the advantages that the maximum shear strain area of the side slope is continuously increased, a potential side slope slip surface is formed, and the stability of the side slope is reduced; fig. 8(c) is a cloud diagram of shear strain of a rock slope with a bedding angle of 45 °, and compared with fig. 8(a) and 8(b), the maximum shear strain area continues to increase, and the potential slip surface of the slope continues to develop; FIG. 8(d) is a shear strain cloud chart of a rock slope with a bedding angle of 60 degrees, wherein a potential slip plane of the slope develops into an arc and then expands towards the upper left (top of the slope); fig. 8(e) is a shear strain cloud picture of a rock slope with a bedding angle of 90 degrees, and compared with fig. 8(d), the potential slip plane of the slope almost reaches the top of the slope, which shows that the possible slip trend of the slope is strip arc-shaped slip. It can be seen from the combination of fig. 8(a) -8 (e) that as the bedding angle of the rock mass increases, the potential slip plane of the rock mass side slope continuously extends to the top of the slope, and meanwhile, the maximum shear strain area gradually increases.
S5: calculating freeze-thaw slope stability coefficients under different freeze-thaw times by adopting a verified nonlinear viscoelastic-plastic creep constitutive model; the method for calculating the stability coefficient of the freeze-thaw slope under different freeze-thaw times is a strength reduction method based on rock bedding-freeze thawing coupling damage and creep characteristics:
the slope stability coefficient is the strength reduction coefficient, the initial reduction coefficient is selected firstly, the soil body strength parameter is reduced, the reduced parameter is used as input, the strength reduction is carried out, if the program is converged, the soil body is still in a stable state, then the reduction coefficient is increased until the soil body is not converged, the reduction coefficient at the moment is the stability safety coefficient of the slope, the slip surface at the moment is the actual slip surface, and the method is called as the slope stability coefficient.
The strength reduction method is that the strength parameters (internal friction angle, cohesion and tensile strength) of the slope rock are gradually reduced in numerical calculation until the structure reaches the limit state, and the ratio of the strength parameter value of the rock to the strength parameter value corresponding to the limit state is the required safety factor, and meanwhile, the position of the potential damage sliding surface can be obtained according to the elastic-plastic calculation result.
The basic principle of the intensity reduction method is to reduce the anti-shearing intensity parameter of the rock in rock elastic-plastic numerical calculation, so that the side slope reaches a critical failure state, and the stability coefficient of the side slope is obtained. When strength reduction calculation is carried out on the freeze-thaw rock mass side slope, the rock mass adopts the Mohr-Coulomb (MoCoulomb) strength yield criterion; at present, when slope stability is calculated, a traditional strength reduction method is usually adopted, in the traditional strength reduction method, mechanical properties of a rock body are represented by an elastic-plastic constitutive model, and the slope is integrally unstable through strength parameters of the reduced rock body. Compared with the traditional strength reduction method, the invention reflects the bedding-freeze-thaw coupling damage and creep characteristics of the bedding rock body generated by the bedding-freeze-thaw influence and time effect based on the rock bedding-freeze-thaw coupling damage in the creep viscoelastoplasticity constitutive model, and takes whether the displacement of the key point of the side slope is stable after a certain time and whether the displacement is mutated when the strength is reduced to a certain degree as the criterion of whether the side slope of the bedding rock body is unstable. Because the bedding-freeze-thaw coupling damage and creep characteristics are considered in the intensity reduction method of the bedding-freeze-thaw coupling damage and creep characteristics, the influence of the bedding-freeze-thaw creep characteristics on the deformation and stability of the side slope can be reflected.
Applying Mohr-Coulomb (MoCoulomb) strength yield criterion to the rock mass:
Figure RE-GDA0003247243090000121
in the formula taunThe shear strength of rock mass under different freezing and thawing times, sigma' is the initial compressive strength of rock, CnIs the cohesion of the rock under different freezing and thawing times, c is the initial cohesion of the unfrozen rock,
Figure RE-GDA0003247243090000122
is the internal friction angle of the rock mass.
The strength reduction method is to reduce the strength parameters Cn and Cn of the material,
Figure RE-GDA0003247243090000123
And simultaneously dividing the slope model by the same reduction coefficient Fs, reducing the strength of the rock, performing trial calculation again, and reducing the strength of the rock by gradually increasing the reduction coefficient Fs until the rock reaches a critical failure state, wherein the critical failure state is the sign that the slope plastic region penetrates from the slope toe to the slope top and the force or displacement non-convergence is adopted as the slope instability. At this time, the corresponding strength reduction coefficient Fs is the freeze-thaw slope stability coefficient. The intensity reduction factor can be expressed as:
Figure RE-GDA0003247243090000124
in the formula FsIs the intensity reduction factor, τnThe shear strength of the rock mass under different freeze-thaw times, sigma' is the initial compressive strength of the rock mass, tausFor breaking down F in rocksThe later shear strength;
wherein:
Figure RE-GDA0003247243090000125
in the formula, csFor reducing F in frozen and thawed rock massessThe adhesive force of the rear part is increased,
Figure RE-GDA0003247243090000131
for breaking down the rock mass FsThe rear internal friction angle;
thus, the intensity reduction factor can also be expressed as:
Figure RE-GDA0003247243090000132
the strength reduction method based on the Mohr-Coulomb strength yield criterion was performed by the method shown in equation (47). FIG. 9 shows a graph of the relationship between the times of freezing and thawing of the rock mass and the safety coefficient of the rock mass slope when the bedding angle is 0 degree, and it can be seen from the graph that the stability coefficient of the freezing and thawing slope is smaller and smaller along with the increase of the times of freezing and thawing.
Specifically, before creep calculation is performed on slope engineering, the traditional strength reduction method is used for analyzing the slope stability, and the sliding surface position and the short-term stability coefficient of the slope rock in the critical failure state are determined. At this time, the molar coulomb model is used as the calculation model. And adopting the traditional intensity reduction method, and repeatedly performing trial calculation by continuously correcting the reduction coefficient to finally obtain the reduction coefficient when the side slope reaches the critical failure state.
Finally, it should be noted that: the above embodiments are only used to illustrate the technical solution of the present invention, and not to limit the same; while the invention has been described in detail and with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; and the modifications or the substitutions do not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the embodiments of the present invention.

Claims (6)

1. A method for analyzing the stability of a geotechnical engineering structure in bedding rocks in a freezing region is characterized by comprising the following steps:
s1: defining a bedding-freeze-thaw coupled damage variable D of a rockβ,nThe bedding-freeze-thaw coupled lesion variable Dβ,nRepresenting the damage of the rock caused by different bedding angles and different freezing-thawing cycle times;
s2: establishing a variable D considering bedding-freeze thawing coupling damageβ,nA nonlinear viscoelastic-plastic creep constitutive model is used for representing stress and strain relations under the influence of different bedding angles and different freezing-thawing cycle times on the rock;
s3: establishing a three-dimensional creep equation to analyze the stability of geotechnical engineering in anisotropic rocks;
s4: verifying the correctness and the applicability of the nonlinear viscoelastic-plastic creep constitutive model according to the results of triaxial creep tests of rocks under different bedding angles and different freeze-thaw times;
s5: and calculating freeze-thaw slope stability coefficients under different freeze-thaw times by adopting a verified nonlinear viscoelastic-plastic creep constitutive model so as to determine the sliding surface position and short-term stability of rock-soil critical failure state in the slope rock.
2. The method for analyzing stability of geotechnical engineering structure in layered rock of seasonal frozen region according to claim 1, wherein the texture-freeze-thaw coupling damage variable D in S1β,nThe establishment method comprises the following steps:
according to the strain equivalence principle, the strain caused by the stress sigma acting on the damaged material is equivalent to the strain caused by the effective stress sigma' acting on the undamaged material, namely:
Figure FDA0003190029220000011
in the formula: e is the elastic modulus of the undamaged material, and E' is the elastic modulus of the damaged material;
variable D for coupling bedding-freeze thawing damage of rockβ,nIs defined as:
Figure FDA0003190029220000012
in the formula: eβ,nThe elastic modulus of the rock with the bedding angle of beta and the freezing and thawing times of n; eβ,0The elastic modulus of the rock with the bedding angle of beta and the freezing-thawing frequency of 0.
3. The method for analyzing the stability of the geotechnical engineering structure in the bedding rock of the freezing zone according to claim 1, wherein the nonlinear viscoelastic-plastic creep constitutive model in S2 is created based on a classical creep model combination; the classical creep model combination comprises a bedding-freeze-thaw coupling damage Maxwell body, a bedding-freeze-thaw coupling damage Kelvin body and a bedding-freeze-thaw coupling damage Binham body; the bedding-freezing-thawing coupled damage Maxwell body represents instantaneous elastic deformation and viscous deformation of a rock mass material in a creep process and comprises a bedding-freezing-thawing coupled damage elastic element and a bedding-freezing-thawing coupled damage viscous element which are connected in series; the bedding-freeze thawing coupled damage Kelvin body represents viscoelastic deformation of a rock mass material in a creep process, and comprises a bedding-freeze thawing coupled damage elastic element and a bedding-freeze thawing coupled damage soft element which are connected in parallel; the bedding-freeze-thaw coupling damage Binham body represents the viscoplasticity deformation of the rock mass material in the creep process and comprises a bedding-freeze-thaw coupling damage plastic element and a bedding-freeze-thaw coupling damage soft element which are connected in parallel.
4. The method for analyzing the stability of the geotechnical engineering structure in the bedding rock of the freezing zone according to claim 3, wherein the nonlinear viscoelastic-plastic creep constitutive model in S2 is established by the following steps:
s21: establishing the constitutive relation of the bedding-freeze thawing coupling damage software element as follows:
Figure FDA0003190029220000021
in the formula: t is time; σ (t) represents the corresponding stress at time t; ε (t) represents the corresponding strain at time t; eta is the viscosity coefficient of the soft element; m is the order of the grading order;
s22: establishing the constitutive relation of the bedding-freeze thawing coupling damage elastic element as follows:
Figure FDA0003190029220000022
the constitutive relation of the Maxwell body considering the bedding-freeze-thaw coupling damage is as follows:
Figure FDA0003190029220000023
in the formula: epsilonMStrain components generated for the Maxwell body damaged by the bedding-freeze thawing coupling; eMThe elastic modulus of the Maxwell body is damaged by the coupling of bedding and freezing thawing;
s23: establishing the constitutive relation of the layering-freeze thawing coupling damage Kelvin body as follows:
Figure FDA0003190029220000024
in the formula: epsilonHStrain components of the elastic elements are damaged by the delamination-freeze thawing coupling in the Kelvin body; epsilonNStrain components of the bedding-freeze thawing coupling damage software elements in the bedding-freeze thawing coupling damage Kelvin body; ekThe elastic modulus of a Kelvin body is damaged by a bedding-freeze thawing coupling mode; epsilonkIs a strain component, eta, of a stratigraphically-freeze-thaw coupled lesion Kelvin bodykThe viscosity coefficient of the bedding-freeze thawing coupling damage software element is shown, and m1 is the fractional order number in the bedding-freeze thawing coupling damage Kelvin body;
from equation (6):
Figure FDA0003190029220000025
when t is 0,. epsilonk(t) is 0, assuming
Figure FDA0003190029220000031
Equation (7) is rewritten as:
Figure FDA0003190029220000032
according to the fractional calculus theory, the conversion of Riemann-Liouville fractional derivatives into Caputo fractional derivatives is as follows:
Figure FDA0003190029220000033
in the formula: c represents the Caputo fractional derivative; k is a positive integer; dt m(t) is the fractional derivative of Riemann-Liouville;
when epsilonk(0) When equal to 0, Dm[εK(t)]＝CDm[εK(t)]Then equation (8) is rewritten as:
b＝aεK+CDm[εK(t)] (10)
laplace transform is carried out on two sides of the formula (9) to obtain
Figure FDA0003190029220000034
In the formula: s ═ σ + j ω is a complex parametric variable; therefore, the temperature of the molten metal is controlled,
Figure FDA0003190029220000035
continuing to perform Laplace transform to obtain
Figure FDA0003190029220000036
Wherein,
Figure FDA0003190029220000037
then the process of the first step is carried out,
Figure FDA0003190029220000038
will be provided with
Figure FDA0003190029220000039
The constitutive relation of the modified smectic-freeze-thaw coupling damage Kelvin body obtained by substitution is as follows:
Figure FDA00031900292200000310
s24: establishing a constitutive relation of the layering-freeze thawing coupling damage viscous element:
Figure FDA0003190029220000041
in the formula:
Figure FDA0003190029220000042
is the strain rate, η, of the Newton bodyMThe Newton body viscosity coefficient;
s25: establishing a constitutive relation of the bedding-freeze thawing coupled damage Binham;
Figure FDA0003190029220000043
in the formula: etaBThe viscosity coefficient of the damaged Binham body by adopting the coupling of bedding and freeze thawing; m is2The number of fractional orders in the Binham body is damaged by bedding-freeze thawing coupling; sigmasThe stress threshold of a plastic element in the Binham body is damaged by the coupling of bedding and freezing thawing;
s26: comprehensively considering a bedding-freeze-thaw coupling damage Maxwell body, a bedding-freeze-thaw coupling damage Kelvin body and a bedding-freeze-thaw coupling damage Binham body, establishing a nonlinear viscoelastic-plastic creep constitutive model:
Figure FDA0003190029220000044
5. the method for analyzing the stability of the geotechnical engineering structure in the bedding rock of the frozen region according to claim 4, wherein the method for establishing the three-dimensional creep equation in S3 is as follows;
the equations are derived by a finite difference method: assuming rock strain εijConsists of three parts, namely: strain of Maxwell body damaged by bedding-freeze thawing coupling
Figure FDA0003190029220000045
Strain of Kelvin body damaged by bedding-freeze thawing coupling
Figure FDA0003190029220000046
And strain of bedding-freeze thawing coupled damaged Binham body
Figure FDA0003190029220000047
Namely, it is
Figure FDA0003190029220000048
The form of the offset strain is as follows:
Figure FDA0003190029220000049
in the formula
Figure FDA00031900292200000410
In order to be subjected to a bias strain,
Figure FDA00031900292200000411
damage by stratification-freeze-thawing couplingPartial strain of Maxwell body,
Figure FDA00031900292200000412
Is a laminated-freeze-thaw coupled damage on the partial strain of Kelvin body,
Figure FDA00031900292200000413
The bias strain of Binham body is damaged by bedding-freeze thawing coupling;
writing the bias strain in increments yields the relationship between bias strain increments:
Figure FDA00031900292200000414
in the formula, Δ eijIn order to be the offset strain increment,
Figure FDA0003190029220000051
the strain deflection increment of Maxwell body is damaged by the coupling of bedding and freeze thawing,
Figure FDA0003190029220000052
Offset strain increment and for damage of Kelvin body by bedding-freeze thawing coupling
Figure FDA0003190029220000053
The method comprises the following steps of (1) damaging the bias strain increment of a Binham body by adopting a bedding-freeze thawing coupling manner;
continuing with the formula derivation, we find: bedding-freeze-thaw coupling damage elastic element:
Figure FDA0003190029220000054
bedding-freeze thawing coupled damage Kelvin body:
Figure FDA0003190029220000055
formula (I) of Chinese SijBias stress, G shear modulus; etaKViscosity coefficient of Kelvin body damaged by bedding-freeze thawing coupling
The strain rate of a bedding-freeze-thaw coupled damaged Binham body can be written as follows
Figure FDA0003190029220000056
Wherein g is the plastic yield potential function, ηBIs a viscosity coefficient of a bedding-freeze thawing coupling damaged Binham body,<F>expressed as a switch function, as follows:
Figure FDA0003190029220000057
writing equation (25) in the form of the bias strain rate:
Figure FDA0003190029220000058
in the formula:
Figure FDA0003190029220000059
damaging the volume strain of the Binham body by adopting a bedding-freeze thawing coupling mode;
the total strain delta can be obtained from equation (26):
Figure FDA00031900292200000510
by adopting a central differential mode, the bedding-freeze thawing coupling damage elastic element can be written into
Figure FDA00031900292200000511
In the formula
Figure FDA00031900292200000512
Is an offset stress in the form of a central differential,
Figure FDA00031900292200000513
the strain bias is a difference mode of the central of a Maxwell body damaged by bedding-freeze thawing coupling; Δ t is the time increment;
by adopting a central difference mode, a Kelvin body with a bedding-freeze-thawing coupling damage can be written
Figure FDA00031900292200000514
In the formula
Figure FDA0003190029220000061
The bias strain is in the form of difference of the Kelvin body center of the bedding-freeze thawing coupling damage; Δ t is the time increment; etaKIs the viscosity coefficient of the Kelvin body of the bedding-freeze thawing coupling damage,
wherein:
Figure FDA0003190029220000062
Figure FDA0003190029220000063
in the formula,
Figure FDA0003190029220000064
an old value representing a stress offset in a time increment;
Figure FDA0003190029220000065
representing a new value of the stress offset in a time increment,
Figure FDA0003190029220000066
an old value representing a stress offset in a time increment;
Figure FDA0003190029220000067
is a new value of the strain offset in a time increment;
shift strain of Kelvin body of bedding-freeze thawing coupling damage
Figure FDA0003190029220000068
In the formula:
Figure FDA0003190029220000069
is an old value of Kelvin bulk partial strain of bedding-freeze thawing coupled damage,
Figure FDA00031900292200000610
The new value of the Kelvin bulk bias strain of the bedding-freeze thawing coupling damage is obtained;
wherein:
Figure FDA00031900292200000611
finally obtaining updated bias stress
Figure FDA00031900292200000612
In the formula: delta eijIn order to be the offset strain increment,
Figure FDA00031900292200000613
and
Figure FDA00031900292200000614
respectively adopting partial strain increments of a bedding-freeze thawing coupling damage Binham body and a bedding-freeze thawing coupling damage Maxwell body;
wherein:
Figure FDA00031900292200000615
Figure FDA00031900292200000616
according to the plastic mechanics knowledge, the ball stress of the whole bedding-freeze-thaw damage creep model is written as:
Figure FDA00031900292200000617
in the formula
Figure FDA00031900292200000618
Is a new value of the ball stress;
Figure FDA00031900292200000619
is the old value of the ball stress, K is the bulk modulus,. DELTA.. epsilonvolIs the volume strain increment;
Figure FDA0003190029220000071
the volume strain increment of the Binham body is damaged by bedding-freeze thawing coupling;
in the molar coulombic destabilization criterion:
Figure FDA0003190029220000072
in the formula
Figure FDA0003190029220000073
Is the strain increment of a bedding-freeze thawing coupling damage Binham body, g infinity is a long-term yield potential function,<F>as a switching function, tc is the starting time for entering the accelerated creep phase, and α is the regulation timeA coefficient of dimension;
under the main stress space:
Figure FDA0003190029220000074
stress tensor
Figure FDA0003190029220000075
Can be decomposed into stress deflection numbers
Figure FDA0003190029220000076
And ball stress tensor
Figure FDA0003190029220000077
Figure FDA0003190029220000078
For shear yield, one can obtain:
Figure FDA0003190029220000079
in the formula
Figure FDA00031900292200000710
As a function of the long-term yield strength at shear yield,
Figure FDA00031900292200000714
is an intermediate variable;
the following can be obtained:
Figure FDA00031900292200000711
wherein:
Figure FDA00031900292200000712
in the formula: lambda [ alpha ]∞Is a plastic hardening factor, c∞In order to ensure the long-term cohesion of the material,
Figure FDA00031900292200000713
is the long-term rubbing angle;
for tensile yield:
Figure FDA0003190029220000081
in the formula:
Figure FDA0003190029220000082
is a long-term yield potential function of tensile yield;
the three-dimensional creep equation is jointly derived from equation (20) to equation (45) as follows:
Figure FDA0003190029220000083
6. the method for analyzing the stability of the geotechnical engineering structure in the bedding rock of the seasonal frozen region according to claim 5, wherein the method for calculating the freeze-thaw slope stability coefficients under different freeze-thaw times in S5 is a strength reduction method:
applying Mohr-Coulomb (MoCoulomb) strength yield criterion to the rock mass:
Figure FDA0003190029220000084
cn＝c(1-D)
in the formula taunThe shear strength of rock mass under different freeze thawing times, sigma' is the initial compressive strength of rock,
Cnis the cohesion of the rock under different freezing and thawing times, c is the initial cohesion of the unfrozen rock,
Figure FDA0003190029220000085
is the internal friction angle of the rock mass;
cn and tan
Figure FDA0003190029220000086
Divided by the same reduction factor Fs at the same time, the intensity reduction factor can be expressed as:
Figure FDA0003190029220000087
in the formula FsIs the intensity reduction factor, τnThe shear strength of the rock mass under different freeze-thaw times, sigma' is the initial compressive strength of the rock mass, tausFor breaking down F in rocksThe later shear strength;
wherein:
Figure FDA0003190029220000088
in the formula, csFor reducing F in frozen and thawed rock massessThe adhesive force of the rear part is increased,
Figure FDA0003190029220000089
for breaking down the rock mass FsThe rear internal friction angle;
thus, the intensity reduction factor can also be expressed as:
Figure FDA0003190029220000091
Figure FDA0003190029220000092
Figure FDA0003190029220000093
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